ASSA
AIDS and Demographic Models
USER
GUIDE
Prepared by Debbie Budlender and Rob Dorrington of the Centre for
Actuarial Research, University of Cape Town, for the AIDS
Committee of the Actuarial Society of South Africa
This guide begins with an overview of modelling of the HIV/AIDS
epidemic in South Africa, which is presented in section 2.
Section 3 provides information on the structure of the model.
It comprises a brief description of the nature and basis of
the assumptions, the location of different aspects of the
model on the worksheets, and information about which
assumptions and values can be changed by the user. Sections 4,
5 and 6 provide instructions on how to use the model. Section
4 describes how to do simple runs so as to get projections for
different years. Section 5 describes the standard output, how
to interpret it, and how to obtain additional output. Section
6 provides a brief overview of the provincial
and urbanrural versions of the model. Finally, section 7 provides
information for the more advanced user who wants to change
parameters. This section includes a discussion of the
calibration that is necessary when making such changes.
As, structurally, the different versions of the model
are all based on the lite version this manual
describes, in the main, the lite
version of the model. However, where appropriate, details of
to other versions of the model are discussed.
In
addition there are several appendices. Appendix A details the
system requirements for running the model. Appendix B lists
all the worksheets in the main workbook of the full
and lite versions and explains where to find particular values. Appendix
C lists all the worksheets in the workbook which pastes the
setup assumptions into the full model to create the
provincial models and explains where to find particular
values. Appendix D is a summary list of all the worksheets,
specifying the name and nature of the worksheet, whether it
contains values that can be changed by users, and whether its
contents change when running the projection engine. Appendix E
lists all the acronyms used in the text of this user guide.
Those
seeking more information about the rationale and evidence
underlying the assumptions and methods used are referred to a
forthcoming monograph on what can be described as the
“metadata” underlying the model(s).
While
reading the guide, it is useful to have the workbook that
makes up the model to hand as there are repeated references to
different parts and features of the workbook in the text.
Although
some actuarial or demographic background will be helpful in
understanding the intricacies of the model’s construction,
the model is designed to be useful to actuaries and
nonactuaries alike. Users who have no need to make changes to
the model and its assumptions, for example those who only want
to use the output, may want to skip the detail in sections 3
and 5. Users who want to change the assumptions underlying the
model must, however, read through this detail as their changes
may otherwise have unintended effects.
The
guide assumes a basic proficiency in using Microsoft Excel. In
particular, it assumes familiarity with naming conventions for
rows and columns, understanding of concepts such as cells,
range names, and macros, and an understanding of the
difference between cells containing ordinary data and those
containing formulae.
Modelling of the AIDS epidemic in
South Africa by actuaries began with the socalled Doyle or
Metropolitan Life model, which was developed in 1989. The
model was based on a population hypothetically divided into
four groups that differed in terms of the relative ease with
which individuals belonging to each group were expected to
contract and transmit the HIV.
The code for the Metropolitan model
is proprietary. The Actuarial Society of South Africa (ASSA)
felt that it was desirable for people to have access to a
nonproprietary programme which users could alter to suit
their needs. In 1996, ASSA therefore released the ASSA500
model. This was very similar in structure to the Metropolitan
model with some simplifications to ease programming and
comprehension and to shorten run times. The model was
primarily designed to make users aware of the likely impacts
of the epidemic on mortality and morbidity.
In 1998, the AIDS Committee of ASSA
decided to develop the model further. There were several
reasons for this:
§
The ASSA500 model represented the epidemic in the black
African population, rather than the population as a whole;
§
There were concerns about the accuracy of the preliminary
results of the 1996 census and there was a need for national
estimates that attempted to correct for suspected
deficiencies;
§
Many South African demographers were continuing to ignore the
impact of AIDS in their projections of the South African
population;
§
The ASSA500 model had inherited a number of demographic
shortcomings from the Metropolitan model, particularly the
assumptions of constant fertility, nonHIV mortality over time
and the assumption of no international migration.
The result was an Excel 95 workbook
called ASSA600, released to the public in early 1999. The
model was designed to be appropriate for use as a national
population model for the Pattern II (heterosexual) HIV
epidemic found in South Africa. The base model contained a
scenario that reflected its builders’ best estimates of
values for the model parameters and was calibrated to fit the
antenatal data up to 1997. The naming convention was also
changed to allow the user to modify the parameter values, for
example for sensitivity analysis and scenario planning. The
idea was that alternative version of the model could then be
saved as ASSA601, 602, etc.
In 2000, the AIDS Committee felt
that a further revision of the model was necessary. The update
was needed because of increased knowledge about the epidemic,
the availability of new data against which to calibrate the
model, and greater awareness of the uses to which the model
was being put. It was also decided to change the naming
convention to reflect the year of the latest antenatal data
used to calibrate the model.
The resultant ASSA2000 model incorporated the following
adjustments reflecting new or updated information about the
epidemic:
Ø
19882000 antenatal clinic (ANC) summary results;
Ø
1998 South Africa Demographic and Health Survey (SADHS) data,
in particular, data on prevalence of STDs and condom usage;
Ø
improved estimates of the population; and
Ø
mortality data on the pattern and level of deaths that
suggested, in particular, that nonHIV mortality for adults
has not improved over time as expected.
In addition, the model was altered to:
Ø
improve the fit to ANC survey data;
Ø
allow for the possibility of making separate male and female
assumptions;
Ø
model the population groups separately;
Ø
limit the trend in mortality and fertility rates over time;
Ø
limit future inmigration;
Ø
change the HIV survival curve to be a function of a Weibull
distribution;
Ø
allow for a bimodal distribution of paediatric HIV survival;
and
Ø
disaggregate the ‘contagion matrix’ (used in ASSA600)
into more measurable and controllable parameters of
heterosexual behaviour. These include the probability that a
partner comes from a particular risk group, the number of new
partners per annum, the number of sexual contacts per partner,
the age of the partner and the probability a condom is used.
The ASSA2000 model has been
produced as a suite of several versions. The lite
version, like the ASSA600 model before it, treats the
population of the country as one population. The full version models each of the four
population groups (Asian/Indian, black African, coloured and
white) separately at a national level, and aggregates to
produce results for the population as a whole. The provincial version is the result of
the aggregation of the application of the full
version of the model separately to each of the provinces. It
thus allows for geographic differences in the spread of the
epidemic. The ASSA AIDS Committee initially delayed the
release of the provincial
version pending the lifting of an embargo by the Department of
Health on the release (to the Committee) of the more detailed
results of the provincial antenatal surveys for 2000. When,
after many months, the Department seemed no nearer releasing
the results, despite having agreed to supply them to the
Committee, the Committee decided that the demand for the provincial
version necessitated that it be released despite the lack of
cooperation from the Department. The urbanrural version allows for
situations where there is significant migration between two
groups with significantly different prevalence levels (e.g.
urban and rural areas in some countries) in the population.
This version is currently under development but will be
released in the coming months.
This user’s guide is intended for
use with all four models. The differences between the lite and full versions will be noted in
the text at relevant places. The approaches in the provincial and urbanrural
versions are described in section 6. A fuller description of
the urbanrural version as well as a note on how to go about fitting
the model to a new country will be made available at the time
of release.
As the course of the disease
progresses and more information about it becomes available,
the model structure and base scenario will be further updated
and future versions of the model will be released.
Any feedback on the model in the
form of comments and criticisms would be appreciated and can
be sent to aids@assa.org.za.
The model is distributed as a
flexible tool to allow researches to make their own
predictions and projections about the HIV/AIDS epidemic. No
level of accuracy is implied, nor can the Actuarial Society of
South Africa accept any responsibility for the way in which
individuals use the model or the results they obtain from it.
The model is offered free via the Internet as a public service
to anyone who has a use for it.
The ASSA2000 model as disseminated has been calibrated
to reproduce the patterns of past antenatal clinic survey data
and the number of adult deaths. As such, the model represents
the triangulation of data from the population census,
antenatal survey and registered deaths by some of the
country’s top actuaries, demographers and epidemiologists.
It is not recommended that users alter the assumptions in the
model in any way unless they have a very good reason for doing
so. If any of the assumptions are altered in any way, the user
must ensure that the model is recalibrated to ensure that it
remains consistent with the recorded experience to date. Users
who have any questions in this regard can consult with the
ASSA AIDS Committee (aids@assa.org.za).
Other sections of this guide note where the user can
change particular parameters on the worksheets to reflect a
change in assumptions. The following points should be observed
when making such changes.
One of the features of the ASSA2000 model is the large
degree of interdependence of different parameters and
assumptions. A change in one will often necessitate a change
in others. There are two broad categories of secondlevel
changes.
§
In some cases the first change of value will result in another change
‘automatically’, in that other values are dependent,
through a formula of the worksheet, or a macro procedure, on
the changed value. This happens, for example, where
proportions must sum to 100%. In these cases, the user does
not need to take any action. However, users should note that
the ‘automatic’ changes will only take effect when the
user presses the F9 (CALC) key or runs a projection. The
automatic CALC function defaults to OFF in the ASSA2000 model
to speed up the projection process.
§
In other cases the changed parameter will require a manual change to
other parameters and assumptions so as to achieve a fit with
the observed values of the ANC surveys, both overall and by
