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Analysis of two-sample truncated data using generalized logistic models

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  • Li, Gang
  • Qin, Jing

Abstract

Parallel to Cox's [JRSS B34 (1972) 187-230] proportional hazards model, generalized logistic models have been discussed by Anderson [Bull. Int. Statist. Inst. 48 (1979) 35-53] and others. The essential assumption is that the two densities ratio has a known parametric form. A nice property of this model is that it naturally relates to the logistic regression model for categorical data. In astronomic, demographic, epidemiological, and other studies the variable of interest is often truncated by an associated variable. This paper studies generalized logistic models for the two-sample truncated data problem, where the two lifetime densities ratio is assumed to have the form exp{[alpha]+[phi](x;[beta])}. Here [phi] is a known function of x and [beta], and the baseline density is unspecified. We develop a semiparametric maximum likelihood method for the case where the two samples have a common truncation distribution. It is shown that inferences for [beta] do not depend the nonparametric components. We also derive an iterative algorithm to maximize the semiparametric likelihood for the general case where different truncation distributions are allowed. We further discuss how to check goodness of fit of the generalized logistic model. The developed methods are illustrated and evaluated using both simulated and real data.

Suggested Citation

  • Li, Gang & Qin, Jing, 2006. "Analysis of two-sample truncated data using generalized logistic models," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 675-697, March.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:3:p:675-697
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    References listed on IDEAS

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    1. Barry E. Storer & Sholom Wacholder & Norman E. Breslow, 1983. "Maximum Likelihood Fitting of General Risk Models to Stratified Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 172-181, June.
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    Cited by:

    1. Zhang, Archer Gong & Chen, Jiahua, 2022. "Density ratio model with data-adaptive basis function," Journal of Multivariate Analysis, Elsevier, vol. 191(C).

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