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Life table analysis of birth intervals for Bangladesh

M. Kabir and A. J. M. Sufian
Department of Statistics, Jahangirnagar University, Savar, Dhaka, Bangladesh


In nutrition field studies the relationship between maternal and child nutrition, infant mortality, and birth interval is often of interest. Infant mortality and hence birth interval is heavily dependent on the nutritional status of the infant The life table approach employed in the following paper is seldom used, but has distinct advantages for some nutrition field studies.


In recent years the study of birth intervals has acquired added importance because of its relationships to fertility. The mean duration of successive birth intervals is obviously related to the fertility rate; the longer the interval, the lower the fertility. The relation between these two measurements of the same phenomenon is, however, far from simple (1). There are two aspects to the family building process. The first is the parity progression ratio, which is related to the quantum of fertility, and the second is the time it takes to make the transition from one parity to the next for those who continue reproduction, or the distribution of birth intervals, which is related to the timing or tempo of fertility. The main objective of this study is to present the pattern of birth intervals through life table techniques; all data used here are from the Bangladesh Fertility Survey (BFS), conducted in 1975 as part of the World Fertility Survey Programme (WFS)*. The basic principle under-lying the analysis of birth intervals is to view the family-building process as a series of stages where women make the transition from marriage to first birth, from first birth to second birth, and so on until they reach their completed family size.

The Data

Ever-married women between the ages of 15 and 49 years were selected with equal probability so as to yield a self weighted sample of women. In all, 6,515 eligible individuals were interviewed in detail regarding their maternity and marriage histories, knowledge and use of contraception, fertility intentions and preferences, and socio-economic background. The sample was selected by a three-stage sample design. The sample selected represents the country as a whole and allows separate estimates according to various socio-economic characteristics.

The primary problem in analyzing birth history data from developing countries is the accuracy of reporting. Different errors may affect the data and lead to false conclusions. The direction and magnitude of the error are influenced by the number of births displaced by women from one period to another and the total number of children born to them. The tendency for the proportion of both births and deaths that are not reported to increase with the age of the mother is well established (2). Brass has recently documented some of the possibilities for detecting error in birth history (3). According to him, most retrospective survey data are deficient because of faulty declarations about children ever-born and children who died. The magnitude of the deficiency increases as the respondents report farther into the past. In addition to this, birth history data may contain erratic errors and biases in the timing and location of births and deaths. The Bangladesh birth history data are of doubtful quality. Dating of birth has been found to be incomplete, with 85 per cent of dates given in years ago: 3 per cent are reported as year only with the month missing, and 12 per cent report the calendar month and Year (4). However, completeness of date reporting is no guarantee of accuracy because of the unknown amount of interviewer estimation and the possibility of digit preferences and more systematic respondents' errors in the dating of events. There are also reasons for believing that maternity histories frequently suffer from event displacement, particularly in the form of a concentration of births prior to the survey. Detailed analysis confirms that displacement of dates of birth is more prevalent than omission of births (4).

Life Table Analysis of Birth Intervals

Life table analysis of birth intervals is not new, However, the method has rarely if ever been systematically used. The WFS enquiry provided a large body of data and thus opened up the possibility of applying the technique more comprehensively. The life table method calculates the probabilities that women who could give birth at the beginning of a month actually do so. The standard life table measures are derived from the series of conditional probabilities. When there is a truncation the life tabir will be incomplete, in the sense that more women will attain the given parity at a later date. Moreover, a full set of life table estimates for every birth interval is a large number of indices that must be summarized for discussion and interpretation. The methodology for constructing life tables from maternity history data is described by Smith (5). The basic information required to construct a life table is a cross tabulation of an ever-married woman by duration of exposure and termination status. By duration of exposure we mean the interval from marriage to either first birth or interview, whichever comes first. By termination status we mean a variable indicating whether exposure was terminated by the lack of further observation or by the first birth. The measure used to estimate the quantity of fertility is the birth function Bx, which stands for the cumulative proportion of women having a subsequent birth by duration x months since the previous birth. We examined Bx in detail and found that the proportions having a birth four, five, and six years later are suitable measurements for adequate description of the results. However, the data from marriage to first birth are quite insufficient for Bangladesh. Since age at marriage is very young, the first birth interval is unusually longer in Bangladesh. Even after six years of marriage, only 70 per cent have had their first child. Besides first births, 90 to 95 per cent of higher order births occurred within six years and the data were available for most tables. We thus conclude that six years is the most suitable indicator of the quantum of fertility. The search for two or three summary measurements that conveyed most of the information contained in the life tables emerged in the choice of B72 because of its availability in most of the tables. Rodriguez and Hobcraft (6) suggest that for each birth interval three summary indices are quite adequate for the interpretation of results: the proportion of women having subsequent births within six years (B72), and the trimean and the interquartile range distribution of intervals to births occurring over the six years.