age, and the national mortality rates by age. This process of
manual changing of parameters to counterbalance previous
changes is what we refer to as ‘calibration’.
Users must be aware of the nature of the information
they are changing. Some of the parameters in the ASSA2000
workbook reflect assumptions or observed data such as numbers
in the population. These are entered as ordinary numbers on
the worksheet. Many other parameters are based on formulae
that draw on values in other cells or cell ranges in the
workbook. The contents of these cells must not be replaced by
numbers. As with ordinary Excel usage, the user can see in the
status bar whether a particular cell is the result of a
formula or range name reference. In some cases, however, a
cell will appear to contain an ‘ordinary’ number that does
not involve a reference or formula but will, in fact, be a
record of the previous year’s numbers used to project the
current year’s numbers. This is the case, for example, with
all the tables labelled as ‘before’.
In changing values on the worksheets, users must be
aware of the very different implications of changing a cell
containing a simple value and changing a cell containing a
formula or reference or a number generated in previous
projections. The Assumptions
worksheet provides some guidance as to which values could be
changed in that calculated values are in black, while
assumptions that affect projection – and could thus
potentially be changed – are in red.
In the past, incorrect results have been attributed to
the Actuarial Society of South Africa or the models in public
documents and in the press. In order to prevent this from
happening in future, we ask that all users adhere to the
following guidelines.
§
If the results have been generated using the models without any
alternation, the user should reference them as “results
extracted from the ASSA2000 (lite if lite
version used) AIDS and Demographic model of the Actuarial
Society of South Africa as downloaded [date] from [site
address]”.
§
If the model has been adjusted and recalibrated, the user must, in
addition to the full reference to the model, explain exactly
how and why it was adjusted. The user must also make it clear
that the resulting estimates are not those produced by the
Actuarial Society of South Africa. This must be done in such a
way that anyone reading the report is clear that the user’s
results do not represent the views of the Society. Ideally, it
should also be done in such a way that another user can
replicate the changes and check the projections.
The ASSA model projects
yearbyyear changes in an initial population profile over a
period of years chosen by the user. It does so on the basis of
a number of demographic, epidemiological and behavioural
assumptions. This section of the guide provides a brief
description of the model, its key parameters and assumptions.
Any user who wants to change any of the parameters must read
this section so as to understand the impact of any proposed
changes.
The model projects on a
yearbyyear basis, with each year’s projections reflecting
changes between 1 July of one calendar year and 30 June of the
following calendar year. For the sake of simplicity, each year
is referred to by a single calendar year rather than by both
of the calendar years. The ‘stock’ numbers for each year
reflect the position as at the middle of the respective year,
while the ‘flow’ numbers reflect the change from the
middle of that year to the middle of the following year.
The model splits the population by
sex and also into three distinct age groupings: young (up to
age 13), adult (1459) and old (60 and above). The full
version of the model also splits the population by population
group. The adult group is divided into four risk groups, which
are differentiated by their level of exposure to the risk of
contracting the HI virus through heterosexual activity. These
risk groups are:
PRO
Individuals whose level of sexual activity is such that
it is similar to that of commercial sex workers, and the level
of condom usage and infection with STDs is similar to that of
the STD group.
STD
Individuals whose level of sexual activity is such that
their HIV prevalence is similar to someone regularly infected
with STDs.
RSK
Individuals with a lower level of sexual activity, but
who are still at risk from HIV in that they have, on average,
one new partner per annum and sometimes engage in unprotected
sex.
NOT
Individuals who are not at risk of HIV infection.
By
definition, someone from the RSK group will not have sex with
someone from the PRO group. Further, those in the NOT group
have sex only with others in that group or, if they have sex
with individuals from other groups, always take effective
precautions.
The
numbers in these risk groups are determined initially
according to the proportions appearing on the Assumptions
sheet. These proportions are applied to all adult ages
equally. The assumptions have been determined, where possible,
on the basis of empirical evidence. Where this was not
possible, either educated guesses were made or the assumptions
were determined so that modelled results fit observed data
such as the antenatal prevalence figures for past years. The
latter method of determining values is part of the
‘calibration’ process discussed later.
The age and risk classifications divide the population
into the following groups, with each group’s calculation
done on a separate worksheet within the workbook. In the full version of the model, there is a set of these worksheets for
each population group. In the aggregate of the provinces,
there is a workbook for each province and a set of worksheets
for each population group within each province:
Young:
All individuals aged 0 to 13. The only infections
assumed are those arising at birth or from breastfeeding. On
their 14th birthday, individuals are allocated to the risk
groups according to the assumed proportions on the Assumptions
sheet. The model assumes that a proportion of those born to
HIV+ mothers are HIV+ at birth. Further, the model assumes
that a further proportion of nonHIV babies contract the virus
from their HIV+ mothers through breastfeeding. It is assumed
that none of the babies with perinatal infection survive to
age 14 and that there are no other sources of infection before
this age. The Young age group is shaded yellow on the
worksheets.
FemPRO:
Female members of the PRO risk group up to age 59,
subdivided by duration since infection.
FemSTD:
Female members of the STD risk group up to age 59,
subdivided by duration since infection
FemRSK:
Female members of the RSK risk group up to age 59,
subdivided by duration since infection
FemNOT:
Female members of the NOT group up to age 59
FemOLD:
On their 60th birthdays all individuals are allocated
to the OLD class. The duration since infection classification
still applies, but no further infections or fertility occur
beyond this age. The OLD worksheets are a runoff of the
population. No one is assumed to survive beyond age 90. The
OLD group is shaded in grey on the worksheets.
Male***:
The same structure as the Fem*** worksheets but with no
births.
The
total population is allocated between male and female and over
the age range according to the distributions given in the Population
worksheet. While it is possible to measure, to some extent,
the size of the STD group and, to a lesser extent, the PRO
group, the RSK and hence NOT groups are hypothetical
constructs whose size is set to reproduce past patterns of
prevalence through the calibration process.
Diagram
1 displays how individuals move from state to state under the
action of the model. Certain transitions are assumed to be
impossible e.g. moving from HIV+ to HIV; and becoming
infected after age 60. The model allows for the inclusion of
migrants in all risk groups and at all ages. Migrants are
assumed to have the same duration since infection profile and
prevalence rate as nonmigrants of the equivalent risk group.
Diagram 1: A schematic diagram of the lite model
The
heterosexual interaction and hence spreading of the virus is
modelled taking into account the following, given the person
is from a particular risk group: the chance that the partner is from a particular risk group, the number
of new partners per year, the number of contacts per partner
and the probability of transmission if no condom used (given
the risk group of the partner), and the probability that a
condom was used.
The number of new partners per year and the number of
contacts per partner for females at a particular age are a
function of a ‘sexual activity’ curve. This curve was
chosen such that the pattern of HIV infections of pregnant
women assumed by the model to be attending antenatal clinics
is more or less the same as the results of the ANC surveys.
Infection is introduced into the
PRO risk group via 300 male and 300 female infected
‘imports’ in the lite model. Smaller numbers are used for each of the population
groups in the full version of the model to allow for
both the smaller size of the populations as well as possible
lags in the start of the epidemic. These imports are not added
to the population, but rather used to create HIV prevalence of
partners in the initial years and hence start the epidemic.
The number of imported HIV need not be a whole number or even
greater than one. This feature allows the model to cater for
situations where the starting date of the epidemic is before
or after 1985, by simply changing the size of this number.
The epidemic spreads through the
population at risk by assumed infection of noninfected
individuals within and between groups. The rate of spread of
the infection is controlled by assumptions about two key
factors, namely the amount of
sexual activity, and a range of factors determining the probability of infection.
The distribution of female sexual
activity by age is represented in the model by the sexual
activity curve, which is found on the SexActivity sheet. The curve involves
an assumption about the relative sexual activity by age for
females. The curve is bellshaped with the following form:
where
a
(the position factor) is determined by the average age of
first sexual intercourse
b (the shape factor) is set, in part, to reproduce the shape
of prevalence by age from the antenatal results as well as the
age distribution of AIDS cases and AIDS deaths
c (the scale factor) is set so that the average of S is 1.
The
activity of males is a function of that of females and the age
of their partners.
By
varying the shape of the curve, the distribution of the new
HIV infections by age is adjusted (separately for different
population groups and province in the two other models). The
user can manipulate both a (position) and b (shape) factors, but must run the ‘Goal seek’ macro after any
changes to restandardise the curves i.e. reset the scale
factor. The macro is run by clicking the ‘Goal seek’
button on the chart on the SexActivity worksheet. The shape and position factors are
recorded at the top of the leftmost table on the worksheet, in
column C.
The
default values for a and b for the female curve have been set to reproduce the age
distribution of ANC HIV prevalence age distributions over
time. The reasonableness of the male curve can be checked
against the age distribution of reported male AIDS cases circa
1995. When changing the shape of the curves and the age
distribution of partners of females, the user should ensure
that the this consistency between the number of deaths and
number of AIDS cases still holds. This can be checked by
looking at the ANC Age
Profile and AIDS Age Profile
worksheets and ensuring that the dotted curves (actual
figures) are reasonably close to the solid ones (modelled
figures).
ASSA2000 models sexual behaviour,
and thus the probability of infection, on the basis of a
combination of several components, as follows:

