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An investigation into the spacing of births among a sample of ever-married women.

INTRODUCTION

During the last several decades, a substantial amount of demographic research and writing has focussed on the fertility of human populations. In most of the underdeveloped countries, with death rates fairly low and stable and international migration increasingly regulated, fertility has been the most variable component of population change. What is fertility? Demographically, fertility generally refers to the number of children born to women across and within cohorts over time and is composed of two parts: one biological and one social. The biological component, fecundity, refers to the capacity to reproduce and, while obviously a sufficient condition for parenthood, it is not sufficient. Whether children will actually be born and how many - given the capacity to reproduce - is largely a result of the social environment in which people live.

This study explores one aspect of the fertility question: the spacing of children or birth intervals among ever-married women in Pakistan. The basic approach underlying the analysis of birth intervals is to view the process of family building. That is why we consider separately the transition from one parity to the next, with marriage defined as parity zero. Also, birth interval analysis provides a powerful tool to study the impact of contraception upon fertility, and this is perhaps its greatest asset to fertility analysis.

In order to study this spacing phenomena, we will make an attempt to show the influence of socio-demographic variables on the expansion and contraction of birth interval. The variables we will employ are spouses' level of education, current use of contraception, rural-urban residence, and duration of marriage.

REVIEW OF RELEVANT LITERATURE

Rodriguez and Hobcroft(1), analyzing the 1976 Columbian Fertility Survey data find that the average birth interval is about one year for first two births and nearly two years for births of higher order with a slight tendency to increase from parities two to six. In the Khanna study(2), spanning 1953 to 1969, Wyon and Gordon, examining Indian data, find that the average birth interval between first and second births is 33.1 months and the second and third births is 31.3 months.

Among the correlates of fertility, current age, age at marriage of the females and duration of marriage are usually found to be the important ones. Age of the female is widely documented to be a strong determinant of birth intervals. It affects biologically and sociologically the length of the birth intervals. Potter(3) et al., utilizing Indian data, find that post-partum amenorrhoea lengthens as mothers age. Their results show that post-partum amenorrhoea averages a little less than 11 months for all ages combined and increases at a rate of one month for every four additional years of age. They also find that the mean length of birth intervals increases gradually from 30 to 35 months between ages 20-39 and then increases more rapidly to an average of 41 months during ages 40 and over.

We know that postponement of marriage to very late ages reduces the probability of short birth intervals owing to a reduction in fecundity. An increase in age at marriage also gives women time to acquire extra-familial interests. Involvement in extra-familial roles may increase the resistance to the transition to motherhood. An increase in age at marriage is, therefore, likely to increase the length of the birth intervals. But again the fecundity factor is strongly correlated with age.

Duration of marriage includes current age of the female as well as the age at first marriage. Analyzing the data from surveys in four rural areas of Bangladesh during 1982-86 and studying determinants of fertility, Ubaidur Rob(4) found that duration of marriage had the strongest positive effect on fertility.

Another important determinant of fertility is the place of residence. Studying 3,610 ever-married Jordanian women, Abdullah(5) claims that the first birth interval can vary by place of residence. He finds a difference of about 2 months in the first birth interval between the rural and urban areas of Jordan but these differences, his study shows, almost disappear at higher parities (7 & 8) where the differences are found to be less than one month.

In western societies, however, numerous studies show that socio-economic differentials in the first birth interval do exit. Pillai,(6) using the 1973 National Survey of Family Growth finds that college educated women have no significant net influence on the first birth interval but that working women do. Studies done on American data also show there is some kind of relationship between the first and second birth interval. Analyzing 3,218 ever-married American women in a study in Illinois, ranging over 20 years time, Marini(7) et al. find that spacing of the first child has a causal effect on the spacing of the second. Having a child within two years after marriage is associated with an increase of .161 in the probability of having a second child within two years after the first. Similarly, Potter(8) et al. find that following a live birth, most American mothers try to delay their next pregnancy at least a few months as shown by their use of contraception.

