期刊
BIOSTATISTICS
卷 6, 期 1, 页码 39-44出版社
OXFORD UNIV PRESS
DOI: 10.1093/biostatistics/kxh016
关键词
Bernoulli likelihood; constrained MLE; convergence problems; method-of-momentsms; Poisson regresison
资金
- AGENCY FOR HEALTHCARE RESEARCH AND QUALITY [P01HS010871] Funding Source: NIH RePORTER
- NATIONAL CANCER INSTITUTE [R01CA070101] Funding Source: NIH RePORTER
- NATIONAL HEART, LUNG, AND BLOOD INSTITUTE [R01HL069800] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE ON DRUG ABUSE [U10DA013727] Funding Source: NIH RePORTER
- AHRQ HHS [HS 10871] Funding Source: Medline
- NCI NIH HHS [CA 70101] Funding Source: Medline
- NHLBI NIH HHS [HL69800] Funding Source: Medline
- NIDA NIH HHS [1 U10 DA013727] Funding Source: Medline
For a prospective randomized clinical trial with two groups, the relative fisk can be used as a measure of treatment effect and is directly interpretable as the ratio of success probabilities in the new treatment group versus the placebo group. For a prospective study with many covariates and a binary outcome (success or failure), relative risk regression may be of interest. If we model the log of the success probability as a linear function of covariates, the regression coefficients are log-relative risks. However. using such a log-linear model with a Bernoulli likelihood can lead to convergence problems in the Newton-Raphson algorithm. This is likely to occur when the success probabilities are close to one. A constrained likelihood method proposed by Wacholder (1986, American Journal of Epidemiology 123. 174-184). also has convergence problems. We propose a quasi-likelihood method of moments technique in which we naively assume the Bernoulli outcome is Poisson, with the mean (success probability) following a log-linear model. We use the Poisson maximum likelihood equations to estimate the regression coefficients without constraints. Using method of moment ideas, one can show that he estimates using the Poisson likelihood will be consistent and asymptotically normal. We apply these methods to a double-blinded randomized trial in primary biliary cirrhosis of the liver.
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