##### Department of Mathematics,

University of California San Diego

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### Biostatistics

## Ronghui Xu

#### Harvard School of Public Health and Dana-Farber Cancer Institute

## Proportional Hazards Model with Mixed Effects

##### Abstract:

In this talk we describe our work on proportional hazards model with mixed effects (PHMM) for right-censored data. Our motivation came from a multi-center clinical trial in lung cancer, where treatment effects were found to vary substantially among the centers. We provide a general framework for handling random effects in proportional hazards regression, in a way similar to the linear, non-linear and generalized linear mixed effects models that allow random effects of arbitrary covariates. This general framework includes the frailty models as a special case. Semi parametric maximum likelihood estimates of the regression parameters, the variance components and the baseline hazard, and empirical Bayes estimates of the random effects can be obtained via an MCEM algorithm. Variances of the parameter estimates are approximated using Louis formula. The model found interesting applications in recurrent events, twin data and genetic epidemiology. Following the introduction of the model, our recent work has included topics on model diagnostics and model selection. We will elaborate on one of these topics during the talk.

Host: Ian Abramson

### March 15, 2004

### 11:00 AM

### AP&M 7321

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