Nonparametric kernel estimation of hazard and density functions from duration of breastfeeding data

Tapan Kumar Chakrabarty, North Eastern Hill University, Shillong

A number of new methods of analyzing time to occurrence variables for events of interest in demography e.g., marriage, mortality, birth, leaving parental home, postpartum amenorrhoea, breastfeeding etc. have been developed in the recent years using the World Fertility Survey (WFS) and the Demographic and Health Surveys (DHS) data. These methods rely upon retrospective information from life or birth histories and recollections of past events. Retrospective information of the sort is known to be affected by recall errors which result in the omission of events, the misplacement of dates, and the distortion of reports of duration. For example, analysis of breastfeeding information using retrospectively reported ages of weaning for all births that occurred during the three or five years preceding the survey commonly display marked heaping at durations 6, 12, and 18 months. The present article proposes to use a nonparametric kernel estimation procedure to obtain a smooth estimate of hazard function based on retrospectively reported duration data that can address the problem of heaping due to recall errors. Following Ramlau-Hansen (1983), smooth estimate of hazard of weaning is obtained by smoothing the increments of Nelson-Aalen (NA) cumulative hazard function estimate and illustrated using duration of breastfeeding data for six North Eastern states of India from the last two National Family and Health Surveys. Approximate bias and 95% confidence interval for these estimates are also obtained using their respective asymptotic expressions. Further, under additive error model, a kernel-type deconvolving density estimator (Wand and Jones, 1995) of durations of breastfeeding is proposed by smoothing the increments of Kaplan-Meier (KM) cumulative distribution function. Using simulated data it has been shown that in small and moderately censored samples these estimators can reduce the bias substantially.