a matrix showing the probability that a partner is from a
particular risk group;

a matrix of maletofemale transmission probabilities per
sexual contact for various combinations of risk group
encounters;

a matrix of the ratio of maletofemale to femaletomale
transmission probabilities for various combinations of risk
group encounters;

a matrix showing the number of new partners per year and the
number of contacts per new partner per year;

a matrix showing the probability that a female partner is
from a particular risk group;

a matrix of condom usage for each risk group by age; and

the effectiveness of condoms.
These components are all recorded
on the Assumptions worksheet.
All
the above information is then brought together in the
following formula:
The
probability of someone in risk group i,
aged x becoming infected in a year
where
represents the probability that the partner is from
risk group j
represents the sex activity weighted prevalence of a
partner from risk group j
represents probability of transmission from partner in
risk group j to partner in risk group i
with sex g
represents
the probability of a condom being used
e
represents the effectiveness of
condoms
represents the number of contacts per new partner
represents the sex activity (i.e. the proportion of sex
at that age)
represents the number of new partners per annum
The combination of components allows the model to be
used to test the impact of interventions that attempt to
change one or more of these variables.
Twenty
five percent of babies born to infected mothers are assumed to
be infected. This is consistent with the 0,250,30 range often
quoted. The lower end of the range was chosen since the infant
mortality rate (IMR) produced by the model appears to be on
the high side in comparison with various demographic estimates
and because the
model allows for later infection via breastfeeding. As
explained below, infection via breastfeeding is assumed to
have a bimodal distribution, with those contracting HIV three
months or more after birth having a much higher median time to
death than those who are infected at birth. The ASSA2000 model
allows for this by assuming a mortality rate of 30% per annum
for those born infected, but a Weibull distribution and median
time to death of six years for those who contract the disease
via mother’s milk.
The
user can modify the proportion of births assumed to be
infected and the proportion assumed to be infected by
mother’s milk on the Assumptions
worksheet. The relevant table is fourth from the top on the
left of the worksheet.
The starting population reflects
the actual population as at 1 July 1985.
This was derived by a process of reconstruction linking
estimates of the population in 1970 to those of the census
population in 1996, ensuring consistency with estimates of
fertility and mortality rates derived independently and
between the numbers of males and females in various age
groups.
The current provinces did not exist
in 1985. For the provincial
version of the model, it was therefore necessary to
reconstruct the base population that could be expected to have
been within these boundaries in that year. This was done by
taking into account a remapping of the 1991 census into the
new boundaries and the patterns of interprovincial migration
between 1985 and 1996.
The mortality data is found in the MortTable
worksheet. The initial rates of mortality apply on average at
1 January 1986, to be consistent with a starting population
six months earlier at 1 July the previous year.
The
nonHIV probability of death and probability of becoming
infected are used in a multiple decrement life table that
applies to individuals not infected by HIV.
The model uses a table of estimated mortality rates at
each age for each of the years 1985 to 1999. After 1999,
mortality rates are projected to trend logistically to
ultimate rates at a rate determined by a ‘mortality
improvement factor’ using the following formula:
where
a
= the mortality rate in 1999
b
= the ultimate mortality rate
c
= the mortality improvement factor
This is contained in the lookup formula which can be
found in the table of current year nonAIDS mortality in the MortTable
worksheet.
The user can alter the tables of
mortality rates for the years to 1999, the ultimate rates of
mortality, the mortality improvement factor, and the formulae
for interpolating future rates of mortality for all ages on
the MortTable
worksheet. The relevant formulae are found in the tables
headed ‘Mortality Improvement factor for NonAIDS
Mortality’ and ‘Current Year=X NonAIDS Mortality Rates’
respectively. In the full
version of the model, these changes need to be made to the
population group specific MortTable sheets.
A mortality rate of 30% per annum
is assumed for babies born infected with the virus. The value
can be changed on the Assumptions sheet or, if more sophistication
is required, the user can change the assumption of a constant
annual rate of mortality for these babies on the Male/Female
HIVTable worksheets. The relevant table on the Assumptions sheet is fourth from the top on the lefthand side.
It is headed ‘Other Assumptions’ and the relevant values
are those for male and female ‘Infant AIDS mortality’. The
relevant table on the Male/Female HIVTable worksheets is second from the right. It records
survival rates by duration in oneyear intervals from 0 to 14
years.
These parameters are recorded in
the Male HIVTable and Female HIVTable worksheets.
For
those aged 14 plus and for those born with HIV, the
proportions (l_{t}) are calculated using a Weibull distribution with
parameters reflecting median time to death and shape.
The median time to death is set on
the Assumptions worksheet. The relevant table on
the Assumptions worksheet is fourth from the top
on the lefthand side, and is headed ‘Other Assumptions’.
The table provides for the possibility of different median
times in respect of three different age groups of males and
females, namely 1424 years, 2534 years, and 35 years and
above. If more sophistication is required, the formula for
defining l_{x}, the proportion alive at age x, can be changed on the Male HIVTable and Female HIVTable
worksheets. For
simplicity, the shape parameter has been set as a function of
the median time to death. This can be replaced with another
value if the user has a better estimate.
A different approach is adopted in
respect of babies infected via mother’s milk. It is becoming
increasingly apparent that paediatic HIV has a bimodal
distribution. Babies who contract HIV three months or more
after birth can be expected to survive much longer than those
who are infected at birth. The ASSA2000 model thus assumes a
Weibull distribution and median time to death of six years and
a shape parameter of 0,8 for those who contract the disease
via mother’s milk.
Although
the available evidence suggests that a median time to death of
around nine years would be appropriate for Africa and that it
becomes shorter with increasing age at seroconversion, such
short median times to death in the model produce a pattern of
deaths by age that is inconsistent with that observed. The
model thus assumes a median time to death of 11 years for
those under 25 and 10 years for those age 25 years and older
when infected.
The parameters relating to
fertility of those not infected are found on the NonHIV
Fertility worksheet. Overall agespecific fertility rates are
determined in a similar way to the mortality rates, with a
table of estimated agespecific fertility rates for the period
to 1996, after which rates are determined by interpolating
between the rates in 1996 and the ultimate rates. The first
table in this worksheet provides nonHIV fertility rates for
each of the four risk groups for the current year by taking
into account the relative fertility of women in each age group
and the proportion of women in the various risk groups at that
age. The relative
fertility factors can be found in the second table from the
top left of the Assumptions worksheet. The results are shown in columns B, C, D
and E in the nonHIV fertility
sheet. The relative fertility factors can be changed on the Assumptions sheet.
The model assumes that PROs have a
lower fertility rate than STDs, who have a lower rate than
RSKs, who, in turn, have a lower rate than NOTs. Although this
may seem counterintuitive, the argument for the assumption is
that, in order to maintain a highly sexually active
lifestyle, PROs would probably use contraception or abort
foetuses. In addition, there is evidence suggesting that STDs
may lead to lower fertility. On the other hand, if awareness
of contraception is high, then individuals choosing to have
children are more likely to be in stable relationships and
therefore at reduced risk of contracting HIV. It is unlikely
that the relative fertility rate assumptions have a great
impact on the results, with the possible exception of the
number of infants born HIVpositive.
These
parameters are found in the HIV+ Fertility
worksheet.
The
model allows for the impact of the duration of infection on
fertility by multiplying the nonHIV fertility rates by a
factor determined as follows:
where
a
= factor allowing for the bias, particularly at the younger
ages, arising from the fact that those falling pregnant are
those having sex and not using condoms
b
= factor allowing for an initial impact of the virus on
fertility
c
= factor allowing for the impact of the virus on fertility
over time
d
= duration of
infection in years
The first three factors can be
changed in the columns entitled ‘Start Ratio’, ‘Initial
Impact’ and ‘Reduction Factor’ towards the right of the
worksheet.
The births resulting from this fertility are split
into males and females according to the assumed proportion of
births that are male. This proportion is found on the Assumptions
worksheet. The relevant table is second from the top and
second from the left side of the worksheet. The births
populate the age zero cells in the next step of the projection
via the Young sheet.
The proportion of births that are boys can be changed by the
user but will have minimal effects on the workings of the
model.
The migrationrelated variables are
found on the Male Migration
and Female Migration worksheets. For ease of computation, the model
assumes that all migration takes place at the end of the
relevant year. ‘Migrant’ can refer to both immigrants and
emigrants. The figures in the Male Migration and Female Migration
worksheets represent net immigration (i.e. inmigrants less
outmigrants).
The
starting population was constructed to include all migrants
received up to 1985.
Migrants
are apportioned to the four risk groups according to the
proportions in the Assumptions sheet. These are found in the table third from the
top on the left side of the worksheet. Currently these
proportions are set to be the same as those of the receiving
population but the values can be changed by the user.
Migration
after 1996 is assumed to fall from its 1996 level,
logistically, towards close to zero over a 30year period.
The
ASSA2000 lite model does not distinguish between
the different population groups defined during the apartheid
era, namely black African, coloured, Asian and white. The full
version of the model allows for separate modelling of the
epidemic in the four population groups. This feature of the
model was developed in response to user demand. This demand
was motivated, in part, by the observation that the impact of
the epidemic is very different in the different groups. These
differences constitute one of the reasons for differences
between the prevalence in the Western and Northern Cape on the
one hand and the other provinces on the other. Further, some
users wanted to extrapolate the results of the model to
socioeconomic groups, and population group is thought to be a
useful proxy for this in South Africa. There were thus both
demographic and economic reasons for modelling the epidemic in
terms of population groups.
Developing
this aspect required a number of demographic assumptions. The
disaggregation presents significant challenges during
calibration of the model. Unfortunately, very limited data
exist about the impact of the epidemic in the different
population groups. Mortality data has not been available on a
population group basis since 1990, and the ANC data has not
been published in disaggregated form since 1995. The mortality
data has, since 1998, again been collected on the basis of