The trimean is defined as:

(see reference 7) where q1, q2, and q3 denote the quartiles of the standardized distribution derived by standardizing the birth function to make B72 = 1. The inter-quartile range, or the spread: S = q3-8. These indices broadly measure the quantum, average timing, and spread of timing of the movements towards the next birth. From the estimated standardized quartiles, many statistical parameters in addition to those above can be derived for discussion and interpretation of the results, as for example, the median, M= q2 (7).

Table 1 shows an abbreviated life table for interval between first and second births. From this table we find B72 = 0.9331. To derive the standardized quartiles (i.e., q1 q2, and q3) we require the duration by which the cumulative proportions having a second birth within six years of the first event are 0.23333, 0.4666, and 0.6998 (these values being 25, 50, and 75 per cent of 0.9331). The quartiles can be estimated by simple linear interpolation. For example, the first quartile is found by linear interpolation between durations 18 and 24 months as q1 = 20.8 months. Similarly, q2= 29.4 and q3= 40.1. The trimean is thus T = 29.9 months and the spread is 19.3 months. Thus, about 93 per cent of Bangladeshi women have their second child within six years of the first child, with an average birth interval of 30 months and a spread of about 19 months. As is evident from table 2, the proportion of women having a subsequent birth by each duration remains almost stable up to the fourth birth and then declines gradually.

Most of the differences are captured by the birth function (B72), which ranges from 93 per cent for the second birth to 88 per cent for the sixth birth. The mean birth interval is about 29 months and is almost the same from second birth order to the sixth birth order. The first birth interval is high (about 36 months), because women marry at so young an age in Bangladesh. Similarly, the spread of the distribution is about 18 months and is approximately the same for all birth orders. These results reveal the differences in the distribution for first birth intervals compared with other order of births. The other birth intervals are more or less homogeneous. The results also suggest that after the birth of the first child, family size does not seem to have any effect on subsequent birth and timing of the next birth.

TABLE 1. Abridged Life Table for the Interval between First and Second Birth

Duration of Exposure (Months) Number of Women at Risk Number of Births Omitted Cumulative Proportion Who Gave Birth
0-3 5,304 0 56 0
3-6 5,252 0 52 0
6-12 5,128 131 40 .0359
12-18 4,624 334 57 .1561
18-24 3,798 421 41 .3257
2436 2,002 304 28 .6415
3648 937 116 19 .8150
48-60 491 57 9 .8947
60-72 275 21 6 .9331
72-84 180 17 11 .9522
84-96 123 5 2 .9630
96- 108 96 3 0 .9692
108-120 75 3 2 .9745
120-132 59 1 0 .9782
132 + 55 0 1 .9787

The Effect of Age at Marriage on Birth Interval

We have shown that first birth interval is longer in Bangladesh than in many populations. In this section, an attempt has been made to examine this more incisively by controlling the age at marriage, i.e., < 15 and 15+years. The results are shown in table 3.

It is evident from the above tables that birth interval is higher for those who married when less than 15 than for those who married at age 15 and older. Thus, most of the difference in the first birth interval is due simply to the longer reproductive life of women marrying early. The proportion of women married before age 15 who had a first birth within six years of marriage was 0.70 compared to 0.90 for those who married at age 15 and older. Most of this difference in the first birth interval by age at marriage can be attributed to the adolescent sub-fecundity and adolescent sterility. Delay of consummation or irregularity of sexual intercourse for women marrying early is another possible explanation of why the first birth interval is longer than usually expected. Delay of consummation in Bangladesh is generally associated with the fact that the girl, although married in most instances, has not reached menarche. Age at marriage has a pronounced cohort effect on the timing of the first birth, with the trimean being nearly 56 months for women marrying before age 15 compared with 25 months for women marrying at age 15 and above. This difference in the timing of first birth is also revealed by the proportion of women having the first birth since first marriage.

