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“The only thing necessary for these diseases to the triumph is for good people and governments to do nothing.”

Griffith Feeney - 1999-06-02 - <>
0.1 Prepared for the Meeting of the Reference Group on HIV/AIDS
Estimates, Modelling and Projections, Geneva, 10-11, June 1999.
This report is based on work carried out at the United Nations
Population Division from September 1998 to March 1999.
0.2 These notes are intended to illustrate in a specific
application some of the general points made in my notes
"Mortality and Aids Deaths in Developing Countries" (1999-05-24).
This is an illustrative analysis of adult mortality in Zimbabwe
from roughly 1970 through 1997. It is not and is not intended to
be definitive. Many particulars can and should be challenged. It
does cover available data and methods reasonable thoroughly.
0.3 This text file should be accompanied by the Excel 97 file
zimbabwe.xls, which contains plots referred to towards the end of
these notes.
0.4 A set of spreadsheet files detailing the calculations is
available on request. Be forewarned that (i) there is a great
deal of technical detail here and that (ii) they will probably be
comprehensible only if you already have a basic understanding of
the various methods applied. The files are contained in a zip
archive of about 101 Kb (iaz.txt gives a list of files).
Uncompressed they occupy about 3.7 Mb.
1.1 Population distributed by age and sex is available from the
population censuses of 1982 and 1992, reference date 18 August in
both cases; and from surveys taken in 1987 and 1997 (probably
with the same reference date, but this has not been definitively
ascertained). Open-ended age intervals vary. Age not stated
numbers are present in most cases. Age not stated numbers have
been prorated and open ended age intervals adjusted to 75+ for
all available distributions.
1.2 The 1992 census and the 1997 survey included questions on
deaths in households during the 12 months prior to enumeration.
From these questions we have tabulations of deaths during the
year prior to census, and during the year prior to the survey,
distributed by age and sex. The 1982 census schedule did not
include such a question. It was apparently included in the 1987
survey, but we have been unable to locate the data. Proration of
age not stated cases and adjustment of open ended intervals as in
1.3 Civil registration provides deaths by age and sex for
calendar years 1982, 1986, 1990-1992 and 1995. It is not known
why data for other years are not available. Data for 1990-92 and
1995, unpublished so far as we know, were obtained from the
Zimbabwe Central Statistical Office at the request from the UN
Population Division. Proration of age not stated cases and
adjustment of open ended intervals as in 1.1.
1.4 Proportions of persons with mother alive by age and
proportions of persons with father alive by age are available
from both the 1982 and the 1992 censuses. Sibling survival data
is available from the 1994 Demographic and Health (DHS) survey.
2.1 Census survival applied to the 1982 and 1992 censuses gives
expectations of life at age 5 years of 64.6 for females and 60.8
years for males. Census survival ratios indicate severe age
misreporting. The male results are more consistent that the
female results.
3.1 The number of deaths that would have been registered by the
civil registration system if data for all pertinent years were
available is estimated from data for available years by
estimating deaths in missing years as the average of registered
deaths in surrounding available years. Intercensal registered
deaths calculated from these numbers with proration of deaths in
census years. Estimated "registered" intercensal deaths are
108,569 for females and 178,828 for males.
3.2 Registration of deaths is incomplete, and differentially so
for males and females. One might guess from the numbers in the
preceding paragraph that male deaths are more completely
registered than female deaths. The analyses below support this
3.3 It is likely that deaths in urban areas are more completely
registered than deaths in rural areas, but we have here no data
to bear this out. We have not been able to locate household
deaths data for urban and rural areas, which might shed light on
this point.