population group but has not yet been published. The ANC
survey continues to collect information on population group.
This information is not publicly available, but ASSA’s AIDS
Committee has been given access to data for 1997 to 1999.
The
model has been fitted to these data and to data from private
sector company and insurance testing by taking into account
differing levels of STDs and condom usage
The update of the model released in
April 2002 allow the user the choice as to whether to give
effect to a pattern of preset changes in
mothertochildtransmission (MTCT), transmission
probabilities (to simulated an STD intervention), number of
new partners per annum, and condom usage. These changes
reflect possible changes in individual behaviour and
government interventions. Lookup tables of the preset changes
are found to the lower right of the Assumptions
worksheets for each of the population groups. The user
indicates whether the change scenario is wanted by selecting a
‘1’ for change, and ‘0’ for no change on the Assumptions worksheet before activating
the projections. The user can choose the start year and rate
of roll out of each intervention by altering the values in the
lookup table.
With the exception of the Western
Cape, the tables reflect the change scenario reflected on the
ASSA website. This scenario has the following assumptions:
§
no antriretroviral therapy (ART);
§
MTCT intervention phased in from 40% of births in the year
starting 1 July 2001, to 90% five years later. The
intervention is assumed to be 50% effective in preventing
infection of babies;
§
treatment of sexually transmitted diseases such that they are
reduced by 15%. This intervention is also phased in over the
five years starting 1 July 2001;
§
a doubling in condom usage over the five year period starting
1 July 2001;
§
a decrease in the number of new sexual partners by 15% over
the five year period starting 1 July 2001.
The change scenario for the Western
Cape allows for a more accelerated roll out of MTCT and STD
interventions, reflecting the provinces clear and early
commitment to these interventions.
For the provincial version of the model, the workbook pastes in a zero for all
provinces except the Western Cape, i.e. the default is no
change.
The model has a start date of 1
July 1985. At this date, each risk group is assumed to be free
of HIV. An initial level of prevalence is then introduced by
setting the number of ‘imported HIV’ on the Assumptions
sheet to start the epidemic. HIV levels and patterns in later
years are generated by the assumptions built into the model.
To run the model, open the
appropriate ASSA2000 workbook. When prompted, click on the
‘Enable Macros’ button. If you click on ‘Disable
Macros’, the workbook will open, but you will not be able to
run any projections.
The copyright notice will appear
automatically after you click ‘Enable Macros’. Click on
the ‘Accept’ button (provided you accept the copyright
conditions). If you are using the lite version,the workbook will open with the Assumptions worksheet on the screen. If you are using the full version, the workbook will open with the Assumptions – All worksheet on the screen. Clicking on the
‘Decline’ button will close the workbook.
Before running the model, click the
‘Reset Projection to Zero’ button on the Assumptions
or Assumptions – All worksheet. This runs the ‘ResetProj’ macro, which
allocates the initial population into age bands and the four
risk groups according to the proportions on the Population
worksheet and the Assumptions worksheet.
The
model allows the user to project in two different ways. The
first is by making use of buttons which run the model for
periods of one, five, ten or forty years at a time. Clicking
more than one button one after the other produces a projection
for the sum of the years.
For example, to estimate the situation as at July
1998, 13 years after the start date, perform the following
actions after having reset the model as described above:
§
Click the ‘Project 10 years’ button on the Assumptions worksheet;
§
Click the ‘Project One year’ on the Assumptions worksheet three times, allowing time for the programme
to run each year between clicks.
After each click, the bottom
lefthand corner of the screen will report on the yearbyyear
progress of the projection. After the four clicks described
above, the sheets, in particular the Results and Population worksheets, will reflect the picture 13 years after the
start date of July 1985.
An alternative method of obtaining
the same output is to specify the end year. To do this,
perform the following actions after having reset the model:
§
Type in the end year required in the cell to the right of the
‘To specific year’ button on the Assumptions
worksheet and <ENTER>;
§
Click the ‘To specific year’ button.
Again, the bottom lefthand corner
of the screen will record the progress of the projection.
For simple runs, it makes little difference which
method of running the projection is chosen. For some users,
however, one way may serve the purpose better than others. For
example, a user who wants to change a particular assumption as
from a certain date, will want to use the first method.
Similarly, a user who wants to record results at particular
points, for example, every five years, should use the first
approach.
By default, the model projects
forward from July 1985. Some users will be more interested in
projections into the future than in what has happened to date.
The model will project the epidemic to July of the current
year if you click the ‘To current date’ button on the Assumptions worksheet. The current year
for the projection is derived from the system date on the
computer on which the projection is performed. As before,
progress is recorded at the bottom lefthand corner of the
screen. The end point of this projection can then be used for
projections into the future.
To run repeated projections from
the current date, or from any other specified date, the user
should perform the following actions:
§
Run the projection to the desired starting date by one of the
methods described above;
§
Click the ‘Store Population’ button to store the results
for the last year of the projection;
§
Click the ‘Reset Projection from Store’ button to
establish the position in the last year of the previous
projection as the new starting point;
§
Run the new projections by one of the methods described
above.
As is the case with all projections, the further into
the future one projects, the less reliability one can place on
the results. This is especially true when projecting the
impact of an epidemic about which there is still much
uncertainty. For this reason it is not recommended to use the
ASSA model to project beyond 40 years. However, some users
will want longer projections, for example, to estimate cohort
life expectancies. Such users will find that the program tends
to become very large and slow on longer projections
irrespective of which of the above methods are adopted to run
the model.
The user can circumvent the problem
by storing the population after 40 years, resetting the base
situation to what has been stored, and projecting forward from
there, as follows:
§
Click the ‘Store Population’ button after projecting for
40 years.
§
Click on the ‘Reset Projection from Store’ button to get
ready for further projections.
These steps need to be repeated if
the projection is longer than 80 years. Unless the user is
only interested in the end point, he or she should save the
output they are interested in (say mortality rates over time)
before resetting.
Key statistics for each year of the
projection can be placed in the Results
worksheet to record their passage over time. Currently the
recorded statistics include:
§
numbers of people as at 1 July in each sex/risk group/HIV
classification and in total;
§
number of deaths in each year (JulyJune) due to AIDS or
other reasons;
§
HIV prevalence rates for different groups;
§
fertility and birth rates;
§
male and female mortality rates by age; and
§
crude extra mortality i.e. additional mortality resulting
from AIDS.
The Results
worksheet contains results for each year of the projection.
Further population results, such as
numbers alive and dead by HIV status for each age, can be
found in the Population worksheet. The Population
worksheet contains information only on the start and end dates
of the projection. Where several projections are performed one
after the other, the start date is the original start date
i.e. July 1985 unless the ‘Store Population’ and ‘Reset
Population from Store’ functions have been used.
To view the Results or Population
worksheets, simply click on the appropriate tabs at the bottom
of the screen.
Other worksheets contain charts of
some of the generated information.
§
The AIDS Age Profile
worksheet shows the distribution of AIDS cases by age;
§
The HIV prevalence
worksheet shows prevalence by risk group and sex for each year
from the first year of the projection to the final year;
§
The ANC Age Profile
worksheet shows the projected distribution of ANC AIDS cases
by fiveyear age groups for the projected year, as well as the
observed distributions for 1995, 1999 and 2000.
§
The Cumulative Deaths
worksheet contains a chart of the cumulative number of people
who have died from AIDS in each year from the start of the
projection to the end;
§
The (noncumulative) Deaths
worksheets contains a chart of the number of people becoming
infected with HIV, dying from AIDS and dying from other causes
in each year from the start of the projection to the end;
§
The Pyramid
worksheet contains a chart of the population pyramid for each
sex in the last year of projection in fiveyear age groups;
§
The Mortality
worksheet contains a chart of the projected mortality curves
for each sex in the last year of projection with and without
AIDS (‘No AIDS’);
§
The Reported deaths – Female/Male
worksheets compare the number of total adult deaths by age for
females and males separately with those estimated to have
actually occurred in South Africa in selected years.
Although
the results of the projection are recorded in each of the
worksheets, in most worksheets this is only done for one year
at a time. The Results worksheet allows the user to record desired output over
time.
The
user can erase items not of interest from the Results
worksheet. In doing so, however, the user should note that
some items are used to produce the charts described above, so
if these are needed, then those specific rows must not be
erased. The user can also add statistics that have not been
included on the standard Results
worksheet. References or formulae for desired statistics
should be inserted in the column headed ‘LATEST’ (column
B). However, the
user must ensure that all rows are inserted above the line
marked ‘NB: Any additions must be inserted above this
line!’
In
the simple case, the user can add statistics computed directly
from data already included in the model. In the more
complicated case, the user can add data from other sources and
calculate additional output data from this and existing data.
A
very simple example would be adding as output the population
in the age group used for calculations of the economically
active population in each year. In South Africa, the age group
1565 is usually used for this purpose. To include the output
on the Population worksheet, the user would
perform the following actions:
§
Insert a row in the Results
worksheet anywhere above line marked ‘NB: Any additions must
be inserted above this line!’;
§
Label the row in the column headed ‘STATISTIC’ (column
A), for example give it the label ‘1565’;
§
Insert in the ‘LATEST’ column the formula for calculating
this number in a
year, i.e. ‘=SUM(Population!L19:L67)’
When
the projection is run, the number of economically active
people in each year of the projection will be recorded in the Results
sheet.
An
alternative way of achieving the same result is to perform the
calculation on the Population worksheet, and then refer to the
calculated cell on the Results
spreadsheet. The detailed steps for doing this are as follows:
§
Insert the formula to calculate the population aged 1565 years on the
Population worksheet at the bottom of the ‘Total
Population’ column. For this example, we assume this is done
in cell C97;
§
On the Results
worksheet, insert and label a new row ‘1565’ as described
above;
§
On the Results worksheet, in the ‘LATEST’ column, type
the reference ‘=Population!C97’.
