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Parametric Estimation of Menarcheal Age Distribution Based on Recall Data

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  • Sedigheh Mirzaei Salehabadi
  • Debasis Sengupta
  • Rituparna Das

Abstract

type="main" xml:id="sjos12107-abs-0001"> Menarche, the onset of menstruation, is an important maturational event of female childhood. Most of the studies of age at menarche make use of dichotomous (status quo) data. More information can be harnessed from recall data, but such data are often censored in a informative way. We show that the usual maximum likelihood estimator based on interval censored data, which ignores the informative nature of censoring, can be biased and inconsistent. We propose a parametric estimator of the menarcheal age distribution on the basis of a realistic model of the recall phenomenon. We identify the additional information contained in the recall data and demonstrate theoretically as well as through simulations the advantage of the maximum likelihood estimator based on recall data over that based on status quo data.

Suggested Citation

  • Sedigheh Mirzaei Salehabadi & Debasis Sengupta & Rituparna Das, 2015. "Parametric Estimation of Menarcheal Age Distribution Based on Recall Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 290-305, March.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:1:p:290-305
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    File URL: http://hdl.handle.net/10.1111/sjos.12107
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    References listed on IDEAS

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    1. Daniel O. Scharfstein, 2002. "Estimation of the failure time distribution in the presence of informative censoring," Biometrika, Biometrika Trust, vol. 89(3), pages 617-634, August.
    2. J. Udry & R. Cliquet, 1982. "A cross-cultural examination of the relationship between ages at menarche, marriage, and first birth," Demography, Springer;Population Association of America (PAA), vol. 19(1), pages 53-63, February.
    3. Daniel Scharfstein & James M. Robins & Wesley Eddings & Andrea Rotnitzky, 2001. "Inference in Randomized Studies with Informative Censoring and Discrete Time-to-Event Endpoints," Biometrics, The International Biometric Society, vol. 57(2), pages 404-413, June.
    4. David B. Dunson & Gregg E. Dinse, 2002. "Bayesian Models for Multivariate Current Status Data with Informative Censoring," Biometrics, The International Biometric Society, vol. 58(1), pages 79-88, March.
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    1. Sedigheh Mirzaei Salehabadi & Debasis Sengupta, 2016. "Nonparametric estimation of time-to-event distribution based on recall data in observational studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 473-503, October.
    2. Mirzaei Salehabadi, Sedigheh & Sengupta, Debasis, 2015. "Regression under Cox’s model for recall-based time-to-event data in observational studies," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 134-147.

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