The simplest growth balance calculation estimates completeness of
registration for female deaths during the intercensal period to
be 35.9 percent. The implied number of female intercensal deaths
is 108,569/0.359 = 302,421. For males the same figures are 58.3
percent and 306,736 deaths. The consistency of the simple growth
balance results is mediocre for both males and females. On
internal evidence, ignoring the possibility of differential
completeness of enumeration in the two censuses, estimated
registration completeness could easily err by plus or minus 10
5.1 Generalized growth balance estimates differential
completeness of census enumeration as well as completeness of
reported intercensal deaths. Both the original Brass method and
the Hill method indicate that the 1992 census was a less complete
enumeration than the 1982 census by about two and one half
percent. The latter method indicates that enumeration of females
in the 1992 census was 2.6 percent less complete than in the 1982
census. For males the same figure is 2.3 percent.
5.2 Accordingly, the estimates of completeness of death
registration are higher, 44.3 percent for females and 63.2 for
5.3 Some of this estimated relative under enumeration in the 1992
census may be due to migration, which is assumed nil but which
may in fact be significant. The proportion of Europeans in the
population declined by about one percent between the 1982 and
1992 censuses. Data on migration is, as usual, inadequate to
5.4 It would be useful to recalculate these estimates for
subpopulations for which the no migration assumption is more
reasonable. This has not been possible as yet for want of
sufficiently detailed data. It might be impossible without
special tabulations of both the 1982 and 1992 censuses. The
practicality of producing such special tabulations is not known.
6.1 A different method of estimating the same quantities from the
same given data indicates intercensal death registration
completeness of 27.6 percent for females and 50.0 percent for
6.2 Results for both females and males are more consistent than
for either growth balance method, but this method, like simple
growth balance, ignores differential completeness of census
6.3 Re-applying the extinct generations method after upward
adjustment of the 1992 census for the relative under enumeration
indicated by generalized growth balance rises estimated
completeness of female death registration only to 30.2 percent
(as compared with 44.3 percent estimated by generalized growth
balance), and estimated completeness of male death registration
to 54.5 percent (as compared with 63.2 percent from generalized
growth balance).
6.4 It is unclear why the extinct generations estimates of
completeness of registration are so much lower that the growth
balance estimates.
7.1 This method estimates 35_q_30, the conditional probability of
survival to age 65 given survival to age 30. There are several
input parameters whose values can only be roughly estimated.
7.2 The median estimate for females from the 1992 census is
35_q_30 = 0.2064, dated 1981.7. The median estimate from the 1982
census is 35_q_30 = 0.2194, dated 1971.7. The between census
comparison thus indicates slow decline in mortality risks during
(roughly) the 1970s and 1980s. The two census variant gives
35_q_30 = 0.1920 for the intercensal period.
7.3 The trend estimates from the 1982 and 1992 censuses indicate
generally declining mortality risks for females through the mid-
to late-1980s, but there appears to be a fair amount of noise in
the trend estimates. A straight line fit to the estimates to
determine level and trend is probably the most information that
ought to be done with these estimates.
7.4 The trend estimates are based on a model life table pattern
that may be distorted by AIDS deaths. This is probably not a
major factor here but should be investigated further. The same
applies to the estimates from paternal and sibling survival
presented below.
8.1 This method is analogous to that based on maternal survival.
Median estimates are 35_q_30 = 0.3309 dated 1982.6 from the 1992
census and 35_q_30 = 0.3847 dated 1972.5 from the 1982 census.
The two census variant gives 35_q_30 = 0.2586 (this is not as out
of line as it looks when the trends are examined).
8.2 As for females, the trend estimates from the 1982 and 1992
censuses indicate generally declining mortality risks for females
through the mid- to late-1980s, as does the between census
comparison. Again, there appears to be a fair amount of noise in
the trend estimates, and a straight line fit to the estimates to
determine level and trend is probably the most information that
ought to be pulled from these estimates.
9.1 The sibling survival methods estimates a different statistic,
35_q_15, conditional probability of survival to age 50 given
survival to age 15. The median of the 1994 DHS survey estimates
gives 35_q_15 = 0.1687 dated 1986.0 for males.
9.2 The time trend shows steadily rising mortality risks for
males during the period 1982-1992 (but for the earliest point,
which is an outlier on the low side).
