Quasi-likelihood estimation for relative risk regression models
Quasi-likelihood estimation for relative risk regression models
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DOI：
10.1093/biostatistics/kxh016
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发表时间：
2005-01-01
期刊：
影响因子：
2.1
通讯作者：
Tilley, BC
中科院分区：
文献类型：
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作者：
Carter, RE;Lipsitz, SR;Tilley, BC
对于两组的前瞻性随机临床试验，相对菲斯克可用作治疗效果的测量，并可直接解释为新治疗组与安慰剂组的成功概率比。对于具有许多协变量和二元结果（成功或失败）的前瞻性研究，可能需要进行相对风险回归。如果我们将成功概率的对数建模为协变量的线性函数，则回归系数是对数相关风险。然而.使用这种具有伯努利似然的对数线性模型可能导致Newton-Raphson算法的收敛问题。当成功概率接近1时，可能会发生这种情况。Wacholder（1986，American Journal of Epidemiology 123）提出的约束似然方法。174-184）。也存在收敛问题。我们提出了一个准似然矩技术方法，其中我们天真地假设伯努利结果是泊松，与平均值（成功概率）遵循对数线性模型。我们使用泊松最大似然方程估计回归系数没有约束。利用矩量法的思想，可以证明他使用泊松似然估计将是一致的和渐近正态的。我们将这些方法应用于原发性胆汁性肝硬化的双盲随机试验。
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.