The role of frailty models and accelerated failure time models in describing heterogeneity due to omitted covariates.

In survival analysis, deviations from proportional hazards may sometimes be explained by unaccounted random heterogeneity, or frailty. This paper recalls the literature on omitted covariates in survival analysis and shows in a case study how unstably frailty models might behave when asked to account for unobserved heterogeneity in standard survival analysis with no replications per heterogeneity unit. Accelerated failure time modelling seems to avoid these difficulties and also to yield easily interpretable results. We propose that it would be advantageous to upgrade the accelerated failure time approach alongside the hazard modelling approach to survival analysis.

[1]  Susan A. Murphy,et al.  Asymptotic Theory for the Frailty Model , 1995 .

[2]  P. Hougaard,et al.  Frailty models for survival data , 1995, Lifetime data analysis.

[3]  A. Yashin,et al.  Correlated individual frailty: an advantageous approach to survival analysis of bivariate data. , 1995, Mathematical population studies.

[4]  John P. Klein,et al.  Estimation of variance in Cox ' s regression model with gamma frailties , 1995 .

[5]  K Borch-Johnsen,et al.  Heterogeneity models of disease susceptibility, with application to diabetic nephropathy. , 1994, Biometrics.

[6]  O. Aalen.  Effects of frailty in survival analysis , 1994, Statistical methods in medical research.

[7]  Susan A. Murphy,et al.  Consistency in a Proportional Hazards Model Incorporating a Random Effect , 1994 .

[8]  Covariates in Clinical Trials: Effects of Adjustment in Regression Models , 1994 .

[9]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

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

[11]  J. Klein,et al.  Estimating Random Effects In the Framingham Heart Study , 1992 .

[12]  Bruce W. Turnbull,et al.  Multivariate Failure Time Analysis: A Discussion of Papers by Oakes; Pons, Kaddour and De Turckheim; and Prentice and Cai , 1992 .

[13]  Jianwen Cai,et al.  Marginal and Conditional Models for the Analysis of Multivariate Failure Time Data , 1992 .

[14]  Odile Pons,et al.  A Nonparametric Approach To Dependence For Bivariate Censored Data , 1992 .

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

[16]  David Oakes,et al.  Frailty Models For Multiple Event Times , 1992 .

[17]  P. Hougaard.  Modelling heterogeneity in survival data , 1991, Journal of Applied Probability.

[18]  S Greenland,et al.  Estimability and estimation of expected years of life lost due to a hazardous exposure. , 1991, Statistics in medicine.

[19]  S Greenland,et al.  The probability of causation under a stochastic model for individual risk. , 1989, Biometrics.

[20]  Ker-Chau Li,et al.  Regression Analysis Under Link Violation , 1989 .

[21]  R. Prentice,et al.  Further results on covariate measurement errors in cohort studies with time to response data. , 1989, Statistics in medicine.

[22]  O. Aalen.  A linear regression model for the analysis of life times. , 1989, Statistics in medicine.

[23]  S. Piantadosi,et al.  A quantitative study of the bias in estimating the treatment effect caused by omitting a balanced covariate in survival models. , 1988, Statistics in medicine.

[24]  C. Huber-Carol,et al.  Effects of omitting covariates in Cox's model for survival data , 1988 .

[25]  M. Schumacher,et al.  The impact of heterogeneity on the comparison of survival times. , 1987, Statistics in medicine.

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

[27]  John D. Kalbfleisch,et al.  Misspecified proportional hazard models , 1986 .

[28]  J. Bretagnolle,et al.  Sous estimation des contrastes due à l'oubli de variables pertinentes dans le modèle de cox pour les durées de survie avec censure , 1985 .

[29]  M. Gail,et al.  Biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates , 1984 .

[30]  Patricia J. Solomon,et al.  Effect of misspecification of regression models in the analysis of survival data , 1984 .

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