Estimating Pregnancy- Related Mortality from the Census Presentation prepared for workshop on Improving National Capacity to Track Maternal Mortality towards the attainment of the MDG5 Nairobi, Kenya: December 2010 Kenneth Hill Stanton-Hill Research, LLC
Three Components of PRMRatio: Deaths of women of reproductive age (D) Proportion of those deaths that were pregnancy-related (PPR) Births (B) PRMRatio= (D*PPR*100,000)/B So evaluation focuses on D, PPR and B
Evaluating Coverage of Deaths of Women of Reproductive Age
Census Questions on Household Deaths Source: South Africa census questionnaire 2001
Evaluating Numbers of Deaths of Women of Reproductive Age Evaluating numbers of deaths of women of reproductive age involves evaluating female deaths at all ages post-childhood. It is MOST IMPORTANT that deaths of older women are recorded. Numbers of deaths are evaluated by comparison with the population age distribution. Source of population data Source of death data Methodology used Single census Single census Brass Growth Balance Method Two censuses 15 years apart or less First census Second census Both censuses General Growth Balance Method, death rates from first census applied to intercensal population Same, but death rates from second census Same, but averaged death rates used
Key Assumptions The methods assume that the errors of reporting (deaths and population) are distributed proportionately by age Put another way, methods assume that recorded population and deaths are representative by age of whole population and all deaths This is unlikely to be correct in the presence of substantial age misreporting More important still (especially for analysis of sub-national differentials) is the assumption that the population is closed to migration The Brass Growth Balance method assumes that the population is demographically stable The General Growth Balance method replaces the assumption of stability by using data from two censuses, but assumes that the age pattern of deaths in the intercensal interval is approximated by the observed pattern (whether recorded at one or both censuses)
General Growth Balance Method In any population, the growth rate is equal to the difference between the entry rate into the population and the exit rate from the population. In a closed population (with no net migration), entries are births and exits are deaths. Thus r = b d or (rearranging) b r = d where b is the crude birth rate, r is the population growth rate, and d is the crude death rate. The difference between b and r is a residual estimate of the crude death rate.
General Growth Balance Method (2) This equation, b r = d, is an identity not only for the whole population but also for open-ended age groups: b(x+) r(x+) = d(x+) where b(x+) is the entry rate (as a result of birthdays) to the age group x and over, r(x+) is the population growth rate x and over, and d(x+) is the exit rate death rate of the age group x and over. As for the total population, the difference between b(x+) and r(x+) is a residual estimate of the death rate x and over, d(x+).
General Growth Balance Method (3) Assume that the completeness of coverage of the deaths is c, constant at all ages. The observed agespecific mortality rates are therefore equal to the true rates multiplied by c, or (equivalently) that the true rates are equal to the observed rates divided by c: b(x+) r(x+) = {1/c}*d obs (x+) If we can estimate b(x+) and r(x+) from census data, there should exist a linear relation between the residual (b(x+) r(x+)) and the direct estimate of the death rate d obs (x+). The slope of the line should estimate {1/c}, the coverage of deaths relative to the population coverage of the census.
