TABLE OF CONTENTS Trials often include covariates with values that do not remain fixed over time. It is tempting, therefore, to consider making allowance for the changes in such variables by taking repeated measures of them during the operation of the trial and by fitting a model that uses these updated covariate values. In fact, this is simply done, merely requiring the survival period of each patient to be divided up into a sequence of shorter survival spells, each characterised by an entry time and an exit time, and within which covariate values remain fixed. Thus the data for each patient is represented by a number of shorter censored spells and possibly one spell ending in failure/death. Datasets can be constructed in exactly this form, each record representing one spell and containing, an entry time, an exit time, and a censoring indicator together with the then current covariate values. With multiple spells per patient, the file thus contains multiple records per patient.
Time-varying covariates are especially tractable within the Cox model. Inspection of Table 8.4 shows how the partial likelihood involves contributions for the conditional probability of failure. These conditional probabilities involve the covariate values that apply at the time of each failure only. The values of the covariates between failure times do not enter the partial likelihood. All that is required is that contemporaneous rather than baseline values of covariates be assigned to each risk set, making the Cox model with time-varying covariates little...
