Page 72 - IJPS-8-2

International Journal of
Population Studies Projecting sex ratio at birth in Pakistan

Appendix For a certain DHS/MICS data series, let {t , t ,…,t } be
n
n−1
1
years with recorded births from recent to past. The merge
Data processing starts from the most recent year t and goes back year by
n
year to t ,…,1. The process is performed by the following
n−1
Appendix A. Sampling errors in the DHS and MICS algorithm for each DHS and MICS data series:
data
Both Demographic and Health Survey (DHS) and Multiple Step Merging process of DHS and MICS data
#
Indicator Cluster Survey (MICS) provide individual- 1 for t ∈ {t , t −1,…, t } do
level data with the full birth history of each woman of n n 1
reproductive age interviewed during the survey fieldwork 2 if t=t then
n
period. We calculated the sampling error in the log- 3 Compute σ as explained above. Compute
transformed sex ratio at birth (SRB) obtained from the DHS 4 if CV<0.1 or t −t > 1 then
n
n−1
and MICS data series using the jackknife method (Efron & 5 stop and move to the previous time point
Gong, 1983; Efron & Tibshirani, 1994; ICF International, 6 else
2012). For a certain DHS or MICS data series, let U denote 7 Set t=t , merge births from tn and, t by summing them up
the total number of clusters (based on the cluster/primary 8 Repeat step 3 n−1
n−1
sampling unit numbers in the survey data (Verma & Le
1996)). The u-th partial prediction of SRB is determined 9 if CV<0.1 or t − t >1 or t −t = 5 then
n−1
n−1
n2
n
by the following equation: 10 stop and move to the previous time point
11 else
N I (x = male ;d ≠ ) u w
r −u = ∑ n =1 n n n n , foru ∈ {1,..., }U 12 Set t=t , merge births from t , t , t by summing them up
n−1
n−2
n
n−2
N
I
∑ n =1 n (x n = female ;d n ≠ ) u w n , 13 Repeat steps 8 – 12 for t ∈ {tn−2,…, t1}
Where, n indexes the live births in each state-survey- A. 1. Further explanations of the motivation and
year; N is the total number of live births; and x , d , and w assumptions of merging DHS/MICS data
n
n
n
are the sex, cluster number, and sampling weight for the The above algorithm is to merging observations from
n-th live birth, respectively. The sampling weight of each single calendar years into observations over short time
birth w is extractable from the survey data and reflects periods from DHS and MICS surveys where full birth
n
the survey sampling design (Verma & Le, 1996). We define histories are available. The merge refers to summing up
I (.) = 1 if the condition inside the brackets is true and I the number of sex-specific births across multiple years
n
n
(.) = 0 otherwise. The u-th pseudo-value estimate of the before computing the SRB for that period. The purpose
SRB on the log-scale is: of the merging process is meant to reduce uncertainties
associated with observations to a reasonable level. Without
log ( ) =r * U log ( ) ( −r ' − U ) 1 log ( ), r where
u −u merging the births from each calendar year, the sampling
errors in these population indicators become unacceptably
N I (x = male )w large due to the small sample sizes (Pedersen & Liu, 2012).
r ' = ∑ n =1 n n n . The underlying assumptions for the following expressions
N
I
∑ n =1 n (x n = female )w n are:
The sampling variance is: • Step 1 for t ∈ {t , t ,…,t } do: this means that we are
n−1
n
1
merging the 1-year observations from the most recent
U  log * r *  2 year t to the earliest year with data t . The reason we
1
n
∑ u =1   ( ) − logr u ( )  u  merge the observations backward in time rather than
σ = , where
2
U ( −1U ) merge forward is that: Usually in countries where
DHS and MICS surveys are conducted, more births
U
( ) .
log ( ) =r * 1 ∑ log r * were sampled in recent years than in older years.
u U u This is largely due to the improvement of surveying
u
=1
technology, more mothers were still alive to recall
In the DHS or MICS data, the annual log-transformed recent births than births born decades ago, and less
SRB observations are merged such that the coefficient of recall bias happened to births born in recent years
variation (CV) for log-transformed SRB is below 0.1 or than in earlier periods. Hence, the 1-year observations
the merged period reaches 5 years (Pedersen & Liu, 2012). in recent years are usually less likely to be merged
Volume 8 Issue 2 (2022) 66 https://doi.org/10.36922/ijps.v8i2.332