9.3 Comparison of 35_q_15 and 35_q30 values would normally be
effected using model life tables. This is complicated by the
distortion of the age pattern of mortality resulting from AIDS
deaths. The distortion may be minimal for these estimates, given
the timing of the epidemic, but no comparisons are made here.
10.1 The 1994 DHS survey median estimate is 35_q_15 = 0.1402
dated 1986.1 for females. The time trends shows (reasonably)
steadily rising mortality risks for females during 1982-1992. The
level is lower than for males.
11.1 Unadjusted death rates may be calculated both from
registered deaths and from the household deaths from the 1992
census and 1997 survey by dividing numbers of deaths in each
age-sex group by corresponding numbers at risk interpolated from
the available census and survey age distributions. Though the
level of the registered death rates is substantially low (the
household deaths data appear to be about right), and
differentially so for males and females, much can be learned from
the age and sex patterns.
11.2 The typical age pattern of human mortality is roughly
U-shaped, with high rates in infancy and childhood declining
sharply to a low in young adult ages, followed by first by a slow
rise and then by a more rapid rise as we reach old age. The age
pattern of death rates based on 1986 registered deaths follows
this pattern. The age pattern for 1992 shows somewhat higher than
expected rates not just in young but also in older adult ages.
The age pattern in 1995 shows much higher than expected rates in
these same ages. Between 1986 and 1995 death rates in prime adult
age groups increased by factors of between three and six, i.e.,
very rapidly.
11.3 For comparisons with estimates derived from relation
survival death rates must be adjusted for under registration. The
unadjusted death rates suggest that completeness of death
reporting was increasing during the period in question. Death
rates for the 10-14 age group, which one would not expect to be
much influenced by AIDS deaths during this period, rise
significantly. A rough estimate of changing completeness of
registration may be made by supposing that death rates at ages
10-14 were constant rather than increasing.
11.4 The resulting adjusted age-specific death rates show the
same age patterns, as they must, the adjustment being a constant
factor applied to all age groups for a given year. The level is
at least roughly corrected, however, so that life tables and
conditional probabilities of death for the various years may be
compared with the corresponding estimates from survival of
mother, fathers and siblings.
11.5 The adjustment used below is that given by generalized
growth balance, which gives the lowest mortality rates of the
three methods noted above. Brief reference is made below to how
much different things look if we use the simple growth balance
estimates of registration completeness (higher death rates) or
the extinct generations estimates (still higher death rates).
12.1 Female and male life tables have been computed from adjusted
death rates for 1982, 1986, 1990-1992 and 1995 from death
registration data and for the year prior to the 1992 census and
the year prior to the 1997 survey from those data. Both males and
females show steadily deteriorating survival over these years.
See Figures 1 and 2 in the accompanying spreadsheet file.
12.2 From these life tables it is possible to compute any
standard mortality statistic, in particular the conditional
probability of death 35_q_30 estimated from survival of mothers
and fathers and the 35_q_15 estimated from survival of siblings.
We may then compared the trends from the adjusted civil
registration data with those derived from the data on survival of
mothers, fathers and siblings. This is done in the following
13.1 The life tables described in the immediately preceding
section do a reasonably good job of exhausting the information
contained in the 1982 and 1992 censuses and the death
registration data, though of course alternative estimates both of
the level of reporting and of its change over time may be made.
13.2 We first compare estimates of 35_q_30 for females from (i)
the 1982 census data on survival of mothers, (ii) the 1992 census
data on survival of mothers, (iii) the two census estimate based
on survival of mothers, (iv) the values calculated from the
female life tables calculated from death rates adjusted for
incomplete registration, and (v) the values calculated from life
tables based on the 1992 census household deaths data, without
adjustment, and on the 1997 survey household deaths data, also
without adjustment.