RESEARCH METHODOLOGY

Single decrement life tables are used to compute the probabilities of birth and average delay in births. In traditional life table analysis, the probabilities of movement over time form one state to another are traced, mainly the movement from life to death. In the present analysis we will use the same methodology but instead of looking at the probabilities of death, we will be looking at the probabilities of birth as the women move from one parity to another.

Where interest is on how births follow each other serially and there are biological and cultural factors, such as lactation and post-partum abstinence, which are controlled by the length of time since a birth, life table is probably the appropriate tool to use. From a methodological point of view, by focusing on birth intervals, the life table approach permits the examination of recent fertility experience, e.g., investigating the open birth intervals of the women under observation. Life tables take into account all those women who had not had any additional birth when interviewed but will eventually have one as well as the experience of women who will have no more children. Moreover, while studying the birth intervals, the use of life tables helps in overcoming data problems associated with censoring i.e., the truncation of reproductive careers before they have been completed.

SAMPLE, SOURCE AND LIMITATIONS OF THE DATA SET

We use data from the World Fertility Survey from Pakistan conducted under the supervision of the United Nations. A total number of 4,949 ever-married females up to the age of 50 years were interviewed, the response rate being 99 percent. In terms of rural-urban breakdown of the sample, 1,886 were urban and 3,063 were rural. The responses include marital birth and pregnancy histories. The sample is rather homogeneous, overwhelming Muslim, predominantly illiterate (89 percent) and largely rural (74 percent). The typical family in Pakistan can be considered traditional, patriarchal, patrilineal and patrilocal. This pattern has evolved over centuries and is firmly entrenched in the people's value system. In Pakistan, fertility takes place almost entirely within marriage, the age of which is quite low (Population Planning Council(9)).

A common problem of retrospective studies is that of recall lapse. This may be a special problem in the data for the women of earlier marriage and birth cohorts who are more likely to have started child bearing many years prior to the survey. These women may not be able to recall accurately, information on the birth and duration of lactation of their children.

HYPOTHESIS

We will be testing the following hypotheses:

1. the higher the educational level of the spouse, the shorter the subsequent birth interval.

2. the longer the duration of marriage, the longer the closed birth interval.

3. use of contraception produces a relatively larger birth interval than non-use.

4. urban women have longer birth intervals than rural women.

ANALYSIS

The analysis is done at various levels. First, the probabilities of second birth are studied using life table functions. Then, the median and mean survival times are studied using life table as well as Kaplan-Meier estimates. Control or stratification is subsequently introduced for the first two parities i.e.; for the interval between first and second birth. Stratification is performed by controlling separately for spouses' level of education, duration of marriage, current use of contraception and place of residence.

The following is the life table for the interval between the first and second birth. Its functions (symbols) are explained in the appendix.

In Table 1, the first column is the yearly birth interval or yearly survival times. The time is arbitrarily set at 12 months which gives a reasonably good picture of the pace of fertility through the attrition process. The second column gives the number of females exposed in a certain cohort which keeps on reducing periodically. For analytical purposes, this column is terminated once the probability of birth reaches zero even if some females are left in the cohort who can possibly give birth. If we look at this column in the table, there emerges a certain pattern. The decline in the number of females is significant in the 12-24 month group, but the dip from 12-24 months 24-36 months is very pronounced. Obviously, the 12-24 month group is the one in which most of the births are occurring. After this group, the decline is more or less monotonic in the rest of the groups. The next two columns are simply the proportion of females giving birth and the proportion failing to give birth at different survival times or at a particular time period. The pattern of these [TABULAR DATA FOR TABLE 1 OMITTED] proportions is not different from the pattern of the attrition of females in absolute numbers. The last three columns are relatively more important for analytical purposes. The cumulative proportion of females (n[c.sub.x]) is the probability of failing to give birth at least to the beginning of a particular time interval or longer.

n[c.sub.x] starts with the value of 1.0000 in 0-12 month time interval. In the next time interval, the proportion of women failing to give birth is relatively small (.0344) as compared to the proportion (.3034) in the 12-24 month time interval. What it means is that as many as 97% of the females from the initial cohort did have the next child within two years of the first child. The percentage drops to 30% for the third and fourth year after the first birth. The analysis suggests that average interval between first and second birth in Pakistan is 2-3 years.

