期刊
INTERNATIONAL JOURNAL OF BIOSTATISTICS
卷 6, 期 1, 页码 -出版社
WALTER DE GRUYTER GMBH
DOI: 10.2202/1557-4679.1138
关键词
misspecified model; targeted maximum likelihood; generalized linear model; Poisson regression
资金
- Ruth L. Kirschstein National Research Service (NRSA) under NIH/NIMH [5 T32 MH-19105-19]
- NIH [R01 AI074345-04]
- NATIONAL INSTITUTE OF ALLERGY AND INFECTIOUS DISEASES [R01AI074345] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF MENTAL HEALTH [T32MH019105] Funding Source: NIH RePORTER
Models, such as logistic regression and Poisson regression models, are often used to estimate treatment effects in randomized trials. These models leverage information in variables collected before randomization, in order to obtain more precise estimates of treatment effects. However, there is the danger that model misspecification will lead to bias. We show that certain easy to compute, model-based estimators are asymptotically unbiased even when the working model used is arbitrarily misspecified. Furthermore, these estimators are locally efficient. As a special case of our main result, we consider a simple Poisson working model containing only main terms; in this case, we prove the maximum likelihood estimate of the coefficient corresponding to the treatment variable is an asymptotically unbiased estimator of the marginal log rate ratio, even when the working model is arbitrarily misspecified. This is the log-linear analog of ANCOVA for linear models. Our results demonstrate one application of targeted maximum likelihood estimation.
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