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Analysis and asymptotic theory for nested case–control designs under highly stratified proportional hazards models

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  • Larry Goldstein

    (University of Southern California)

  • Bryan Langholz

    (University of Southern California)

Abstract

Nested case–control sampled event time data under a highly stratified proportional hazards model, in which the number of strata increases proportional to sample size, is described and analyzed. The data can be characterized as stratified sampling from the event time risk sets and the analysis approach of Borgan et al. (Ann Stat 23:1749–1778, 1995) is adapted to accommodate both the stratification and case–control sampling from the stratified risk sets. Conditions for the consistency and asymptotic normality of the maximum partial likelihood estimator are provided and the results are used to compare the efficiency of the stratified analysis to an unstratified analysis when the baseline hazards can be semi-parametrically modeled in two special cases. Using the stratified sampling representation of the stratified analysis, methods for absolute risk estimation described by Borgan et al. (1995) for nested case–control data are used to develop methods for absolute risk estimation under the stratified model. The methods are illustrated by a year of birth stratified analysis of radon exposure and lung cancer mortality in a cohort of uranium miners from the Colorado Plateau.

Suggested Citation

  • Larry Goldstein & Bryan Langholz, 2023. "Analysis and asymptotic theory for nested case–control designs under highly stratified proportional hazards models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 342-371, April.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:2:d:10.1007_s10985-022-09582-4
    DOI: 10.1007/s10985-022-09582-4
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    References listed on IDEAS

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    1. Bryan Langholz & Duncan C. Thomas & Marilyn Stovall & Susan A. Smith & John D. Boice Jr. & Roy E. Shore & Leslie Bernstein & Charles F. Lynch & Xinbo Zhang & Jonine L. Bernstein, 2009. "Statistical Methods for Analysis of Radiation Effects with Tumor and Dose Location-Specific Information with Application to the WECARE Study of Asynchronous Contralateral Breast Cancer," Biometrics, The International Biometric Society, vol. 65(2), pages 599-608, June.
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