The hazard function (n[r.sub.x]), also termed as the force of fertility, provides us with what is known as the instantaneous birth rate. For further details, see Cutler.(10) For the interval between first and second birth, the birth rate is highest (59 per thousand females) in the second and third year after the first birth, corroborating our earlier results.

The last column of the life table is the birth density function, the probability of birth for a specified time interval in a specific birth interval. The pattern of probabilities of second birth is similar to that of instantaneous birth rates as we find the highest probability (.028) of birth in the third year after the first birth. Probabilities do show a rapid decline subsequently.

STRATIFICATION OF FIRST TWO PARITIES

In order to see the changes in the mean survival time, the first two parities are studied by controlling for spouses' level of education, current use of contraception, rural/urban place of residence and duration of marriage. The following section deals with the analysis of intervals between first and second birth at different levels of these covariates. In stratification, we can use the various tests of significance along with the Brookmeyer and Crowley(11) range of the median survival times, to test the null hypothesis that the survival curves at different levels of the co-variates are identical i.e., S1 = S2 = S3 = 0, or in other words, the birth intervals are the same at different levels of the variables.

Spouses' Level of Education

Starting with the "no education" category, the variable on spouses' level of education has seven categories of formal education.

It is widely documented especially in the western world that education has a depressing effect on fertility but this negative relationship is not very evident in our results. In the "no education" category, although the instantaneous birth rate is highest (63 per thousand) in the fourth year after the first birth, the probability of birth is highest (.028) in the third year after the first birth. With two years of education, the probability of birth in the year after the first birth reduces to .026 which is in the expected direction. But then the probability of birth in the third year after the first birth, with five years of education increases to .031. The probability of birth goes down to .027 with 10 years of education and then stays the same with more than 12 years of education i.e.; the university level education. What this means is that there is no consistent pattern.

In terms of the delay of the subsequent birth, with two years of education, although there is a median delay of second birth by 1.41 months, there is not much delay even with 12 years of education. But then there is a delay of 1.86 months with more than 12 years of education or university-level education. The median delay, based on the product-limit estimates, do not support the above pattern and there is no delay of second birth even if the spouse has attended the university. In contrast, the mean estimate does show a delay of second birth by 3.42 months when the spouse has attended the university. However the mean estimates are somewhat suspect because they are subject to the extreme skewness of the distribution (see Table 2).

Table 3 shows the probability values of the four non-parametric linear rank tests of significance. The review of their relative merits and demerits and their weighting schemes are mentioned in Appendix 2. Mantel-Cox(12) and Tarone-Ware(13) are statistically insignificant whereas Breslow(14) and Peto-Prentice are statistically significant at 5% level of significance. Based on the above results, spouses' level of education for the interval between first and second birth does not seem to have a strong negative impact on fertility. The reader may be cautioned that eighty-five percent of the respondents have no formal education, meaning that the number of cases in the various educational categories become too low to do any meaningful analysis.
Table 2. Median and Mean Survival Times for Spouses' Level of
Education


Levels of Education (in years)      Life Table       Product-Limit


0                                   29.87     -      29.00    41.93
                                     (.38)   (-)      (.43)
(1.55)


0-2                                 31.28     -      30.00    39.30
                                    (1.47)   (-)     (1.49)
(2.74)


3-5                                 29.53     -      28.00    37.55
                                     (.75)   (-)      (.70)
(2.16)


6-8                                 29.96     -      28.00    43.36
                                     (.74)   (-)      (.68)
(3.18)


9-10                                27.83     -      26.00    38.29
                                    (1.01)   (-)      (.92)
(3.06)


11-12                               27.63     -      26.00    36.49
                                    (1.71)   (-)     (2.00)
(4.13)


12+                                 29.49     -      26.00    39.91
                                    (1.96)   (-)     (1.77)
(4.39)
Table 3. Test Statistics for Spouses' Level of Education


                                        Statistic   D.F.   P-Value


Generalized Savage (Mantel-Cox)           7.253       6     .2981
Tarone-Ware                              10.447       6     .1070
Generalized Wilcoxon (Breslow)           13.301       6     .0385
Generalized Wilcoxon (Peto-Prentice)     12.996       6     .0431


We can raise the question as to what kind of education is being imparted in the educational institutions of Pakistan. Apparently the formal education is not making much impact in terms of changing individual's views on birth control. It seems that social pressures are strong enough in Pakistani society to prevent even highly educated individuals from practicing birth control. Since the education system does not include the knowledge of birth control, even educated people can hardly perceive the advantages of limiting their family sizes.

