On partial likelihood
本文梳理了偏似然与复合似然、轮廓似然、边际似然和条件似然之间的联系，并简要讨论了Cox比例风险模型在医学中的两个近期应用。
Abstract Partial likelihood, introduced in Cox (1975, Partial likelihood. Biometrika, 62(2),269–276), formalizes the construction of the inference function developed in Cox (1972, Regression models and life-tables (with discussion). Journal of the Royal Statistical Society Series B, 34(2),187–220) and referred there to as a conditional likelihood. Partial likelihood can also be viewed as a version of composite likelihood, a different example of which was studied in Cox, and Reid (2004, A note on pseudolikelihood constructed from marginal densities. Biometrika, 91(3),729–737). In this note, I describe the links between partial and composite likelihood, and the connections to profile, marginal, and conditional likelihood. Somewhat tangentially, two recent applications of the Cox proportional hazards model from the medical literature are briefly discussed, as they highlight the model’s ongoing relevance while also raising some more general questions about inference.