Correlated Binary and Survival Data Analysis参考.pptx

Correlated Binary and Survival Data AnalysisCorrelated Binary and SurvivalCorrelated binary and survival response data can occur in similar condition as correlated continuous response. Cardiovscular disease in for individuals coming from several familiesSurvival time for patients coming from several institutions Methods for Correlated Binary ResponsesGeneralized mixed effects model (GLMM)Generalized estimating equations (GEE)Generalized Linear Mixed Effects ModelsGeneralized mixed effects models (GLMMs) are generalized linear models with fixed and random effects as covariates. These models are useful for correlated non-normal response.The model notations are as follows: Conditional on fixed random effects,the probability of observing an event for jth subject in ith cluster is Example:Dataset Bacteria: Tests of the presence of the bacteria _H. influenzae_ in children with otitis media (middle ear infection) in the Northern Territory of Australia.Data were recorded on weeks 0,2,4,6 and 11 on 50 subjects. Data were missing for 30 observations. The response is presence/absence of a particular bacteria. There are three treatments, placebo, drug with and without extra effort on compliance (drug vs. drug+). It is expected that the response declines with time, and perhaps treatment.Variables in this dataset are:ypresence or absence: a factor with levels n and y.ap active treatment/placebo: a factor with levels a and p.hilo hi/low compliance in treatment : a factor with levels hi amd lo.week week of test.IDsubject ID: a factor.trt a factor recoding ap and hilo with levels placebo, drug and drug+‘ (drug with ap=“a” and hilo=“hi”)library(MASS) bacteria[1:10,] y ap hilo week IDtrt1 y p hi 0 X01 placebo2 y p hi 2 X01 placebo3 y p hi 4 X01 placebo4 y p hi 11 X01 placebo5 y a hi 0 X02drug+6 y a hi 2 X02drug+7 n a hi 6 X02drug+8 y a hi 11 X02drug+9 y a lo 0 X03 drug10 y a lo 2 X03 drug ?dim(bacteria)[1] 2