Rather than being ethnocentric, the lack of impact of education on fertility should be understood in the context of Pakistani society. In that society, education is not exclusively seen as a means of financial security and individual independence. Barring a small segment of urban middle class, education is primarily a status symbol for the rest of the society. In rural areas broadly, there are two social classes: feudals and peasants and their statuses are ascribed. Educational attainments among these classes is not going to alter the social statuses of such individuals as social mobility is almost non-existent in a society like Pakistan's. For the elite class such as the Bhutto family, education is only a symbol of prestige. Education does not change their status but helps them to maintain a political hold. Religion is another social institution which reverses the advances made in education. Strong Islamic values probably nullify any gains in female education because of the absence of inter-spousal communication on the issue of birth control. Sex segregation in public institutions such as public transportation, theatres, mosques etc. with a strong norm of purdah prevents any possible contact across the gender lines. Purdah and sex-segregation is practiced in educational institutions as well. The tradition starts early as there are separate elementary schools for boys and girls and the tradition continues at higher levels although both the sexes are allowed to go to the same university but then a curtain in the class room separates the two groups. The author did experience that when he was attending the Punjab University during the 1960's. Such a strict Islamic value system probably nullifies any gains in female education. It may also be pointed out that the country was created solely on the basis of religion as Muslims who wanted to come out of Hindu yoke demanded a separate homeland when British colonials decided to leave the sub-continent after the second world war.

Duration of Marriage

Duration of marriage is an important indicator of fertility and can provide useful insight in the study of birth intervals. It is a measure of looking into the change of fertility levels over generations representing differences in marriage cohorts.

The age at marriage was measured in five year age groups with the first group containing women who were married when they were below 15 years of age. The last group had women who were married when they were at the age of thirty or more. This group was left open-ended, assuming that there will be few cases in this category. The variable on wife's current age is measured in 5-year age groups except the first and the last group. In the first group we lumped all women aged nineteen and less because of the possible variation in the age of menarche. In the last group we included women who were 45 years and older, expecting a few fecund women in this age group because of the onset of menopause.

The analysis reveals that for couples who are married for 5 years or less, the probability of birth keeps on increasing until the marriage is about 30 years old. The instantaneous birth rate follows the same pattern. What this means is that the second birth is delayed only by the women who are at least 35 years old. A possible explanation for the short spacing for younger cohorts is that the women do not see any incentive in restricting their family sizes or having longer spacing in the early years of their married life. Delaying early births is probably seen as equivalent to losing potential fertility when the women's fertility is at its peak. This attitude is social rather than individual and emanates from the social pressures which could possibly result in social sanctions in case of deviant fertility behavior. A possible explanation for longer birth intervals for older marriage cohorts could be the lower fecundity because of a lower level of nutrition in older populations.

Looking at the median survival times the picture is not very different. The threshold point seems to be 15 years of marriage as there is no evidence of the delay of the second child until this point. Even after this point, the delay is rather insignificant i.e., a delay of 1.6 months. On the other hand, the mean survival time, based on the product-limit estimate, shows no such threshold point and keeps on increasing monotonically. This probably reflects the asymmetrical (positively skewed) nature of the distribution of survival time which affects the mean more than the median. This is also evident from the fact that standard errors of these means go up substantially along with the durations of marriage and are, in general, higher than the median survival times.
Table 4. Median and Mean Survival Times for Various Durations of
Marriage


Durations of Marriage (in years)     Life Table       Product-Limit


[less than] 5                       32.94     -      30.00    32.08
                                    (1.60)   (-)     (1.43)
(.96)


5-9                                 28.72     -      27.00    32.36
                                     (.62)   (-)      (.64)
(.81)