When
inserting the above and other formulae, remember that the
cells will not necessarily be updated until after you run a
projection, as ASSA2000 sets the default of the CALCulation
function from Automatic to Manual. To see the updated
calculation without running a projection, press the F9 key on
the keyboard.
Another
simple example would be to calculate the death rate of male
and female PROs. To do this, the user would perform the
following actions:
§
Insert four rows in the Results
worksheet, for example in the ‘Deaths’ section;
§
Label the rows in the column headed ‘STATISTIC’, with the
labels ‘AIDS Male PRO deaths’, ‘Normal Male PRO
deaths’, ‘AIDS Female PRO deaths’ and ‘Normal Female
PRO deaths’;
§
Insert in the ‘LATEST’ column of these rows the
appropriate references for these statistics, namely
‘MalePRO!AO51’, ‘MalePRO!AL51’, ‘FemPRO!AO51’ and
‘FemPRO!AL51’;
§
Insert two rows in the Results
worksheet, for example in the ‘Fertility and Growth’
section;
§
Label the rows in the column headed ‘STATISTIC’, with the
labels ‘Male PRO Death Rate’ and ‘Female PRO Death
Rate’
§
Insert in the ‘LATEST’ column of these rows the
appropriate formulae for calculating the death rates, namely
‘=(B39+B40)/(B10+B11)’ AND ‘=(B41+B24)/(B12+B13)’;
When
the projection is run, the death rates for male and female
PROs in each year of the projection will be recorded in the Results
sheet.
A
more complicated example would be adding as output the number
of workdays lost to AIDSrelated disease. To obtain this
output, the user would need to perform the following actions:
§
On the HIVTable worksheet,
create a table setting out the estimated number of workdays
lost per annum. This could be indexed by any or all of age,
sex, duration since infection and risk group. These data would
have to be obtained from elsewhere.
§
On the Results
worksheet, insert a new row, for example above the mortality
tables.
§
In the new row, in the column labelled ‘LATEST’, type in
the formula that will calculate the new statistic based on the
table and the population worksheet.
The
new statistics will be recorded on the Results
sheet for each step of the projection. Charts using any of the
new statistics can also be produced.
The
provincial version of the ASSA2000 model consists of an aggregation of
the application of the full ASSA2000 model to each of
the provinces. By projecting and calibrating each province
separately, the provincial model has the potential to allow for differences between the
provinces in respect of particular characteristics, such as
different demographic composition of the population, different
levels of STDs and different starting times for the epidemic.
The provincial
version of the ASSA model utilises two workbooks – the
workbook for the full version of the model, together with a workbook that contains
the initial assumptions relating to each province. The user
creates the workbook for a particular provincial model by
first loading the full model and the AssumptionsProv
workbook and then running a macro on the AssumptionsProv
workbook which pastes in the provincespecific starting
assumptions into the full version of the model. The full
version can then be operated in the usual manner, as described
above, to give results pertaining to a particular province and
can be save as the provincial version of the model.
The workbook of provincial
assumptions consists of an Initializer
worksheet where the user specifies the province, destination
file, and whether the model allows for a change scenario.
There are a further nine Prov – Common worksheets, and 36 Prov –
Population Group worksheets containing initial assumptions which are pasted
into different worksheets of the full
version worksheet once the user has specified the province and
asked that the paste operation take place. The cells of the
workbook consist of a mix of absolute values and formulae.
Some of the latter appear to give invalid or incorrect values
when viewed in the workbook of provincial assumptions.
However, once the formulae are pasted into the full version worksheet, the
cells referred to in the formula take effect and the values
become valid.
The urbanrural
version also allows for the case where available data on HIV
prevalence consists of inconsistent and irregular samples
surveys from urban and rural clinics. The user can input data
from all the sites, specify each site as either urban or
rural, and indicate how the data should be aggregated to
produce average urban, rural and national figures.
Calibrating the urbanrural model is somewhat more difficult than calibrating the
full version of the model. Not only does one have to calibrate are three levels (urban,
rural and national) but in many situations one has no data for
setting the size of the risk groups (STD in particular) (or a
number of the other parameters) and these have to be set by
trial and error to produce the best fit.
As far as possible, the parameters of the ASSA2000
model have been set by reference to studies of empirical
evidence. This was possible, for example, in respect of the
size of the STD group, the probability of transmitting the
virus, age of the partners, and condom usage. Where it was not
possible, parameters are set within bounds of reasonableness
to produce output comparable with observations of antenatal
seroprevalence levels and estimates of the actual number of
deaths based on the registered deaths.
Calibration involves adjustments of parameters that
have not been estimated independently so that the
‘results’ of the model more or less match observed
reality. In particular, the model results should match the
results of the annual ANC surveys both in terms of overall
level and by age. The model results should also match the
number of adult deaths estimated on the basis of those
recorded by the Department of Home Affairs on the population
register after adjusting for an estimate of underrecording.
Calibration can be done visually,
using the charts on the Calibration,
ANC Age Profile and Reported deaths
worksheets.
The Calibration
worksheet looks at the fit with ANC survey data. In judging
the fit, it must be borne in mind that the ANC points before
1997 are probably biased upwards, perhaps as a result of an
urban bias in the location of data collection sites over a
period when prevalence levels were higher in the urban areas.
The ‘target’ points are therefore the ones that should be
used when calibrating the model. Further, the 1998 ANC survey
value is incorrect as the Department of Health made an error
in weighting the provincial results to get the national
estimate. The correct value should be some 2% lower than the
published value.
The user can obtain a fullscreen
calibration graph of the antenatal clinic prevalence each year
by clicking the ‘Calibration data’ button on the Assumptions
worksheet after running a projection. The aim is to get the
solid curves to follow the points marked by the data as
closely as possible. These points correspond to HIV prevalence
among:
§
ANC attendees;
§
Commercial sex workers (CSWs); and
§
STD clinics;
in respect of each:
§
actual surveyed prevalence; and
§
‘target’ expected prevalence.
The ‘target’ prevalence is
based on the patterns found in other African countries where
the epidemic has been experienced for longer than in South
Africa.
The variables for HIV prevalence
among women aged 1549 are found on the HIVTable
worksheet.
The procedure used in the original
calibration of the model was first to fit the prevalence
figures for the PRO group. This group is roughly equivalent to
CSWs but not identical in that some CSWs will be at less risk
than PROs as defined in the model because, for example, they
use condoms and have STDs treated. The next step after fitting
the PRO group, was to fit the STDs and finally the ANC
attendees. It was assumed that most sexual activity occurs
between partners in the same risk group. Further, by
definition, members of the RSK group do not have sexual
contact with members of the PRO group, and members of the NOT
group do not have unprotected sexual contact with members of
any of the other groups.
Based on evidence that suggests
that women only visit a clinic late in their second trimester,
the projection intervals run from the middle of one year to
the middle of the next year. This assumes that women are, on
average, six months pregnant when they first visit the clinic.
In order to model the prevalence of
women attending public antenatal clinics rather than that of
all pregnant women, the ASSA2000 model increases the
agespecific rates of all pregnant women in the population by
a multiple to allow for the fact that the prevalence of women
attending public antenatal clinics is likely to be higher than
that of pregnant women in general.
Adopting this approach, it is impossible to get
anything but a crude fit to the PRO and STD target points.
Modelled prevalence plateaus at a far higher level than the
observed and ‘target’ points suggest. One possible
explanation for this mismatch is that the survey and target
CSW prevalences may include people from the (lower risk) RSK
and STD risk groups, while the model definition of the PRO
group is narrower, including only people at higher risk.
The ANC Age
Profile sheet compares the prevalence by age from the
antenatal survey with that generated by the model. It can be
accessed by clicking the ‘ANC Age profile’ button on the Assumptions
sheet. Calibration should aim to ensure as close a fit to the
age profile of the antenatal prevalence data as possible by
changing such factors as the female curve of sex activity and
the age distribution of partners.
The Reported
deaths worksheets contain charts which look at the fit with deaths
recorded by the Department of Home Affairs. There are two such
worksheets, one for male deaths and one for females. The user
can view these worksheets by selecting the appropriate tabs on
the workbook after running a projection. A full screen view is
obtained by choosing the ‘Full screen’ option on Excel’s
View menu.
The charts show the estimated
number of deaths in the country based on the registered deaths
by age for each of the years 1996 (calendar), 1997/98, 1998/99
and 1999/2000, as well as deaths projected by the model for
the last year of the projection. The aim in calibration is to
match as closely as possible the estimates of the number of
deaths based on the registered deaths.
Theoretically the user can change a
wide range of parameters on the worksheet. In practice,
however, there are only a limited number of combinations of
parameters for which changes could provide a potentially
realistic picture of the AIDS epidemic in South Africa.
Further, because of the interdependence of different parts of
the model, it is sometimes not easy to predict the effects of
a particular change. This subsection therefore provides some
tips as to type and extent of changes in output that are
likely to result from changing particular parameters.
The following pointers suggest the effect of changing some of
the key parameters on the outcome:
§
The size of the NOT group determines to a large extent the
level at which the antenatal prevalence is expected to plateau
in the long run.
§
Provided it remains fairly small (around 1% of the
population), the PRO group does not impact much on the
longterm course of the epidemic.
§
The STD group is conceptually defined to be those infected
with STDs to such an extent that the average transmission
probability is expected to be that recorded on the Assumptions
sheet. In constructing the model, the proportions were set
equal to those recorded in the 1998 Demographic and Health
Survey, which implied that this proportion were infected with
STDs about 25% of the time.
§
The age profile of prevalence is determined largely by the
sex activity, age of partner and age distribution of condom
usage assumptions.
Pentium III 500Mhz (or better from
a speed perspective)
Windows 98 or later
Microsoft Excel 98 or later
64MB Ram
This
is the worksheet that appears on the screen when the user
opens the model. At the centre it contains a number of buttons
that allow the user to run projections, jump to worksheets
containing output graphs and calibration checks, and reset the
model.
§
The ‘Project One Year’, ‘5’, ‘10’ and ‘40’
buttons allow the user to run the model for that number of
years cumulatively, in other words, in addition to the point
to which the model has already been run.
§
The ‘To Date’ button runs the model to the current year