General Growth Balance Method (4): Estimating b(x) Assume that the two census counts are k1 and k2 complete respectively, such that N1(x)=(1/k1)*N1 o (x) and N2(x)=(1/k2)*N2 o (x) x y o o o o x o y y x N N N N x b x b 2 * 1 2 * 1 * 5 1 5 5 5 5 5 Substituting observed values for true values (given that k1 and k2 are constant by age), the k1 and k2 terms cancel out in numerator and denominator, and the entry term b(x) can be approximated as
General Growth Balance Method (5): Estimating r(x+) 2 1 *ln 1 1 / 1 2 / 2 *ln 1 1 2 *ln 1 5 5 5 5 k k t x r k N k N t N N t x r o x y o x y o x y y x y y y y So assuming that census coverage does not vary by age, the true growth rate is equal to the observed growth rate plus a constant determined by the ratio of coverages and the intercensal interval t
General Growth Balance Method: Good Example (Honduras 1988 to 2001).08 Residual Estimate of Death Rate x+.07.06.05.04.03.02.01 0 5+ 75+ 0.01.02.03.04.05 Observed Death Rate x+ Observed Fitted
Calculations (a) Entry Rate The Entry Rate b(x+) is the number of x th birthdays in the intercensal period B(x) divided by the person-years lived x+ in the intercensal period PYL(x+). Number of x th birthdays can be estimated as B(x) = (t/5)*sqrt( 5 N1 o x-5 * 5 N2 o x) where t is the intercensal interval in years, N1 o is the population at the first census, N2 o the population at the second census Number of person-years can be estimated as PYL(x+) = t*sqrt(n1 o (x+)*n2 o (x+))
Calculations (2) (b)growth Rate The Growth Rate x+ is calculated from the ratio of the population x+ between the two censuses. Specifically, r o (x+) = (1/t) ln{n2 o (x+)/n1 o (x+)} where ln{. } is the natural logarithm
Calculations (3) (c) Observed Death Rate The Death Rate d obs (x+) is the number of deaths x and over in the intercensal period divided by the person-years lived x+ in the intercensal period. The Census will typically provide deaths by age in the 12 months before the second census, not the number for the intercensal period. The number of intercensal observed deaths x+ can be estimated from age-specific mortality rates and estimated personyears lived: 5M x = 5 D2 x obs / 5 N2 x The number of intercensal deaths can then be estimated as 5 D x obs = 5 M x * 5 PYL x = 5 M x *{SQRT( 5 N1 x * 5 N2 x ) }
Calculations (4) (c) Observed Death Rate x+ (continued) Then the Death Rate d obs (x+) is calculated as the estimated number of deaths x and over in the intercensal period divided by the person-years lived x+ in the intercensal period: d obs (x+) = {Σ x+ 5 D y obs }/ PYL(x+) Number of person-years can be estimated as PYL(x+) = t*sqrt(n1(x+)*n2(x+))
Calculations (5) (d)computation of Adjustment Factor for Deaths: Remember that b(x+) r(x+) = {1/c}*d obs (x+) Across values of x, there should be a straight line relationship of slope {1/c}. This slope is the adjustment factor needed for deaths relative to population..08 Residual Estimate of Death Rate x+.07.06.05.04.03.02.01 0 0.01.02.03.04.05 Observed Death Rate x+ Observed Fitted The slope can be estimated in many ways, using a range of possible ages. We use a form of regression.
The Spreadsheet: Input Data (Partial) Age Initial Initial Final Final Average Group Population Date Population Date Annual Census 1 Census 2 Deaths 0-4 795,728 18-Aug-92 838,007 18-Aug-02 17,860 5-9 832,469 18-Aug-92 769,247 18-Aug-02 2,469 10-14 731,848 18-Aug-92 757,657 18-Aug-02 1,625 15-19 632,510 18-Aug-92 766,890 18-Aug-02 2,148 60-64 84,213 18-Aug-92 99,420 18-Aug-02 2,081 65-69 50,902 18-Aug-92 67,851 18-Aug-02 1,578 70-74 62,479 18-Aug-92 62,464 18-Aug-02 1,828 75+ 68,403 18-Aug-92 92,311 18-Aug-02 4,920 Total 5,310,977 18-Aug-92 5,972,223 18-Aug-02 84,774