10-14                               28.05     -      26.00    32.12
                                     (.60)   (-)      (.42)
(.94)


15-19                               29.08     -      28.00    37.09
                                     (.61)   (-)      (.70)
(1.35)


20-24                               30.63     -      29.00    40.89
                                     (.86)   (-)      (.74)
(2.04)


25-29                               31.05     -      30.00    42.32
                                     (.78)   (-)      (.83)
(2.31)


30+                                 31.63     -      32.00    47.62
                                    (1.00)   (-)     (1.07)
(3.70)


Despite some irregularities in the pattern of survival times of various durations of marriage, the values of all tests of significance are high enough to reject the null hypothesis (statistically significant at .001 probability level), meaning that the probabilities of second birth do vary with the various marriage cohorts.

Current Use of Contraception

Use of contraception is perhaps the most important determinant of fertility. In our study, we consider only those respondents who are currently using some kind of contraception. Thus the ever-users are ignored because their current status of the use of contraception is unknown.

Our results suggest that the relationship of the use of contraception and fertility does not seem to be as straightforward as it usually sounds. Until the third year after first birth, the contraceptive users have a higher probability of second birth than non-users. This is not what one would expect theoretically. This reversed situation continues until the eighth year after the first birth when all the respondents are exhausted in the attrition process.

The question is: what is going on during those three years after the first birth in which the contraceptive users have the higher probability of second birth than the non-users? One possible explanation of such a phenomena is that most of these respondents were first time contraceptive users, assuming that they did not use contraception before the first birth because of the social pressure to have the first child as early as possible after marriage. Perhaps these were the contraception failure cases and we assume that most of these cases were educated, urban women. One possible explanation for this phenomenon could be that these urban educated women had had contraceptive failures and, at the same time, had not been lactating their first child, thereby causing a relatively quicker second child. It is also possible that many respondents who were using contraception at the time of survey were not using prior to having the second child.

How does this situation get reversed after the third year since the first birth? It could be that by the fourth year after the first birth, only those women who are successful contraceptive users are left in the attrition process. But the number of such respondents (55) is too low to make the differentials in contraceptive use look really meaningful.

In a society like Pakistan's, use of contraception is considered unethical and un-Islamic. Muslims share the Catholic belief of "be fruitful and multiply" and see the use of contraception as sinful, believing that the birth control technology basically blocks the soul to come to this world, thereby standing in the way of God's will. Large families are considered to be socially functional and economically beneficial. In agricultural areas, a small family can bring poverty in the family because then you have to hire labor from outside in order to carry out the agriculturally related chores. The society tends to be strongly in favor of having sons because sons are considered to be assets; security in old age as being the major vested interest of the parents and the girls as liabilities mainly because of the dowry system and in rural areas, giving some land to the daughter as dowry is quite common. More daughters in the family means the reduction of land for the family. For a farmer, nothing is more devastating than losing a chunk of his land which he had inherited from his ancestors. In that society, the sons usually get better care from their parents than the daughters. Studies have repeatedly shown that girls less than two years old have a substantially smaller chance of survival than boys of the same age; they die from the same causes as boys do but their parents give boys higher quality medical care and possibly more supplementary food.

In terms of tests of significance, all tests show significance at the .001 probability level, meaning that the probabilities of second birth for users and non-users are different from each other. But this overall statistical significance does not really explain the peculiar behavior of the variable when we study the results in detail.
Table 5. Median and Mean Survival Times for Current Use of
Contraception


                                     Life Table       Product-Limit


Use                                 28.49     -      27.00    30.93
                                     (.36)   (-)      (.32)
(.39)


Non-use                             25.96     -      25.00    26.43
                                     (.94)   (-)      (.77)
(.70)
Table 6. Median and Mean Survival Times for Place of Residence


                                     Life Table       Product-Limit


Urban                               28.02     -      26.00    40.72
                                     (.45)   (-)      (.40)
(1.76)


Rural                               30.65     -      30.00    26.43
                                     (.36)   (-)      (.38)
(1.52)


Place of Residence

In most of the developing countries, the urban/rural dichotomy is considered important for understanding fertility differentials. The most widely documented result, especially in the western world, is that urban fertility is always lower than rural fertility. Our results vindicate that hypothesis only partially. The results show that the probabilities of second birth in the urban areas are higher than in the rural areas until the second year of the first birth. The picture reverses from third year onwards after the first birth.

