Analyzing Contraceptive Use Dynamics as a Simplified Markov Process Using Demographic and Health Survey Data

Background

This analysis was performed as part of preparing the "Strategic Plan for the Bangladesh National Family Planning Program 1995-2005", Abul Barkhat et al, Technical Review Committee, Ministry of Health and Family Welfare, Government of Bangladesh. The data for the analysis was derived from the "Bangladesh Demographic and Health Survey 1993-1994", S. N. Mitra et al, Macro International Inc. (BDHS94). Perhaps unique in this regard, all of the parameters used in the model were obtained from indigenous data. No reliance was placed on international sources.

Reproductive history

Although BDHS94 is a cross sectional survey, it contains six years of reproductive history and contraceptive use. This calendar forms the basis for estimating transition probabilities. Future usage is based on women's declared intentions to use contraceptive methods in the future. Unlike most population and contraceptive usage projections, this analysis does not depend on a priori prevalence or fertility targets.

Statistical processing

All of the analysis was performed using "SPSS for Windows", SPSS Inc.,Chicago, Illinois. Cross tabulations and standard descriptive measures form the bulk of the statistical procedures employed. Syntax for all of the calculations is available and repeatable.

Population and contraceptive use projection model

The model used to project population and contraceptive use was FamPlan, developed by Dr. Dennis Chao, Center for International Development, Research Triangle Institute, Research Triangle Park, NC. Based on Bongaardts' proximate determinants fertility model, this variant uses acceptance and continuation as input instead of prevalence or fertility. Since this variant depends on rates and changes in rates, it may be characterized as a first (and second order) model, whereas the more traditional model depends on levels which may be characterized as a zeroth order model. Another way of looking at the difference is that Target models are based on fixed prevalence or fertility levels and FamPlan is based on flows from the non user pool to the user pool (acceptance) and flows from the user pool to the non user pool (discontinuation). Since six years of history is available in BDHS94, future work could explore rates of change in acceptance and continuation and form a true second order model. Only the derivation of input parameters is discussed here.

Cairo - United Nations International Conference on Population and Development

By focusing on past dynamics of contraceptive use and future market demand for contraceptive use, this analysis is an important step in meeting the aspirations of the Cairo conference by emphasizing women's needs (market) over population control (state). Fortunately in Bangladesh, there is a strong convergence between state and market goals in family planning. Of course, in a free market, population control is best served by meeting the demand for family planning services.

Calendar

The calendar consists of 72 monthly observations. The survey was performed over a four month period. All of the calendars end with the culmination of the survey. Consequently, there are missing values after the month of interview up to the end of the survey, and we had 69 to 72 monthly observations of reproductive state.

States

The BDHS94 calendar records 13 reproductive states: not using any contraceptive method (0), using one of nine contraceptive methods (pill (1), IUD (2), injectables (3), condoms (4), female sterilization (5), male sterilization (6), rhythm (7), withdrawal (8) and other (W)), and three pregnancy related states (birth (B) or termination (T)in the month and pregnant (P)).

Ending state

The ending state was defined as the last non-missing observation of reproductive state. Some argument can be made for backing up the observation a month or two to allow women more time to know if they are pregnant.

Beginning state

The beginning state was defined as the observation 12 months prior to the ending state.

Transition Matrix

A cross tabulation of beginning state (rows) by ending state (columns) produces a square matrix.

SS\ES	0	1	2	3	4	5	6	7	8	B	P	T	W	Total
0	3721	353	35	134	63	7		88	52	56	562	8	18	5097
1	174	1042	14	69	31	3	1	28	19	8	115	1	3	1508
2	19	16	121	3	2	1	2		7		171
3	35	32	5	159	1	1		7	2	2	10	2	256
4	26	17	4	0	129	5	4	4	14		203
5		753		753
6	1	96	97
7	39	16	5	1	6	1	278	4	3	32	1	386
8	11	10	1	1	0	1		115	15	154
B	85	18	2	7	3	2	2		3		1	123
P	638	71	12	30	39	9		28	20	26	11	884
T	3	2		3	1	1	1	1	5		17
W	10	2	1	1		2	1		7		62	86
Total	4762	1580	202	411	279	779	104	447	230	74	796	9	98	9735

Transition Probabilities

Dividing ending states by the total in each starting state we get the transition probabilities.

SS\ES	0	1	2	3	4	5	6	7	8	B	P	T	W	Prev.
0	73.0%	6.9%	0.7%	2.6%	1.2%	0.1%	0.0%	1.7%	1.0%	1.1%	11.0%	0.2%	0.4%	52.4%
1	11.5%	69.1%	0.9%	4.6%	2.1%	0.2%	0.1%	1.9%	1.3%	0.5%	7.6%	0.1%	0.2%	15.5%
2	11.1%	9.4%	70.8%	1.8%	1.2%	0.0%	0.0%	0.6%	1.2%	0.0%	4.1%	0.0%	0.0%	1.8%
3	13.7%	12.5%	2.0%	62.1%	0.4%	0.4%	0.0%	2.7%	0.8%	0.8%	3.9%	0.0%	0.8%	2.6%
4	12.8%	8.4%	2.0%	0.0%	63.5%	0.0%	0.0%	2.5%	2.0%	2.0%	6.9%	0.0%	0.0%	2.1%
5	0.0%	0.0%	0.0%	0.0%	0.0%	100.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	7.7%
6	1.0%	0.0%	0.0%	0.0%	0.0%	0.0%	99.0%	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%	1.0%
7	10.1%	4.1%	1.3%	0.3%	1.6%	0.0%	0.3%	72.0%	1.0%	0.8%	8.3%	0.0%	0.3%	4.0%
8	7.1%	6.5%	0.6%	0.6%	0.0%	0.6%	0.0%	0.0%	74.7%	0.0%	9.7%	0.0%	0.0%	1.6%
B	69.1%	14.6%	1.6%	5.7%	2.4%	0.0%	0.0%	1.6%	1.6%	0.0%	2.4%	0.0%	0.8%	1.3%
P	72.2%	8.0%	1.4%	3.4%	4.4%	1.0%	0.0%	3.2%	2.3%	0.0%	2.9%	0.0%	1.2%	9.1%
T	17.6%	11.8%	0.0%	17.6%	5.9%	0.0%	0.0%	5.9%	5.9%	5.9%	29.4%	0.0%	0.0%	0.2%
W	11.6%	2.3%	1.2%	1.2%	0.0%	0.0%	0.0%	2.3%	1.2%	0.0%	8.1%	0.0%	72.1%	0.9%
Prev.	48.9%	16.2%	2.1%	4.2%	2.9%	8.0%	1.1%	4.6%	2.4%	0.8%	8.2%	0.1%	1.0%	100.0%