As we move to a higher order of births, the effect of age at first marriage is minimal, since there is no significant difference in the trimean (see table 3). In fact, the trimean varies from 28.5 to 29.2 months.

TABLE 2. Summary Measurements of Birth Intervals

Summary Measurement Birth Order
1 2 3 4 5 6
B12 .0836 .0359 .0393 .0417 .0429 .0364
B36 .2312 .6415 .6443 .6412 .6182 .6178
B60 or Quantum (P) .6152 .8947 .8918 .8878 .8678 .8451
B72 .6943 .9331 .9334 .9208 .9051 .8805
Trimean (T) 35.4 29.9 29.6 29.5 29.5 29.4
Spread (S) 30.2 19.3 19.6 19.3 19.7 19.2
No of cases 6,009 5,304 4,497 3,766 3,113 2,499

TABLE 3. Summary Measurements of Birth Intervals by Age at Marriage

Summary Measurement Age at Marriage
< 15 Birth Order 15+ Birth Order
1 2 3 1 2 3
B 12 .0836 .0349 .0401 .1960 .0407 .0341
B24 .2212 .3241 .3418 .4402 .3345 .3275
B72 .7044 .9328 .9279 .8941 .9556 .9208
q1 20.1 21.0 20.6 13.0 20.2 20.8
q2 36.0 28.5 28.1 24.0 27.8 28.9
q3 50.6 38.9 38.4 37.7 38.0 38.9
Trimean (T) 35.7 29.2 28.8 24.7 28.6 29.4
Spread (S) 30.5 17.9 17.7 24.7 18.3 18.0
No. of cases 5,043 4,404 3,823 1,181 900 674

Birth Intervals by Some Selected Socio-Economic Characteristics

In this section we investigate the effect of some selected socio-economic characteristics on the quantum and tempo of fertility. For our analysis here we consider variables, namely by type of place of residence and level of education, as measured by years of schooling. These two are the important determinants of fertility. Table 4 shows the summary measurements of birth intervals by place of residence and level of education as well as by religion. For the first birth interval we find a higher mean for rural areas than for urban areas (40 months as against 35 months!.

This difference can be explained in terms of difference in the age at marriage between the two areas. As we move on to the higher order of births, we find no significant difference in trimean, although there is evidence that trimean is slightly lower for urban areas for the higher order births compared to rural areas. A similar conclusion can be reached for the two religious groups (Moslem and Hindu women).

We examine the effect of education on birth intervals by constructing life tables by birth order separately for three educational groupings: No schooling, one for four years of schooling, and five or more years of school. These results are also summarized in table 4. Women with no schooling show a slightly higher mean than women with some education or five and more years of school. After the birth of the second child, however, women with higher education begin to show a lower fertility than women with less than five years of schooling. The group with no schooling shows a similar pattern to those with some education, suggesting that a few years of schooling have little effect on subsequent fertility. Examination of the trimean demonstrates that there is no systematic educational differential in the timing of fertility. The question may arise as to whether the observed educational differences in the quantum of fertility can be partly explained by the age of the women at the start of each interval. For instance, the more educated women tend to marry later, and will therefore be relatively older than women with no education by the time they reach the second birth, a fact that should decrease the proportion having a third birth within six years.

TABLE 4. Summary Measurements of Birth Intervals by Socio-Economic Characteristics

Summary Measurements Socio- Economic Characteristics
Residence Education Religion
Birth Order
Birth Order
Birth Order
1-5 Years'
Birth Order
5 Years'+
Birth Order
Birth Order
Birth Order
2 3 2 3 2 3 2 3 2 3 2 3 2 3
B12 . 041 .044 .031 .039 .037 .038 .030 .057 .032 .025 .035 .037 .041 .051
B24 . 366 .363 .240 .338 .321 .336 .327 .343 .372 .370 .326 .337 .334 .359
B72 .925 .917 .934 .928 .932 .925 .930 .936 .951 .948 .934 .930 .939 .922
q1 19.1 19.4 20.8 20.9 21.0 23.8 20.8 19 9 20.3 20.8 20.9 20.8 20.4 20.1
q2 27.3 26.9 28.4 28.4 29.4 28.4 27.9 28.4 27.7 26.9 28.4 28.3 28.2 28 0
q3 38.0 37.4 38.3 39.0 38.8 38.5 38.5 38.9 38.9 37.8 39.1 38.4 37.7 39.0
Trimean (T) 27.9 27.6 29.2 28.9 29.7 29.6 28.7 28.9 28.7 28.1 29.2 28.9 28.6 28.7
Spread (S) 18.9 18.0 18.1 17.1 17.8 15.3 17.7 18.9 18.6 17.0 18.1 17.6 17.4 18.9
No. of cases 420 349 4,274 4,147 4,203 3,622 592 489 441 339 4,385 3,729 854 717