In terms of spacing, the results are in the expected direction. The urban women, on the average, delayed the second child by 2.63 months more than the rural women. Such delay is of 4 months when we use the product-limit estimates.

In fact, Urban/rural differentials in fertility should be understood in terms of the extent to which the migrants have become urbanites i.e., to what degree these rural-urban migrants have internalized urban norms and values during a certain period of time. Most of the first generation migrants to urban areas are more likely to practice rural values such as marrying back in rural areas and keeping a high fertility norm even in urban areas. This high fertility norm probably does not change until the third generation of rural-urban migrants.

Summary and Conclusions

To understand the dynamics between the first and second birth, birth histories of ever-married Pakistani females were analyzed. The analysis suggests that the average birth interval between the first two parities is 2-3 years as the birth rate is highest (59 per thousand) in the second and third year after the first birth.

Spouse's education does not seem to be a strong depressant of fertility. The delay in the second birth shows an inconsistent pattern across educational categories. The probability of second birth decreases by .014 and the second birth is delayed by 1.86 months as the couples move from five years of formal education to some education at University level. Looking at the relationship between duration of marriage and spacing, the threshold point seems to be 15 years of marriage as there is no evidence of the delay of a second child until this point. Even after this point, the delay is rather insignificant i.e.; of 1.6 months. The urban women, on the average, delayed the second child by 4 months more than the rural women. No significant difference in spacing was found by contraceptive use mainly because of the small proportion of contraceptive users.

Policy Recommendations

We suggest that the Government of Pakistan introduce some education on birth control at a certain level in the educational system, and that education should be more internationalized so that the Pakistani society is exposed to world development.

We also suggest that the population census of Pakistan redefine the definition of urban areas. Apparently a substantial proportion of people living on the fringe of the cities are classified as urban although they might be the first generation of rural-urban migrants and have completely rural fertility norms. We also suggest that the Government should encourage lactation across all sections of the society, especially targeting the relatively more educated women living in urban areas and discourage the use of formula milk.

Directions for Future Research

Instead of measuring rural-urban differentials in fertility, we suggest that fertility studies should focus on just the urban areas because we suspect that within the urban areas, there are substantial variations in life style, living conditions and fertility preferences whereas this is not the case in rural areas where there is more homogeneity in terms of social life. We know that in the hinterland of the city, we get a substantial number of first generation rural-urban migrants whose fertility norms are more or less rural but who are counted in urban areas by census officials, thus inflating urban fertility. There is reason to believe that most of the first-generation rural-urban migrants are young, un-married males who, when they decide to marry, would prefer to marry rural women. These rural women are more than likely to carry out the traditional rural fertility norms, not realizing the dysfunctionality of a large family in urban areas (shortage of available land being one of the biggest problems in the cities). We suggest that this particular segment of the urban areas i.e.; the hinterland first generation rural-urban migrants should be tapped for future fertility research in Pakistan. Assuming that the fertility levels do not go down until about the third generation of rural-urban migrants, some dynamic models should be used to study the possible changes in fertility levels over three generations within the urban areas which should shed some light on social change in Pakistani society. This area of fertility research in Pakistan seems to be very important, given the fact that the rate of rural-urban migration is extremely high.

APPENDIX 1

Following is the text-book pattern of the life tables. For details: see Smith.(15)

1. x is completed number of months since marriage or previous birth.

2. [S.sub.x] is the number of women still under observation.

3. n[W.sub.x] is the number of women leaving observation with a birth between x and x + n months; deaths, widowhood, menopause (age 50). For single decrement tables, we can omit this function.

4. n[b.sub.x] is the number of confinements occurring between x and x + n months.

5. n[q.sub.x] is the estimated conditional probability of the absence of a birth between x and x + n months and can be written as n[q.sub.x] = n[b.sub.x]/(Sx - 1/2 n[W.sub.x]). For a single decrement life table, this formula would become as n[q.sub.x] = n[b.sub.x]/[S.sub.x].

