Estimating Pregnancy- Related Mortality from the Census

Transcription

1 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

2 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

3 Evaluating Coverage of Deaths of Women of Reproductive Age

4 Census Questions on Household Deaths Source: South Africa census questionnaire 2001

5 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

6 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)

7 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.

8 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+).

9 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.

10 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 * 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

11 General Growth Balance Method (5): Estimating r(x+) 2 1 *ln 1 1 / 1 2 / 2 *ln *ln 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

12 General Growth Balance Method: Good Example (Honduras 1988 to 2001).08 Residual Estimate of Death Rate x Observed Death Rate x+ Observed Fitted

13 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+))

14 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

15 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 ) }

16 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+))

17 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 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.

18 The Spreadsheet: Input Data (Partial) Age Initial Initial Final Final Average Group Population Date Population Date Annual Census 1 Census 2 Deaths , Aug , Aug-02 17, , Aug , Aug-02 2, , Aug , Aug-02 1, , Aug , Aug-02 2, , Aug-92 99, Aug-02 2, , Aug-92 67, Aug-02 1, , Aug-92 62, Aug-02 1, , Aug-92 92, Aug-02 4,920 Total 5,310, Aug-92 5,972, Aug-02 84,774

19 The Spreadsheet: Calculations (Partial) Age Pop1 Pop2 Deaths Average Person- Pop Growth Group a+ a+ a+ Birthdays Years Lived Rate Age a a+ a ,310,977 5,972,223 84,774 5,631, ,515,248 5,134,216 66, ,475 4,814, ,682,780 4,364,969 64, ,837 4,009, ,950,934 3,607,312 62, ,833 3,262, , ,046 10,407 25, , , ,626 8,326 18, , , ,775 6,748 15, , ,311 4,920 11,277 79,

20 The Spreadsheet: The Results Age Observed Residual Fitted Group Death Rate Death Rate Death Rate a+ a+ a

21 The Graph: Zimbabwe Entry Rate - Growth Rate Death Rate Slope (5+ to 65+) : 1.27 Intercept: ( 1% worse coverage in 1992 than 2002) Observed Fitted

22 Interpretation: Things Go Wrong General Growth Balance- Benin, male, Entry - Growth Rate x Observed values Fitted values Death Rate x+

23 Interpretation If the points line up nicely with 0.0 intercept (cf Zimbabwe ), 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!

24 Evaluating the Proportion of Deaths Pregnancy-Related

25 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

26 Proportions of Births and Pregnancy- Related Deaths by Age Group: Mali 2006 Proportion of Total in Age Group Broadly speaking similar patterns; no apparent flattening at tails Age Group Births Pregnancy-Related Deaths

27 Evaluating Numbers of Births

28 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)

29 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

30 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

31 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 for births last year by age of mother at census, or for true rates b(x) can be taken as for births last year by age of mother at census, or 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, and can be used as adjustment factors

32 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

33 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 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

34 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 , ,455 51, , ,575 56, , , , , , , , ,180 77, ,783 1,065,311 85, ,299 1,312,175 58, ,277 1,088,263 48, ,555 1,370,045 37, ,789 1,101,057 25, ,509 1,186,628 15, ,716 1,215,454 12, , ,556 4, ,154 1,088,320 3,002

35 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 (0.178) (1.046)

36 Interpretation P/F ratios for women aged 20 to 34 range are virtually identical, average 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

37 Putting the Pieces Together

38 Pregnancy-Related Mortality Ratio PRMRatio = PRDeaths*100000/B = (FDeaths(15-49)*Adj1)*PropPregRelated* /(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