as determined by the clock on the machine running the model.
§
The user can specify the year to which he or she wants to
project, by entering the year and clicking on the ‘To
specific year’ button.
§
The ‘Reset Projection to zero’ button returns the
workbook to the start year.
§
The ‘Store Population’ and ‘Reset Projection from
Store’ allow the user to run the projection to a point in
time, store the population details at this point, and then to
use this as a new starting point for projections, resetting
from the stored population each time.
Around
the central buttons, the worksheet contains a number of tables
and matrices containing key parameters.
Several
of the matrices reflect assumptions underlying the modelling
of sexual behaviour. These include:
§
a matrix showing the probability that a partner is from a
particular risk group. The relevant table is the topmost table
second from the left;
§
matrices of maletofemale and femaletomale transmission
probabilities per sexual contact for various combinations of
risk group encounters. The relevant tables are the topmost
tables third and fourth from the left;
§
a matrix showing the number of new partners per year and the
number of contacts per new partner per year. The table is the
topmost table fifth from the left;
§
a matrix showing the number of contacts per male partner from
different risk groups of females of the different risk groups,
as well as the averages. The table is the rightmost table on
the worksheet;
§
a matrix of condom usage for each risk group by age. This is
the long thin table in the middle of the worksheet; and
§
the effectiveness of condoms. This is a single value shown on
the worksheet just above the condom usage table.
Other
tables reflect further basic assumptions, as follows:
§
a table, at top left, showing the total of the starting
population;
§
a table, second down from the top left, showing the
percentage distribution of the male and female adult
populations across the four risk groups, as well as relative
fertility of females in each risk group;
§
a table, third down from the top left, showing the percentage
distribution of the male and female immigrant adult population
across the four risk groups;
§
a table, fourth down from the top left, reflecting
assumptions about infant AIDS mortality and median time to
death and imported infection for male and female;
§
a table, fifth down from the top left, showing assumed
proportions of perinatal and breastfeeding infection and AIDS
median time to death;
§
a table, second from the left and second from top, giving
proportion of male births. (This table is not utilised in the
current version of the model.)
This
worksheet is used to store output over time. It thus
summarises the results for each year from the start to end
date of a projection. From top to bottom it records
information on the clear and infected populations, deaths,
accumulated AIDS deaths, HIV prevalence rates, fertility and
growth, advocacy output, male and female mortality by age, and
force of infection. None of this information is used in the
running of the model although some of it is used to produce
the graphs. Much of it could be removed if the user had no use
for it. However,
there is no need to remove or replace any of it in order for
the user to produce his or her own output. To add their own
output, users can insert rows above the line marked ‘NB:
Any additions must be inserted above this line!’ and
enter the required extraction formula in column B.
The
full
version of the model contains a separate Results
worksheet for each population group in addition to the one
which is used for aggregate results.
This
worksheet summarises population statistics for the start and
end date of a projection. Where several projections are done
one after the other, the start date is the original start
date. Working from left to right on the worksheet, we have:
§
Details of starting population by age and sex;
§
Infected and noninfected population by age and sex as at 1
July of the current year;
§
Deaths by age and sex projected for the twelve months
beginning 1 July of the current year. In this table, age
‘B’ represents deaths of babies born during the projected
year. Deaths marked ‘0’ represent deaths of those who were
under 1 year of age at the start of the projected year;
§
Numbers used to construct the population pyramid as at 1 July
of the current year;
§
A summary table of male and female deaths in the twelve
months beginning 1 July of the current year in fiveyear age
groups;
§
A summary table used for calculating the number of people
sick with AIDS.
Below
these tables, we find:
§
A table showing numbers and proportions of new adult
infections;
§
A table summarising numbers and proportions of AIDS deaths in
five year age groups.
The
full
version of the model contains a separate Population
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole. The groupspecific Population
worksheets do not have the second set of tables contained in
the Population worksheet of the lite
model, namely the table showing the numbers and proportions of
new adult infections, and the table summarising numbers and
proportions of AIDS deaths in five year age groups.
This
sheet produces the nonHIV mortality rates for each year, by
looking up the rates up to 1999 and interpolating between the
1999 rates and ultimate rates for years after 1999. Working
from left to right, the worksheet reflects:
§
1(NonAIDS survival) (i.e. nonAIDS mortality), by oneyear
age group for age last birthday and sex, for the current year;
§
Mortality improvement factors, by oneyear age group and sex;
§
NonAIDS mortality rates by sex and one year age group for
exact ages, for the current year;
§
Ultimate nonAIDS mortality rates for oneyear age group and
sex;
§
Mortality to date in respect of nonAIDS mortality rates by
oneyear age group and year, with separate tables for male and
female;
§
Projected vs recorded deaths for fiveyear age groups, for
each of the years 1996 to 1999, and for male and female
separately. These are used to produce the graphs for
calibrating the model against the recorded deaths.
The
full
version of the model contains a separate MortTable
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole. The groupspecific MortTable
worksheets do not contain a table of projected vs recorded
deaths as described above. The aggregate MortTable
worksheet
contains a table of weights by population group and age for
ages 0 to 12 years which is used to compute the aggregate
mortality rates.
This
sheet calculates the relative amount of sex at each age for
males and females. The distribution of male sex activity by
age is derived from the distribution for females and the age
and risk group mix of the partners of the women.
The leftmost table on this sheet contains separate
indices for male and female sex activity in oneyear age
groups. (The values for male sexual activity at ages 14 to 59
do not sum exactly to 100% because it is assumed that there is
some male sexual activity after age 59.) The next table from
the left contains f(x),
representing the percentage of total female sexual activity
occurring at age x.
The third table contains the parameters used to generate f(yx),
the percentage of partners of females aged x
who are aged y.
The next table is the table of
f(yx)
values. The table below that contains the values for g(xy),
the distribution of female partners of men aged y.
The SexActivity
worksheet includes a chart that displays the male and female
sexual activity curves, and one, on the far right, that
displays the age distribution of male partners of women at
selected ages.
The
full
version of the model contains a separate SexActivity
worksheet for each population group, but no aggregate
SexActivity worksheet for the population as a whole.
This
sheet records the survival curves (i.e. the proportion of
people surviving by duration since becoming infected) for
adults, those born with the virus and those becoming infected
through mother’s milk.
Reading from left to right, the worksheets contain the
following tables:
§
HIV survival rates by broad age group (1424, 2534 and 35
plus) of adults, and duration of infection in oneyear
intervals;
§
Survival of HIV births by duration of infection in oneyear
intervals;
§
Survival of babies infected by mother’s milk by duration of
infection in oneyear intervals.
The
columns marked ‘Surviving’ refer to the proportion of
infected people still alive t
years
after infection.
The
mortality curves are displayed in a chart below the topmost
set of tables.
The
full
version of the model contains separate Male
and
Female HIVTable
worksheets for each population group, as well as aggregate Male
and Female
worksheets for the population as a whole. While most of the
other aggregate worksheets are constructed through simple
summation of the values in the groupspecific worksheets, the
values in the aggregate HIVTable
worksheet have two differences.
First the estimated prevalence levels of those
attending antenatal clinics in the top table are derived as a
weighted average of the same figures in the each of the
population groups, weighted by the proportions of pregnant
women from each group attending public antenatal clinics.
Secondly, the second table down contains the national
prevalence figures as published or estimated elsewhere and is
not derived from the populationgroup specific sheets.
This
sheet is used to produce the estimates from the model of the
prevalence of women attending antenatal clinics by fiveyear
age group and in total. It also contains a table of observed
values against which the estimates can be compared for
calibration purposes. The top table of this worksheet contains
data in fiveyear age groups. Two columns for pregnant women
show the numbers who are HIV positive and negative. A series
of columns represents the prevalence of women attending ANC
clinics. Finally, there is an adjustment factor which adjusts
the prevalence in the population as a whole to allow for the
fact that it includes women who attend private clinics, in
order to arrive at an estimate of the prevalence of those who
attend public antenatal clinics.
The
second set of tables when moving from top to bottom contains
three sets of data – for ANC, STD clinics and commercial sex
workers. The ANC columns record survey and target data. The
columns for STD clinics and CSWs record South African and
target data for each year.
The
full
version of the model contains a separate HIVTable
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
This
sheet produces age specific fertility rates for HIV negative
women in each of the risk groups.
Reading from left to right, this contains the following
tables:
§
NonHIV fertility rates by the four risk groups and age of
the woman in oneyear agegroups, from age 14 to 59, for the
current year;
§
NonHIV fertility rates by year for the period 1985 to 1996
by oneyear agegroups, from age 15 to 49 for all HIV positive
women irrespective of risk group;
§
A fertility improvement factor and ultimate rates by oneyear
age groups, from age 15 to 49;
§
The ratio of HIV+ fertility to nonHIV fertility by oneyear
age groups, from age 15 to 49, for the current year (produced
by the HIV+ Fertility sheet);
§
The proportion of women in each risk group in oneyear age
groups, from age 15 to 49.
The
full
version of the model contains a separate NonHIV
Fertility
worksheet for each population group. There is a single
aggregate Fertility worksheet which combines information from
the groupspecific NonHIV
Fertility
and HIV+
Fertility
worksheets. The Fertility worksheet contains the following
tables:
§
Population group female weights for each age from age 14 to
49 years;
§
Percentage change in fertility attributable to HIV, which
among others, records HIV prevalence and aggregates the HIV+
and HIV fertility rates from the groupspecific worksheets
for each age from 14 to 49 years.
This
sheet calculates the adjustment ratio for converting the
fertility rates of HIV negative women to fertility rates for
women infected with the virus. The worksheet contains a single
table. The rows record the age of the individual, from 14 to
59 years. A first set of columns records the duration of
infection, from one to 29 years. The third last column records
the start ratio – the ratio of HIV positive to HIV negative
ruling immediately before becoming infected. The second last
column records the initial impact on the fertility ratio of