6. [P.sub.x] is the estimated conditional probability of births by month x and can be written as n[P.sub.x] = (1 - n[q.sub.x]) n[P.sub.x] - n.

7. [B.sub.x] is the estimated number of births per 1,000 women and can be written as (0.001) [B.sub.x] = n[P.sub.x] - n[P.sub.x] + n = (n[q.sub.x])(n[P.sub.x]).

8. Fx is the relative frequency distribution of intervals and can be written as [F.sub.x] = [B.sub.x]/[Sigma][B.sub.x] (x=1,2,3,....).

From this frequency distribution, mean birth intervals can be computed for various characteristics of the respondents. But the computer output shows the functions of the life table in a slightly different form. The last function of the life tables will now be the conditional probabilities of birth instead of relative frequency distributions as is the case with the traditional life tables.

Following is the description of each function of the life tables we are using in our current analysis, generated by the BMDP program. The definition of these functions is as follows:

1. n[t.sub.x] is the time between x and x + n months, the completed number of months since the previous birth.

2. n[E.sub.x] is the number of females exposed between x and x + n months.

3. n[b.sub.x] is the proportion of females giving births between x and x + n months.

4. n[f.sub.x] is the proportion of females failing to give birth between x + n months.

5. n[c.sub.x] is the cumulative proportion of females failing to give birth at the beginning of each interval between x and x + n months.

6. n[r.sub.x] is the instantaneous birth rate between x and x + n months.

7. n[P.sub.x] is the probability of birth between x and x + n months.

APPENDIX 2

Mantel and Cox use scores based on the expected value of order statistics from an exponential distribution. Also known as log-rank test, this test gives equal weight to all observations. Breslow's statistic is analogous to the Kruskal-wallis test. Because the Breslow test gives greater weight to early observations, it is less sensitive than the Mantel-Cox test to late events when few respondents remain in the study. This statistic is probably more meaningful for our analysis because of the fact that majority of the births are occurring in the second, third and fourth year after the first birth. The Tarone-Ware statistic provides a compromise between the Mantel-Cox and Breslow statistics with an intermediate weighting scheme. They suggest that their test maintains power across a wide range of alternatives than do the other two tests.

APPENDIX 3

The hazard rate represents the limiting value of the age-specific birth rate when the age interval to which the rate refers becomes infinitesimally small. It is defined as

[[Lambda].sub.x](X) = -d/[d.sub.x] [S.sub.x](X)

and is estimated at the mid-point of each interval i.e.,

[[Lambda].sub.i] = 2[q.sub.i]/[h.sub.i](1+[p.sub.i])

where [q.sub.i] is the probability of giving birth in a particular interval, [p.sub.i] is the probability of no-birth and hi is the width of the i the interval. For further details see Cutler.

NOTES

1. German Rodriguez and John N. Hobcroft, "Illustrative analysis: Life-Table analysis of birth interval in Columbia," (Scientific Reports, no: 16: Worm Fertility Survey, 1980).

2. John B. Wyon and John Gordon. "The Khanna study: Population problems in the rural Punjab" (Cambridge, MA: Harvard University Press, 1971).

3. Robert G. Potter, Jr. and John B. Wyon, Margaret Parker, and John E. Gordon, "A case study of birth interval dynamics," Population Studies, 1(1965):81-96.

4. A.K. Ubaidur Rob, "Determinants of fertility in Bangladesh," Biology and Society, 1(1990):31-37.

5. Aziz Abdullah, "A study of Birth Intervals in Jordan" (Scientific Reports Number 46, 1983).

6. Vijayan Kumara Pillai, "Determinants of first birth interval" (Unpublished Dissertation, University of Iowa, 1983).

7. Margaret Marini and Peter Hodson, "Effect of timing of marriage and first birth on the spacing of subsequent birth," Demography, 4(1981):529-548.

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Author:Raajpoot, Uzzer A.
Publication:The Social Science Journal
Date:Jan 1, 1996
Words:6157
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