Multilevel Models for Survival Analysis with Random Effects

Summary. A method for modeling survival data with multilevel clustering is described. The Cox partial likelihood is incorporated into the generalized linear mixed model (GLMM) methodology. Parameter estimation is achieved by maximizing a log likelihood analogous to the likelihood associated with the best linear unbiased prediction (BLUP) at the initial step of estimation and is extended to obtain residual maximum likelihood (REML) estimators of the variance component. Estimating equations for a three‐level hierarchical survival model are developed in detail, and such a model is applied to analyze a set of chronic granulomatous disease (CGD) data on recurrent infections as an illustration with both hospital and patient effects being considered as random. Only the latter gives a significant contribution. A simulation study is carried out to evaluate the performance of the REML estimators. Further extension of the estimation procedure to models with an arbitrary number of levels is also discussed.

[1]  David R. Cox,et al.  Regression models and life tables (with discussion , 1972 .

[2]  N. Breslow.  Covariance analysis of censored survival data. , 1974, Biometrics.

[3]  C. R. Henderson,et al.  Best linear unbiased estimation and prediction under a selection model. , 1975, Biometrics.

[4]  Robin Thompson.  Maximum likelihood estimation of variance components , 1980 .

[5]  Rupert G. Miller,et al.  Survival Analysis , 2022, The SAGE Encyclopedia of Research Design.

[6]  Philip Hougaard,et al.  Life table methods for heterogeneous populations: Distributions describing the heterogeneity , 1984 .

[7]  P. Hougaard.  A class of multivanate failure time distributions , 1986 .

[8]  P. Hougaard.  Survival models for heterogeneous populations derived from stable distributions , 1986 .

[9]  William H. Fellner,et al.  Sparse matrices, and the estimation of variance components by likelihood methods , 1987 .

[10]  R. Schall.  Estimation in generalized linear models with random effects , 1991 .

[11]  D G Clayton,et al.  A Monte Carlo method for Bayesian inference in frailty models. , 1991, Biometrics.

[12]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[13]  Robert Gray,et al.  Flexible Methods for Analyzing Survival Data Using Splines, with Applications to Breast Cancer Prognosis , 1992 .

[14]  Richard D. Gill,et al.  A counting process approach to maximum likelihood estimation in frailty models , 1992 .

[15]  J P Klein,et al.  Semiparametric estimation of random effects using the Cox model based on the EM algorithm. , 1992, Biometrics.

[16]  C A McGilchrist.  REML estimation for survival models with frailty. , 1993, Biometrics.

[17]  McGilchrist Ca.  REML estimation for survival models with frailty. , 1993 .

[18]  N. Breslow,et al.  Approximate inference in generalized linear mixed models , 1993 .

[19]  M. Tanner,et al.  Maximization of the marginal likelihood of grouped survival data , 1994 .

[20]  C. Mcgilchrist.  Estimation in Generalized Mixed Models , 1994 .

[21]  D. Lin,et al.  Cox regression analysis of multivariate failure time data: the marginal approach. , 1994, Statistics in medicine.

[22]  C. Mcgilchrist,et al.  The derivation of blup, ML, REML estimation methods for generalised linear mixed models , 1995 .

[23]  J. Nelder,et al.  Hierarchical Generalized Linear Models , 1996 .

[24]  T M Therneau,et al.  rhDNase as an example of recurrent event analysis. , 1997, Statistics in medicine.

[25]  J. Klein,et al.  Survival Analysis: Techniques for Censored and Truncated Data , 1997 .

[26]  V. Yohai,et al.  Robust estimation of variance components , 1998 .

[27]  M. Kenward,et al.  Contribution to the discussion of the paper by Diggle, Tawn and Moyeed , 1998 .

[28]  C. Mcgilchrist,et al.  ML and REML estimation in survival analysis with time dependent correlated frailty. , 1998, Statistics in medicine.

[29]  D.,et al.  Regression Models and Life-Tables , 2022 .