Proportional hazards models for current status data: Application to the study of differentials in age at weaning in Pakistan

One common variable of interest in many areas of demographic research is the age at which a certain event or "milestone" occurs, for example, age at weaning, menarche, first intercourse, first marriage, menopause, or death. Data on the age at which a milestone occurs are usually collected retrospectively by surveyor census. Unfortunately, retrospective age data may contain serious reporting errors of unknown size and direction that result from such factors as the fallibility of memory and age-heaping. These age reporting errors may be especially severe in cultures in which age is relatively unimportant. Rather than base an analysis on unreliable reported age at the time of the event data, many analysts prefer to base an analysis on reliable current status data, that is, on the occurrence or nonoccurrence of the event at the time of the surveyor census, when the date of birth data are felt to be relatively reliably reported. Since age data are usually collected in the form of completed years or years and completed months of age and are often grouped for analysis, only the grouped data case will be discussed. The methods of survival analysis can be used to study the association between explanatory variables and the age at which the event of interest occurs. This paper shows how to fit a nonparametric proportional hazards model to current status data. Unfortunately, the computational cost of model fitting and screening becomes prohibitive in certain situations. Therefore, we address the important question of whether a more complete but flexible specification of the baseline hazard function using splines may reduce the computational cost to manageable size by reducing the number of parameters that need to be estimated while retaining the essential nonparametric representation of the baseline hazard function. The advantages and disadvantages of each model are discussed and their use in practice is compared by fitting both models to World Fertility Survey data on age at weaning in Pakistan

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