Prevalence

By dividing the sum of each ending state by the total of all ending states we get the prevalence at the end of the year. Similarly by dividing the sum of the beginning states by the coresponding total we get the prevalence at the beginning of the year. By comparing beginning and ending prevalences we can get a quick glimpse of the contraceptive usage picture. In this case all contraceptive methods are increasing, and births, pregnancies and terminations are decreasing.

Retention - Continuation

The first method continuation rate is found in the diagonal. For example, 69.1% of all women using pills at the beginning of the year were using pills at the end of the year. The all method continuation rate is the complement of the losses to not using, pregnancy, birth and termination. Thus the all method continuation rate of pills (0) is 100-(11.5+0.5+7.6+0.1) or 80.3%. The all method continuation rate more closely matches the needs of FamPlan.

Gain - Acceptance

The acceptance rate by method of non users is found in row 0. FamPlan requires the acceptance rate of non users, and women who were pregnant or had a birth or termination in the starting month. Grouping those women who had starting states of not using, pregnant, birth or termination by contraceptive method produces the following table.

Acceptors	1	2	3	4	5	6	7	8	W	Total Acc.	Total
0	353	35	134	63	7	88	52	18	750	5097
B	18	2	7	3		2	2	1	35	123
P	71	12	30	39	9	28	20	11	220	884
T	2	3	1		1	1		8	17
Total	444	49	174	106	16	0	119	75	30	1013	6121
Acc Rate.	7.3%	0.8%	2.8%	1.7%	0.3%	0.0%	1.9%	1.2%	0.5%	16.5%
Method Mix	43.8%	4.8%	17.2%	10.5%	1.6%	0.0%	11.7%	7.4%	3.0%	100.0%

Acceptance rate

Dividing acceptors by ending state by total women by starting state we get the acceptance rate.

Method mix of acceptors

Dividing acceptors by state by total acceptors we get the method mix of acceptors.

Effectiveness

We can obtain a rather raw measure of effectiveness by comparing the probabilities of becoming pregnant for each starting state.

State	Pregnant	Total	Prob.	Effect.	Effect. (1)
0	626	5097	12.3%	0.0%	0.0%
1	124	1508	8.2%	33.0%	57.4%
2	7	171	4.1%	66.7%	78.8%
3	12	256	4.7%	61.8%	75.7%
4	18	203	8.9%	27.8%	54.1%
5	0	753	0.0%	100.0%	100.0%
6	0	97	0.0%	100.0%	100.0%
7	35	386	9.1%	26.2%	53.0%
8	15	154	9.7%	20.7%	49.5%
B	3	123	2.4%	80.1%	87.4%
P	26	884	2.9%	76.1%	84.8%
T	6	17	35.3%	-187.4%	-82.9%
W	7	86	8.1%	33.7%	57.8%
Total	879	9735	9.0%	26.5%	53.2%

(1) controlled for subfecundity

The figures are low in part because many of the non users are subfecund. FamPlan controls for both age and subfecundity so women can be filtered on evidence of fecundity (e.g. pregnancy or contraceptive use in the last five years). In either case, only the clinical methods show high degrees of effectiveness.

Rate of Change in Transition Probabilities

Intentions

Acceptance

FamPlan uses acceptance rates by age and acceptor method mix by parity to forecast gain into the user pool. These parameters are derived from other questions in the survey. The first is based on response to the question "Do you intend to use a contraceptive method in the next twelve months?"

Age	Intend
15	49.2%
20	53.3%
25	51.4%
30	46.0%
35	30.3%
40	8.1%
45	2.3%

When compared to acceptance in the last year, these numbers are large. Thus we may infer that prevalence at the current time is constrained by supply.

Acceptor method mix

Women were also asked which method they intend to use in the future. These responses were grouped by parity.

0	1	2	3	4+
Condom	4.0%	3.3%	3.4%	1.1%	3.2%
Pill	69.3%	66.6%	58.6%	58.1%	47.1%
Injectable	20.2%	20.5%	25.4%	28.4%	33.8%
IUD	1.6%	3.0%	3.0%	2.0%	2.6%
M.Ster	0.0%	0.0%	0.2%	0.0%	0.0%
F.Ster	0.6%	2.6%	4.1%	5.6%	6.6%
Rhythm	2.0%	1.6%	2.6%	1.7%	3.2%
Withdrawal	0.6%	0.3%	0.2%	0.6%	0.9%
Other	1.6%	2.1%	2.4%	2.5%	2.6%
Total	100.0%	100.0%	100.0%	100.0%	100.0%

Conclusions

Contraceptive use dynamics can be straightforwardly obtained by fairly simple statistical analysis of DHS surveys.

The parameters thus obtained provide substantial insight into quantitative and qualitative issues in program management.

Projections based on these parameters more accurately represent market forces than state norms.