Nonparametric estimation of time-to-event distribution based on recall data in observational studies

Sedigheh Mirzaei Salehabadi () and Debasis Sengupta ()
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Sedigheh Mirzaei Salehabadi: Indian Statistical Institute
Debasis Sengupta: Indian Statistical Institute

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2016, vol. 22, issue 4, No 1, 473-503

Abstract: Abstract In a cross-sectional observational study, time-to-event distribution can be estimated from data on current status or from recalled data on the time of occurrence. In either case, one can treat the data as having been interval censored, and use the nonparametric maximum likelihood estimator proposed by Turnbull (J R Stat Soc Ser B 38:290–295, 1976). However, the chance of recall may depend on the time span between the occurrence of the event and the time of interview. In such a case, the underlying censoring would be informative, rendering the Turnbull estimator inappropriate. In this article, we provide a nonparametric maximum likelihood estimator of the distribution of interest, by using a model adapted to the special nature of the data at hand. We also provide a computationally simple approximation of this estimator, and establish the consistency of both the original and the approximate versions, under mild conditions. Monte Carlo simulations indicate that the proposed estimators have smaller bias than the Turnbull estimator based on incomplete recall data, smaller variance than the Turnbull estimator based on current status data, and smaller mean squared error than both of them. The method is applied to menarcheal data from a recent Anthropometric study of adolescent and young adult females in Kolkata, India.

Keywords: Informative censoring; Interval censoring; Nonparametric maximum likelihood estimator; Self consistency algorithm; Turnbull estimator (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10985-015-9345-9

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