becoming infected. The final column records the reduction
factor, which is equal to 1 minus the rate at which fertility
drops per year infected.
The
full
version of the model contains a separate HIV+
Fertility
worksheet for each population group.
These
sheets contain the net numbers of migrants into the population
at each age for each year.
Each of these worksheets contains a single table. The
rows of the table reflect the age of the individual in
oneyear age groups. The columns of the table reflect the
year, from 1985 to 2025.
The model assumes that beyond 2025 the number of
migrants remains the same as those in 2025.
The
full
version of the model contains separate Male
and
Female
Migration
worksheets for each population group, as well as aggregate Male
and Female
worksheets for the population as a whole.
This
sheet calculates the numbers of females in the PRO risk group
at each duration since becoming infected, the number of new
infections and the number of infected and uninfected births at
each age. The worksheet has a BEFORE table at the top, with an
AFTER table below it. The BEFORE position consists of data
reflecting the population at the start of the year. The first
set of columns contain, for each year of age and each year of
duration of being infected, the number of people in that
group. The columns to the right of this series contain a range
of other parameters that affect the change in position over
the projection period. The AFTER table again provides a value
for each year of age and each year of duration. The AFTER
position is calculated from the BEFORE position during
projections using the formulas in the cells of the AFTER table
to provide the BEFORE table for the next year. The final
columns of the AFTER table provide for calculation of
necessary adjustments to account for migration.
Below
these tables is a STORE table. This is used for storing the
population profile when the ‘Store Population’ button on
the Assumptions
sheet is clicked, so that one can revert to the stored
population using the ‘Reset Population from store’ button.
The
full
version of the model contains a separate FemPRO
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
As
for FemPRO.
The
full
version of the model contains a separate FemSTD
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
As
for FemPRO.
The
full
version of the model contains a separate FemRSK
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
This
sheet is analogous to the above sheets but without the
complication of having to allow for infected people. The
worksheet has a BEFORE table at the top, with an AFTER table
alongside. The BEFORE position consists of data reflecting the
population at the start of the year. The columns contain, for
each year of age, the starting position, the number of deaths
during the year, and net immigration. The AFTER table provides
a value for each year of age reflecting the position at the
end of the year. The AFTER position is calculated from the
BEFORE position during projections to provide the BEFORE table
for the next year. The small NEW table below the AFTER table
reflects the number of male YOUNG people joining the FemNOT
category over the year.
The
full
version of the model contains a separate FemNOT
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
As
for FemPRO.
The
full
version of the model contains a separate MalePRO
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
As
for FemPRO.
The
full
version of the model contains a separate MaleSTD
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
As
for FemPRO.
The
full
version of the model contains a separate MaleRSK
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
As
for FemNOT.
The
full
version of the model contains a separate MaleNOT
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
This
sheet is analogous to the above sheets without sexual
intercourse, i.e. there are no newly infected and no births.
The worksheet has a BEFORE table at the top, with an AFTER
table below it. The BEFORE position consists of data
reflecting the population at the start of the year. The first
set of columns contain, for each year of age and each year of
duration, the number of people in that group. The columns to
the right of this reflect total infected, total clear and
infected, and number of AIDS and nonAIDS deaths. The AFTER
table again provides a value for each year of age and each
year of duration. The final columns of the AFTER table provide
for calculation of necessary adjustments to account for
migration. The AFTER position is calculated from the BEFORE
position during projections using the formulas in the cells of
the AFTER table to provide the BEFORE table for the next year.
The
full
version of the model contains a separate MaleNOT
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
As
for MaleOLD.
The
full
version of the model contains a separate FemOLD
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
This
sheet calculates the number of survivors from birth at each
age up to age 14. The worksheet has a BEFORE table at the top,
with an AFTER table below it, and several calculation tables
and a STORE table below that. The BEFORE position consists of
data reflecting the population at the start of the year. The
first set of columns contain, for each year of age and sex,
the number of people in that group who are clear, who were
born HIV+, and who have become infected through mother’s
milk. The table includes a row for babies born during the
year. The columns to the right of this series reflect the
number of female and male deaths predicted for each of the
three HIV categories, and estimated female and male net
migration. The AFTER table again provides a value for each
year of age and sex in respect of each of the three HIV
categories. The AFTER position is calculated from the BEFORE
position during projections using the formulas in the cells of
the AFTER table to provide the BEFORE table for the next year.
The tables between the AFTER and STORE table contain the
formulae for calculation of the number of infected and
noninfected babies born during the year, and surviving to the
end of the year, as well as the number infected through
mother’s milk.
The
full
version of the model contains a separate Young
worksheet for each population group, as well as an aggregate
worksheet for the population as a whole.
The
worksheet contains a chart showing the distribution of AIDS
cases by age. The data refer to to cases up until 1995, as
data have not been collected since this date.
The
worksheet contains a chart showing HIV prevalence by risk
group and sex for each year from the first year of the
projection to the final year. The risk groups charted are
female PRO, female STD, male STD, female POP and male POP. The
POP lines represent the prevalence for the total female and
male populations aged 1549 years.
The
worksheet contains a chart showing the projected distribution
of ANC AIDS cases by fiveyear age groups for the endyear of
the projection, as well as the observed distributions for
1995, 1999 and 2000.
The
worksheet charts actual, ‘target’ and modelled prevalence
among ANC attenders and STD clinic attenders as well as
modelled CSW and RSK prevalence and CSW ‘target’
prevalence from the first year of projection to the end year.
The ‘target’ data reflect patterns found in other African
countries that have more experience of the epidemic than South
Africa.
The
worksheet contains a chart showing the cumulative number of
people who have died from AIDS in each year from the start of
the projection to the last year of the projection.
The
worksheet contains a chart showing the numbers of people
becoming infected with HIV, dying from AIDS, and dying from
other causes in each year.
The
worksheet contains a chart of the population pyramid for each
sex in the last year of projection in fiveyear age groups.
The
worksheet contains a chart of the projected mortality curves
for each sex in the last year of projection with and without
AIDS. The label qx
on the Yaxis refers to the probability of a male or female
individual aged exactly x
dying within the next year of age.
These
worksheets chart reported deaths, after adjustment for
underrecording, by fiveyear age group for 1996 (calendar
year) and 1997/98, 1998/99 and 1999/2000 against total
projected deaths for the last year of the projection.
The
copyright worksheet opens automatically when the user opens
the model workbook with macros enabled. (If macros are not
enabled, the user will be unable to run any projections.)
This
workbook is used to paste starting assumptions into the
ASSA2000 full
model to create a model of a chosen province.
In order to run it the user must first ensure that the
ASSA2000 full
version of the model is open.
This
worksheet allows the user to specify:
§
whether the ASSA2000 file being used contains behaviour
change;
§
the province for which the data should be copied; and
§
the name of the file into which the assumptions are to be
pasted (the source or destination file).
By
clicking the square buttons under the specification table, the
user causes data to be copied from this workbook to the
specified destination file.
This
worksheet contains the following tables:
§
a table giving the formulae used to calculate the modelled
ANC prevalence, as well as the observed prevalence for 1995,
1999 and 2000 in fiveyear age groups;
§
a table giving observed and target rates of infection for
ANC, STD clinics and CSW for each of the years from 1985 to
2005.
The
values in these tables are copied into the corresponding cells
of the HIVTable
worksheet of the destination workbook.
This
worksheet contains the following tables:
§
a singlerow table giving the initial population. This is
copied to the Assumptions – Asian
worksheet;
§
a table showing the percentage distribution of the male and
female adult populations across the PRO, RSK and STD risk
groups, as well as relative fertility of females in each risk
group. The values are copied to the Assumptions – Asian worksheet, where the percentage in the NOT group is
derived;
§
a table showing the percentage distribution of the male and
female immigrant adult population across the PRO, RSK and STD
risk groups. The values are copied to the Assumptions – Asian
worksheet, where the percentage in the NOT group is derived;
§
a table showing infant AIDS mortality, median term to death
of HIV+ in three age groups, and the equation used to compute
imported infectivity of PROs for male and female. The values
are copied to the Assumptions – Asians worksheet;
§
a table showing the equation for determining the proportion
of babies
infected perinatally, proportion infected via breastfeeding,
and AIDS median time to death. The values are copied to the Assumptions – Asians
worksheet.
§
a table showing, for each year of age, condom usage for the
RSK group, age distribution of the starting population, the
mortality improvement index and ultimate mortality for male
and female, nonAIDS mortality to date for each year for male
and female, the fertility improvement factor and ultimate
rate, the start ratio, initial factor and reduction factor for
the impact of HIV duration on fertility, and net male and
female migration for each year from 1985 to 1996. The RSK
condom usage data is copied to the Assumptions – Asians worksheet.
The age distribution is copied to the Population
 Asians
worksheet. The mortality data is copied to the MortTable
– Asians
worksheet. The fertility data is copied to the NonHIV
Fertility – Asians
worksheet. The migration data is copied to the Male
Migration – Asians
and Female
Migration – Asians
worksheets.
§
a set of four tables relating to MTCT, PROPRO transmission
probability, the number of new partners of females, and condom
usage under the change scenario. These data are copied to the
relevant tables on the Assumptions – Asians worksheet.
The
remaining worksheets names take the form Prov
– Common
or Prov
– Population Group
and contain the same tables as the EC
– Common
and EC
– Asian
worksheets respectively.
In
theory, the user can change virtually any value or formula in
the workbook. In practice, there are a limited number of
values and formulae which can usefully and sensibly be
changed. The third column of the table below indicates which
worksheets contain cells with assumptions that can sensibly be
changed. The fourth column indicates which worksheets are
altered by the model during each projection.
Worksheet
name

