Fertility measures based on birth interval data

Abstract

In this paper a new measure of fertility is proposed which is calculated from birth interval data. The measure is a distribution function which may be defined as follows: Given that there is an ( i − 1)th birth, the function F i ( x) is defined as the probability (in the absence of competing risks) that there is an ith birth within x units of time. F i ( x) is assumed to be independent of age. F i(x ¦ a) is the corresponding age dependent probability that is conditional on an ( i − 1)th birth occurring at age a. The F i are defective, in that, in general F i (∞) or F i(∞ ¦ a) is not equal to one. The estimation of the density functions corresponding to F i ( x) and F i(x ¦ a) is considered for the following five sampling schemes for marriage cohorts of women: 1. (i) The women are followed from marriage to some time t and their reproductive experience is assessed—prospective cohort; 2. (ii) The survivors at some time t of a marriage cohort are sampled and their reproductive histories assessed—retrospective cohort; 3. (iii) The survivors at time t are sampled and asked about the date of the last closed interval (if existent)—retrospective last intervals; 4. (iv) The survivors at time t are sampled and followed until their next event occurs (i.e., birth, death, widowhood, divorce). The interval between the event prior to t and the one immediately after t is recorded—prospective next intervals or straddling intervals; 5. (v) The survivors to time t are followed to time T and the intervals falling in ( t, T) are recorded—prospective interior intervals. Estimators are obtained in all cases except (iv) for the density of F i(x ¦ a) . The problem of estimation of F i(x ¦ a) ( or f i(x ¦ a )) in a general population of married women is considered and a life table approach is recommended. Some estimates are obtained from simulation results and compared with the parameters which they estimate. The problem of obtaining an average of the F i(x ¦ a) over i and a is discussed and finally a brief study of the sensitivity of the proposed measure to changing contraceptive practice is conducted via simulation.