The Spreadsheet: Calculations (Partial) Age Pop1 Pop2 Deaths Average Person- Pop Growth Group a+ a+ a+ Birthdays Years Lived Rate Age a a+ a+ 0-4 5,310,977 5,972,223 84,774 5,631,904 0.0117 5-9 4,515,248 5,134,216 66,915 156,475 4,814,796 0.0128 10-14 3,682,780 4,364,969 64,446 158,837 4,009,292 0.0170 15-19 2,950,934 3,607,312 62,822 149,833 3,262,658 0.0201 60-64 265,997 322,046 10,407 25,749 292,683 0.0191 65-69 181,784 222,626 8,326 18,572 201,171 0.0203 70-74 130,882 154,775 6,748 15,118 142,328 0.0168 75+ 68403 92,311 4,920 11,277 79,463 0.0300
The Spreadsheet: The Results Age Observed Residual Fitted Group Death Rate Death Rate Death Rate a+ a+ a+ 0-4 0.0151 0.0182 5-9 0.0139 0.0197 0.0167 10-14 0.0161 0.0226 0.0195 15-19 0.0193 0.0258 0.0235 60-64 0.0356 0.0443 0.0442 65-69 0.0414 0.0549 0.0516 70-74 0.0474 0.0625 0.0593 75+ 0.0619 0.0777
The Graph: Zimbabwe 1992-2002.06 Entry Rate - Growth Rate.05.04.03.02.01 0 0.01.02.03.04.05.06 Death Rate Slope (5+ to 65+) : 1.27 Intercept: -0.0010 ( 1% worse coverage in 1992 than 2002) Observed Fitted
Interpretation: Things Go Wrong General Growth Balance- Benin, male, 1992-2002 0.0600 0.0500 Entry - Growth Rate x+ 0.0400 0.0300 0.0200 0.0100 Observed values Fitted values 0.0000 0.0000 0.0050 0.0100 0.0150 0.0200 0.0250-0.0100 Death Rate x+
Interpretation If the points line up nicely with 0.0 intercept (cf Zimbabwe 1992-02), choice of points to fit makes little difference If the points don t line up nicely, choices have to be made: For population known to be exposed to net migration, fit line to ages 35+ to 65+ Otherwise, accept wide uncertainty in adjustment For Zimbabwe, slope is 1.27, meaning recent deaths need to be adjusted by 1.27 ( 80% of deaths reported) Benin would be more of a challenge!
Evaluating the Proportion of Deaths Pregnancy-Related
Proportion of Deaths Pregnancy-Related No formal evaluation methods exist Since births are the risky events, the proportion of PRDs in each age group can be compared to the proportion of births in the age groups Comparisons can be made with other data sources for the same population (e.g. with sisterhood data) Comparisons can be made with WHO/Unicef/UNFPA/World Bank model for countries lacking comparable data
Proportions of Births and Pregnancy- Related Deaths by Age Group: Mali 2006 Proportion of Total in Age Group.3.25.2.15.1.05 Broadly speaking similar patterns; no apparent flattening at tails 0 15-19 20-24 25-29 30-34 Age Group 35-39 40-44 45-49 Births Pregnancy-Related Deaths
Evaluating Numbers of Births
P/F Ratios Most developing country censuses collect two types of data on fertility: Lifetime fertility (children ever born) Recent fertility (births in last 12 months or date of most recent live birth) Our interest is in intercensal births Data will often be available from BOTH recent censuses Or from the recent census and earlier surveys, e.g. DHS Evaluation is of recent fertility against lifetime fertility (P/F Ratios)
Evaluating Numbers of Births The standard method for evaluating numbers of births is the comparison of cumulated recent fertility rates with recorded average numbers of children ever born by age (P/F ratios). Source of lifetime fertility data Single census Two censuses (or recent census and earlier survey) 15 years apart or less Source of recent fertility data Single census (or or survey) First census Second census Both censuses Methodology used Standard P/F Ratio method P/F Ratio method for synthetic cohorts, using age-specific fertility rates from first census or survey (not common) Same, but age-specific fertility rates from second census Same, but averaged age-specific fertility rates used
