title: Influence of trial duration on the bias of the estimated treatment effect in clinical trials when individual heterogeneity is ignored.
abstract: In randomized clinical trials where the times to event of two treatment groups are compared under a proportional hazards assumption, it has been established that omitting prognostic factors from the model entails an underestimation of the hazards ratio. Heterogeneity due to unobserved covariates in cancer patient populations is a concern since genomic investigations have revealed molecular and clinical heterogeneity in these populations. In HIV prevention trials, heterogeneity is unavoidable and has been shown to decrease the treatment effect over time. This article assesses the influence of trial duration on the bias of the estimated hazards ratio resulting from omitting covariates from the Cox analysis. The true model is defined by including an unobserved random frailty term in the individual hazard that reflects the omitted covariate. Three frailty distributions are investigated: gamma, log-normal, and binary, and the asymptotic bias of the hazards ratio estimator is calculated. We show that the attenuation of the treatment effect resulting from unobserved heterogeneity strongly increases with trial duration, especially for continuous frailties that are likely to reflect omitted covariates, as they are often encountered in practice. The possibility of interpreting the long-term decrease in treatment effects as a bias induced by heterogeneity and trial duration is illustrated by a trial in oncology where adjuvant chemotherapy in stage 1B NSCLC was investigated.
authors.affiliation: Inserm U1018, CESP Centre for Research in Epidemiology and Population Health, Villejuif, France; Faculté de Médecine, University Paris-Sud, Le Kremlin-Bicêtre, France.
authors.forename: Elsa
authors.initials: E
authors.lastname: Cécilia-Joseph
authors.forename: Bertran
authors.initials: B
authors.lastname: Auvert
authors.forename: Philippe
authors.initials: P
authors.lastname: Broët
authors.forename: Thierry
authors.initials: T
authors.lastname: Moreau
mesh_terms: D000970:Antineoplastic Agents / Q000627:therapeutic use*; D015982:Bias; D002289:Carcinoma, Non-Small-Cell Lung / Q000188:drug therapy* / Q000453:epidemiology; D002986:Clinical Trials as Topic / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D008137:Longitudinal Studies; D008175:Lung Neoplasms / Q000188:drug therapy* / Q000453:epidemiology; D015233:Models, Statistical; D010043:Outcome and Process Assessment, Health Care / Q000379:methods*; D015995:Prevalence; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity; D016896:Treatment Outcome
chemical_list: D000970:Antineoplastic Agents
keywords: Clinical trials; Cox model; Frailty; Heterogeneity; Omitted covariates