13.3 Given the different times to which these various estimates
refer, plotting is the simplest means of effecting the
comparison. The plot, Figure 3, is shown in the accompanying
spreadsheet file. The estimates derived from survival of mothers
show substantial irregularity but an overall slight downward
trend through the 1970s and 1980s. The average level is a
conditional probability of death by age 65 given survival to age
30 of about 0.2, with a decline of roughly 0.04 per decade.
13.4 There is a substantial discrepancy between the maternal
survival estimates and the life table values derived from
adjusted death registration, The overall level of the life table
values is substantially higher than the that of the maternal
survival estimates, and the trend of the life table estimates is
up, whereas that of the maternal survival estimates is down.
13.5 One should, on the one hand, be skeptical of the extremely
rapid increase of the death registration life table values, if
not of the overall high level. On the other hand, the increase is
confirmed by the life tables from the (unadjusted) household
deaths data from the 1992 census and 1997 survey. Since the
errors in these two sources are quite different, the coincidence
is evidence that the increase is real.
13.6 Quite possibly the dating procedure for the maternal
survival estimates, which assumes a smooth and not too rapid
change in mortality levels, performs poorly in the face of a
sudden rise in mortality risks. On the other hand, the pattern of
the 1992 census estimates is generally similar to that of the
1982 census estimates, which wouldn't have been affected. Some
part of the discrepancy may be due to imperfect adjustment for
changing death registration completeness, though the rise here is
so rapid that plausible adjustments seem unlikely to explain very
13.7 The level difference between the estimates from registered
deaths and from household deaths could be explained by over
adjustment of the former. Using generalized rather than simple
growth balance estimates of completeness of death registration
would lower the values from the registered deaths life tables.
Using the extinct generations estimates, on the other hand, would
increase them.
13.8 The same comparison may be carried out for males. Levels are
higher for males, but the patterns are very similar. See Figure 4
in the accompanying spreadsheet file.
13.9 In the same way, we compare the conditional probabilities of
death 35_q_15 calculated from the registered deaths (adjusted)
and household deaths (unadjusted) life tables with the estimates
from survival of brothers and sisters. The comparison is again
effected graphically and shown in the accompanying spreadsheet
13.11 The comparison for females, figure 5, is remarkably good.
The 35_q_15 estimates from the life tables derived from
registered deaths adjusted for incomplete registration appear to
be somewhat low in relation to the other estimates, possibly
indicating under adjustment for death registration completeness.
From the practical point of view, however, this discrepancy may
not be very important, for all estimates agree in indicating an
extremely sharp and accelerating rise in adult mortality risks.
13.12 The agreement for males, figure 6. is nearly as good, the
pattern similar.
14.1 Available data, suitably handled, gives strong evidence of
rapidly rising adult mortality risks in Zimbabwe beginning
sometime in the 1980s and accelerating through 1997, the latest
year for which data is available. 
14.2 The exact level of mortality appears to be more difficult to
establish than its trend. The comparison with sibling survival
estimates suggests that the adjustment made for incomplete
reporting of deaths in the civil registration system may be
approximately correct. Substantially different adjustments might
be made and defended, however.
14.3 The critical role of the death registration data in the
analysis should be noted. It seems that far too little use has
been made of this data, though to be sure in is unavailable in
many countries. Data for missing years should be vigorously
pursued. While there are seriously problems of incompleteness,
and attendant problems on non-representativeness, these are
probably no worse than those characterizing, e.g., ANC data on
HIV prevalence.
14.4 The performance of the sibling survival estimates suggests
strongly urging the inclusion of the appropriate questions in
suitable surveys, and perhaps in censuses as well, with follow up
production of tabulations from the results (the questions have
been included in many DHS surveys, but seem not to have been
14.5 In conclusion it should be reiterated that this is an
illustrative analysis that requires further development. It may
also be mentioned, however, that differences between countries
are likely to be so great that it is unwise to based general
conclusions on the study of any single country, no matter how
thoroughly studied. A good rule of thumb may be that general
conclusions should be held back until a minimum of three
reasonably diverse countries are examined.
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