title: Model inconsistency, illustrated by the Cox proportional hazards model.
abstract: We consider problems involving the comparison of two or more treatments where we have the opportunity to adjust for relevant covariates either conditionally in a regression model or implicitly in repeated measures data, for example, in crossover trials. It is seen that for data arising from non-Normal distributions there is the possibility that models adjusting for covariates and those not adjusting for covariates will be inconsistent, that is, at most one of the models can be valid. Alternatively, even if conditional and unconditional models are valid, parameters in each model may have different interpretations. We note that this presents difficulties for the specification and interpretation of the analysis. It is also clear that model validation is critical. Specific attention is paid to survival data analysed by the Cox proportional hazards model.
authors.affiliation: Robertson Centre for Biostatistics, Glasgow University, U.K.
authors.forename: I
authors.initials: I
authors.lastname: Ford
authors.forename: J
authors.initials: J
authors.lastname: Norrie
authors.forename: S
authors.initials: S
authors.lastname: Ahmadi
mesh_terms: D000704:Analysis of Variance; D015982:Bias; D018592:Cross-Over Studies; D003627:Data Interpretation, Statistical; D015987:Effect Modifier, Epidemiologic; D016014:Linear Models; D016015:Logistic Models; D016011:Normal Distribution; D016016:Proportional Hazards Models; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D015203:Reproducibility of Results; D012107:Research Design; D016019:Survival Analysis