Worksheet
function

Can
be changed

Changed
by model during projections

Assumptions

Sets
overall assumptions

YES

NO

Results

Displays
numeric results


YES

Population

Sets
assumptions

YES

YES

MortTable

Sets
assumptions

YES

YES

SexActivity

Sets
assumptions

YES

NO

Male
HIVTable

Sets
assumptions

YES

NO

Female
HIVTable

Sets
assumptions

YES

NO

HIVTable

Used
for calibration projection

NO

YES

NonHIV
Fertility

Sets
assumptions

YES

YES

HIV+
Fertility

Sets
assumptions

YES

NO

Male
Migration

Sets
assumptions

YES

NO

Female
Migration

Sets
assumptions

YES

NO

FemPRO

Calculates
steps of projections

NO

YES

FemSTD

Calculates
steps of projections

NO

YES

FemRSK

Calculates
steps of projections

NO

YES

FemNOT

Calculates
steps of projections

NO

YES

MalePRO

Calculates
steps of projections

NO

YES

MaleSTD

Calculates
steps of projections

NO

YES

MaleRSK

Calculates
steps of projections

NO

YES

MaleNOT

Calculates
steps of projections

NO

YES

MaleOLD

Calculates
steps of projections

NO

YES

FemOLD

Calculates
steps of projections

NO

YES

Young

Calculates
steps of projections

NO

YES

AIDS
Age Profile

Graphs
results

NO

YES

HIV
Prevalence

Graphs
results

NO

YES

ANC
Age Profile

Graphs
results

NO

YES

Calibration

Tests
results against reality

NO

YES

Cumulative
Deaths

Graphs
results

NO

YES

Deaths

Graphs
results

NO

YES

Pyramid

Graphs
results

NO

YES

Mortality

Graphs
results

NO

YES

Reported
deaths – Female

Tests
results against reality

NO

YES

Reported
deaths – Male

Tests
results against reality

NO

YES

Copyright




ANC
Antenatal clinic
ART
Antiretroviral therapy
ASSA
Actuarial Association of South Africa
CSW
Commercial sex worker
HIV
Human immunodeficiency virus
IMR
Infant mortality rate
MRC
Medical Research Council
MTCT
Mothertochildtransmission
SADHS
South African demographic and health survey
SALT
South African Life Tables
STD
Sexually transmitted disease