P/F Ratios: Principle Basic idea is that cumulated age-specific fertility rates to age x should equal lifetime fertility at x Information on recent fertility may suffer from different biases than that on lifetime fertility: Recent fertility: error of completeness but not different by age Lifetime fertility: errors of omission by older women but good reporting by women under age 30 Unbiased age distribution of recent fertility can be scaled to level of lifetime fertility of young women
P/F Ratios: Application Calculate age-specific fertility rates from recent births: 5ASFR x = 5 B2 x / 5 N2 x If ASFRs are available from both first and second census (or a survey and second census) average the rates Cumulate ASFR s to be parity-equivalents: 5 F x = Σx-5 5 ASFR a + a(x)* 5 ASFR x + b(x)* 5 ASFR x+5 a(x) can be taken as 3.392 for births last year by age of mother at census, or 2.918 for true rates b(x) can be taken as -0.392 for births last year by age of mother at census, or -0.418 for true rates Calculate average parities for each age group: 5P x = 5 CEB2 x / 5 N2 x Calculate ratios of P/F: values for 20-24, 25-29 and 30-34 can be used as adjustment factors
P/F Ratios: Complications Cumulated recent fertility and lifetime fertility will not be equivalent when fertility is changing If data on lifetime fertility are available from both censuses (or from the second census and an earlier survey) we can calculate period-specific lifetime fertility: Calculate intercensal parity changes for each cohort Cumulate parity changes from young to old
P/F Ratios: Intercensal Parity Changes a) For intercensal periods of about 5 years: t, t 5 t 5 5 Px, x 5 5 Px 5 5 5 PSC x t, t 5 x 5 P y, y 5 y 15 P t x and where 5 PSC x is the parity for the synthetic cohort at age x,x+4 b) For intercensal periods of about 10 years: t, t 10 t 10 5 Px, x 4 5 Px 10 5 P t x 5 PSC x t, t 10 x 5 P y, y 10 y 15
The Spreadsheet: Input Data (2 Censuses 10 Years apart): Zimbabwe 1992 and 2002 First Census Second Census Age Number Children Births in Number Children Births in Group of Women Ever Born Preceding of Women Ever Born Preceding x,x+4 Alive 12 Months Alive 12 Months 15-19 632,510 119,455 51,532 766,882 136,575 56,223 20-24 523,061 585,382 113,965 658,857 689,022 120,600 25-29 376,495 955,180 77,393 513,783 1,065,311 85,742 30-34 326,299 1,312,175 58,693 360,277 1,088,263 48,182 35-39 259,555 1,370,045 37,559 268,789 1,101,057 25,718 40-44 189,509 1,186,628 15,224 239,716 1,215,454 12,168 45-49 143,441 966,556 4,520 191,154 1,088,320 3,002
The Spreadsheet: Results (2 Censuses 10 Years apart) Age Group Average Parity Age-Specific Fertility First Second Change Syn. Cohort Average Cumulated Parity Equiv. P/F Ratio 15-19 0.189 0.178 (0.178) 0.178 0.077 0.000 0.184 0.968 20-24 1.119 1.046 (1.046) 1.046 0.201 0.220 0.994 1.052 25-29 2.537 2.073 1.885 2.063 0.186 0.882 1.959 1.053 30-34 4.021 3.021 1.901 2.947 0.157 1.562 2.805 1.051 35-39 5.278 4.096 1.559 3.622 0.120 2.060 3.486 1.039 40-44 6.262 5.070 1.049 3.996 0.066 2.401 3.918 1.020 45-49 6.738 5.693 0.415 4.037 0.024 2.577 4.120 0.980
Interpretation P/F ratios for women aged 20 to 34 range are virtually identical, average 1.052 At these age groups, synthetic cohort lifetime fertility is higher than cumulated recent fertility by about 5% Recent age-specific fertility rates should be adjusted upwards by 1.05 Coverage of births approximately 95% Annual intercensal births can be estimated by applying the adjusted rates to the average intercensal population
Putting the Pieces Together
Pregnancy-Related Mortality Ratio PRMRatio = PRDeaths*100000/B = (FDeaths(15-49)*Adj1)*PropPregRelated*100000 /(Births*Adj2) So, need to decide upon Adj1 (Growth Balance) and Adj2 (P/F Ratios); we do not estimate an adjustment factor for the proportion of deaths pregnancy-related. For Zimbabwe: Adj1 is estimated as 1.27 Adj2 is estimated as 1.05