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Maximum Likelihood Estimation of Logistic Regression Parameters under Two‐phase, Outcome‐dependent Sampling

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  • Norman E. Breslow
  • Richard Holubkov

Abstract

Outcome‐dependent sampling increases the efficiency of studies of rare outcomes, examples being case—control studies in epidemiology and choice–based sampling in econometrics. Two‐phase or double sampling is a standard technique for drawing efficient stratified samples. We develop maximum likelihood estimation of logistic regression coefficients for a hybrid two‐phase, outcome–dependent sampling design. An algorithm is given for determining the estimates by repeated fitting of ordinary logistic regression models. Simulation results demonstrate the efficiency loss associated with alternative pseudolikelihood and weighted likelihood methods for certain data configurations. These results provide an efficient solution to the measurement error problem with validation sampling based on a discrete surrogate.

Suggested Citation

  • Norman E. Breslow & Richard Holubkov, 1997. "Maximum Likelihood Estimation of Logistic Regression Parameters under Two‐phase, Outcome‐dependent Sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 447-461.
    • Handle: RePEc:bla:jorssb:v:59:y:1997:i:2:p:447-461
    DOI: 10.1111/1467-9868.00078
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    Cited by:

    1. Brady Ryan & Ananthika Nirmalkanna & Candemir Cigsar & Yildiz E. Yilmaz, 2023. "Evaluation of Designs and Estimation Methods Under Response-Dependent Two-Phase Sampling for Genetic Association Studies," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 510-539, July.
    2. Jichang Yu & Haibo Zhou & Jianwen Cai, 2021. "Accelerated failure time model for data from outcome-dependent sampling," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 15-37, January.

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