Truncation Effect in Closed and Open Birth Interval Data

Abstract

Abstract The lengths of the “closed” intervals from the ith to the (i + 1)th birth (Xi ) and of the “open” intervals since the most recent birth (Un ) for women who have had exactly n births have been considered useful indicators of current changes in natality patterns. Particularly, it has been hoped that such data will provide information regarding the p.d.f. of χ i , the corresponding interval that would be observed if there were infinite time for reproduction. Since Xi and Un depend on the convolution of the p.d.f.'s for xj (j = 0, 1, …, i) and on t (the duration of fecund marriage at the time of survey), a set of Xi forms a truncated sample of the corresponding xi . The Un also depend on analogous convolutions and on t. As a result, even given uniform t for all the subjects, a change in the p.d.f. of xi , such as a shift to the right, will not necessarily be reflected in observed data on Xi or Un . This difficulty is not overcome by life table analysis except under highly restrictive assumptions. It is doubtful whether the current emphasis on securing such data is justified. Certainly, further investigation is needed to provide a better basis for the definition and analysis of interval data if they are to be used.