The m ethod used for the m easurem ent and analysis of the ages at first m arriage and at first birth, the first birth interval, the interbirth intervals and the p o stp artu m variables is the life table m ethod. W ith regard to interbirth interval analysis, the m ethod essentially involves the attrition of a cohort of
w om en w ith p n u m ber of births w ho go on to have a subsequent birth at
observed intervals, or w ho are censored by a data collection event w ithout having had a birth. The interval for those censored is the interval betw een the date of the last birth and the data collection event. Interest in the life table is in the time it takes for w om en w ith parity p to move to parity p+1, and for those w ho did not close th eir interval, the interest is in how long the interval rem ain ed o p en u n til the ex p o su re of the w om en w as censored. This inform ation is used to estim ate various life table functions, am ong which are the proportions not having a birth by various time intervals, or s(x) The s(x) is
analogous to lx (or survivors) in a conventional life table. The cum ulative
proportions who have a birth (that is, 'fail to survive' not having a subsequent birth) by time t is obtained by subtracting s(x) values from 1.
This new function is the birth function, and m easures the cum ulative p ro p o rtio n s of w om en having a birth by various du ratio n s after a previous
birth. Sum m ary m easures such as the m edian, quartiles, trim ean and the
sp read of the b irth interval d istrib u tio n s, w hich are explained below are calculated from the birth functions. The advantages of using quartiles of the d istrib u tio n to estim ate the characteristics of the d istrib u tio n are m ainly robustness and resistance to biases in truncated data (Casterline and Trussed, 1980; Rodriguez and Hobcraft, 1980).
Life table techniques based on survival analysis are not only especially suited to handling censored data of this nature, but can also show the shape of the distribution of survival times experienced by homogeneous groups of subjects. In this particular case, the life table methodology involves the estimation of a survival function from information on survival times (or elapsed time) between an initial event , for example, the date of birth of a woman, and a terminal event, for example, her date of first marriage (or date of first motherhood). These data may be used to estimate an age-specific failure rate, or the time-dependent risk of getting married (or having a first birth). In the actuarial and epidemiologic literature, this may also be called the hazard function Mt), and may be defined as the (conditional) probability that a woman who is known to be single (or nulliparous) at least until time t will marry (or have a first birth) before time t + 1. 6 Thus if r(t) is the number of single women at risk between times t and t + 2, and m(t) is the number of single women who marry between times t and t + 1, then the marriage hazard function Mt) is estimated by the proportion of marriages among single women between times t
and t + 2:
Mt) = m(t)/r(t) ... (1.1)
A woman who reaches interview at time t without marrying (or having a first birth) is considered censored at some time between t and t+1, and is counted as being at risk for half of the interval. The hazard function may then be used to estimate the survivor function sit,), or the probability that a single woman at time t will not marry before time t + n . For example, s(t+l), or the probability that a single woman at time t will not marry before time t + 2 could be estimated as:
6 The Mt) is equivalent to nqx in standard demographic notation; s(t) is therefore equivalent to i-Afi)
sfc* 0 = (1-X(0))(1-A.(1))(1-A.(2))... (1-Mt))
= s (t)d -M t))
(1.2) (1.3)
For a m arriage life table, current age and age at m arriage are recorded for all ever-m arried women, together w ith the current ages for all single women. The m arriage rate for the youngest age (say age 15), ^qQ , is found as the proportion
m arrying u p to exact age 15 am ong all w om en 15 years and over at interview (Anderson, 1980 :205-209). For the next interval, that is, m arriages from age 15
to 16, the rate of m arriage, ^ q ^ , the proportion m arrying in this interval
am ong w om en aged 16 years and over and still single. The cum ulative
proportion married by age 16 is:
Survival functions m ay be estim ated for any length of time, from which the tem po and quantum or sum m ary m easures such as quantiles may be obtained. For the first birth interval, the group subjected to the survival analysis is all ever-m arried w om en w ithout a prem arital birth. The initial event is the date of first m arriage, and the term inal event is the d ate of birth of the first postm arital child. The initial and term inal events may then be substituted into equations 1.1 to 1.5 to obtain survival functions which refer in this instance to
the probability that a nulliparous m arried wom an at a given time t will not
have a child before time t+1.
15q0+ (1 ' 15q0)(l q 15) - (1.4)
and for subsequent ages, up to age x:
Selected key birth functions (defined as l-s(x)) are examined. For example, for the interbirth intervals, the birth functions at durations 24, 36 and 60 months are selected for analysis. For the first birth interval, in addition to the birth functions at durations 24, 48 and 60 months, the birth function at duration 9 months is also selected for analysis. Duration 24 months coincides with a relatively short birth interval and is selected to provide an estimate of the cumulative proportions of women having a relatively short birth interval. Three years (36 months) approximates very closely the mean birth interval, or the length of a birth interval traditionally approved as reasonable, and allows for the full integration of the index child into the economic and social activities of his family, while 60 months provides an estimate of the quantum of fertility or the cumulative proportions of women who will close an interval after a reasonably long duration. Following Rodriguez and Hobcraft (1980), the quantum is referred to as the quintum because it is based on five years' experience.
Quartiles of the birth interval distribution are also estimated and defined as the duration by which 25, 50 and 75 per cent of the women who have initiated an interval will have closed that interval. These are designated respectively as the first quartile (q^), second quartile or the median and the third quartile (q3), and are based on the complete distribution of women who initiated the interval. Other measures of location and of dispersion such as the trimean and spread can then be calculated from the quartiles. The trimean is calculated as:
T = (qi + q2 + q3)/4 .... (1.5)
The spread, calculated as,
provides a measure of the dispersion of the birth intervals about the median. Measures that reflect the distribution of birth intervals and can be interpreted in terms of the tempo of fertility are also estimated. The measures are based on the quintum, or the proportions of women having a subsequent birth within five years. The procedure is to standardize the birth functions to make B ^q=1, so as to obtain the proportions of women having a subsequent birth among women who have another child within five years (Rodriguez and Hobcraft, 1980:12). Quartiles of this standardised distribution, q'^, q' 2 and q3 can then be
calculated and defined as the durations by which 25, 50 and 75 per cent of the women who will have a subsequent birth within five years will have done so. Standardized estimates of the trimean and spread could also be calculated from the standardized quartiles as was done for the unstandardized distribution.