Cohort and Period Effects

We examine the experience of birth intervals of different cohorts of women using life tables by birth order constructed separately. The results are summarized in table 5. Examining the interval from marriage to first birth, we see that the older cohorts have experienced their first birth with a longer duration compared to younger cohorts. For instance, the trimean for the cohort 20 to 24 is 34.0 months compared to 40 months for the cohort 45 to 49. This may be due to the changing pattern of age at first marriage. Surprisingly, the difference in the trimean for different cohorts becomes insignificant when we compare second and higher order births.

We examined period effects by calendar period. Since the survey occurred in 1975, women in the most recent period have been exposed to the risk of having another child for a shorter period. Thus, the most recent period represents an incomplete experience. Here we find no trend over time in trimean except in transition from marriage to first birth. The trimean is the same for both the periods. The average length of the third birth interval has changed by two months between the periods 1960-1964 and 19651969. These results must be viewed with caution because there is a possibility of the effect of selectivity in retrospective period data. As we move farther back in time we are faced with a progressively younger group of women. The birth intervals for past periods are based on women who, on average, were comparatively younger at the beginning of the interval. Since comparatively young women are more likely to have another birth within a short interval, may yield a spurious time trend.

The Effect of Infant Mortality on Birth Interval

Among many factors that can contribute to the wide variations in completed family size, infant mortality is considered to be one of the important factors in the variation of natural fertility. In societies where breast. feeding is common and extends for more than a few months, its ovulatory suppressant effects result in longer average birth intervals to the next birth if the previous child survives the breast-feeding period than if he dies therein (8; and A.K. Jain, "Lactation and Natural Fertility," paper presented at a Seminar on Natural Fertility, Paris, 1977)

In order to examine this more incisively and to assess the magnitude of the effect of infant mortality on fertility, we have constructed life tables by birth order according to whether or not the previous child survived the first year of life. The results are presented in summary form in table 6. It is evident that for each of the birth orders, the death of the previous child within the first year of life increases the proportion of women who go on to have another child within six years and reduces the waiting time before the next birth. The death of the first child in the first year of life reduces the average birth interval from 30.8 months to 24.1 months. Similarly, the death of the fourth child increases the proportion of having a fifth birth within six years from 92 to 94 per cent and reduces the average interval by 3.6 months.

TABLE 5. Summary Measurements of Birth Intervals by Cohort and Period

Birth Order Summary Measure meets Cohort Period
20-24 25-29 30-34 35-39 40-44 45-49 1960-64 1965-69
1 B12 .1031 .0867 .0731 .0838 .0616 .0438 .0921 .1044
B24 .2645 .2410 .1899 .1881 .1431 .1312 .2387 .2581
B 72 .7784 .7672 .6838 .6491 .6247 .5067 .7130 .7887
T* 34.3 34.5 36.6 36.2 38.9 40.2 33.8 33.7
S** 21.7 31.2 29.1 35.5 29.8 32.1 30.7 29.5
2 B12 .0325 .0333 .0291 .0214 .0190 .0225 .043 .044
B24 .3257 .3629 3132 .2888 .3020 .2493 .358 .387
B72 .0343 .9515 .9461 .9369 .9197 .8991 .953 .938
T 29.4 30.1 28.7 29.2 28.5 31.5 27.5 27.3
S 19.1 20.5 16,9 16.4 17.5 20.2 15.9 17.9
3 B12 .0337 .0310 .0361 .0287 .0339 .0218 .034 .049
B24 .2974 .3768 .3343 .3146 .3331 .2743 .395 .346
B72 9197 .9498 .9375 .9386 .9101 .8845 .953 .923
T 28.2 27.5 28.0 29.4 29.4 30.1 26.8 29.0
S 18.5 17.5 16.1 18.6 20.0 17.5 15.1 19.0

* T = trimean.
** S = spread.

TABLE 6. Birth Interval by Survivorship of Previous Child

Birth Order Summary Measurement Survivorship Status
Survived Died in First Year
2 B72 930 .944
  T* 30.8 24.1
3 B72 .931 .958
  T 29.0 26.8
4 B72 .922 .938
  T 28.8 25.2
5 B72 .907 .920
  T 29.1 25.7
6 B72 .872 .904
  T 28.6 24.3

*T = trimean.


The results presented here reflect the pattern of the family-building process into a series of stages, including marriage and births of successive orders, and investigates the transition from one stage to another. In Bangladesh, age at first marriage is a poor indicator of entry into risk of childbearing and therefore the inclusion of marriage as the first stage in the process may yield doubtful results. In this situation, an analysis of age at first birth would have been more useful than analysis of the interval from marriage to first birth. Differentials in the quantum and tempo of fertility have been studied using life table techniques by birth order separately. The process of transition to each birth order has been examined in terms of birth function or cumulative proportion of women having a birth of a certain order by successive intervals since the previous birth, which was estimated using life table techniques.

Several findings reported here deserve comment. First, the first birth interval is consistently high in Bangladesh, possibly because of low mean age at marriage. In this situation, first birth interval can be studied by controlling age at marriage. There is, however, little difference in the birth intervals between second and higher order of births, although the quantity, i.e., proportion of women having a particular birth order, varies. In Bangladesh child mortality shortened median birth intervals. There is, however, a suggestion that mortality control programmes could reduce fertility through a biological mechanism. Better survivorship of infants would facilitate lactation and prolong the period of postpartum sterility and thus the birth interval (9). It is important to point out that this fertility reducing effect of better infant survival is more complex when viewed in terms of population growth rates. While fertility would be reduced, survivorship, a central element of net reproduction, would be improved.

From the perspective of a population replacing itself in the next generation, reduced mortality of infants would have dual effects: a reduction of fertility but better survivorship of those infants who are born. The outcome of these dual changes would result in a reduction of fertility but an overall increase in net reproduction (9). Perhaps the most important contribution of this study has been that overall birth interval is about 30 months. The birth interval is a useful measurement of fertility. Thus, future studies dissecting out actual components of birth intervals, such as postpartum amenorrhoea, the waiting time to conception, gestation, and the time required for foetal wastage would permit a more precise quantification of mortality effects on fertility.


1. L Henry, Human Fertility: The Basic Components (The University of Chicago Press, Chicago and London, 1973).

2. W. Bass, ''The Assessment of Validity of Fertility Trend Estimates from Maternity Histories'', Proceedings of an International Population Conference, International union for the Scientific Study of Population (IUSSP) Mexico City, August, 1977.

3. W. Brass, "Screening Procedures for Detecting Errors in Maternity History Data." Asian Population Studies Series No. 44, Regional Workshop on Techniques of Analysis of World Fertility Survey Data, Report and Selected Papers, Economic Commission for Asia and the Pacific (1980).

4. V.C. Chidambaram, "Some Aspects of WFS Data Quality: A Preliminary Assessment."Comparative Series No. 16,World Fertility Survey, London, U.K.lnternational Statistical Institute, Voorburgh, Netherlands (1980),

5. D. Smith, Life Table Analysis World Fertility Survey Bulletin No. 6, World Fertility Survey, London, U.K. (1980).

6. G. Rodriguez and J.N. Hobcraft, "Illustrative Analysis: Life Table Analysis of Birth Intervals in Colombia." Scientific Reports No. 16, World Fertility Survey, London, U.K. International Statistical Institute, Voorburg, Netherlands (1980).

7. J.W. Tukey, Exploratory Data Analysis (Addison Wesley Publishing, Reading, Massachusetts, 1977).

8. R.G. Potter, Jr., M. New, J.B. Wyon, and J.E. Gordon, "Application of Field Studies to Research on the Physiology of Human Reproduction: Lactation and Its Effects Upon Birth Intervals in Eleven Punjab Villages, India", in: Public Health and Population Change: Current Research Issues, M.C. Sheps and J.C. Ridley (Eds.) (Schenkman Publishing Company, Cambridge, Massachusetts, 1965).

9. Committee for International Coordination of National Research in Demography (CICRED), Seminar on Infant Mortality in Relation to the Level of Fertility, 6-12 May 1975, F.C. Madigan (Ed,) (CICRED, Cedex-14, Paris, France, 1975).


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