EXAMPLE
CANMAT
DISEASE, RECRUITMENT
To demonstrate how to compute estimates in Sections The CANMAT trial had severe recruitment challenges and if this is typical for trials in this disease, clinical trials in this condition could benefit from two‐stage adaptive designs because, for example, it offers opportunity to stop early for futility. The CANMAT trial recruited from 17 sites in Canada and Brazil. The target sample size was 180 patients per group however the trial stopped after a total of 159 patients (52, 54, and 53 in control and treatments 1 and 2, respectively) because of slower recruitment than anticipated and funding expiry.Worked example estimates based on Cox's proportional hazards modelAbbreviation: HR, Hazard ratio.
In the constructed phase II/III clinical trial, we assume uniform recruitment and since the CANMAT trial had recruitment difficulties, that this is over three years. We assume 1:1:1 random allocation for the control, treatments 1 and 2 within blocks of size three. Allocation of patients from each treatment, for example 52 patients for control, to different blocks was random with equal probability.Figure Constructed two‐stage trial based on CANMAT trial. Vertical lines correspond to key timepoints in the design. A horizontal line ending with a circle corresponds to a patient with the left hand side edge being parallel to time of recruitmentment. A filled circle corresponds to time of relapse whilst a nonfilled circle indicates that a relapse has not yet occurred at that key timepoint in the design. Lines with a continuous segment correspond to stage 1 patients whilst dotted lines correspond to stage 2 patientsFor the follow up in stage 2 of stage 1 patients who have not relapsed at the interim analysis, from recruitment, the natural choice is to follow them for 52 weeks which was the maximum follow up of patients in the CANMAT trial.The constructed phase II/III clinical trial data, their format and the R code used to compute various estimates are in the repository “Bias adjusted estimates are given in Table Covariance of stage 1 log hazard ratios estimates is 0.0522 (correlation is 0.4377). The joint density of stage 1 treatments 1 and 2 log HR estimates, the expression for probability of continuing to stage 2 with both treatments and the expressions for the expected values for the two log HRs are given in the Supplementary Material. Using those expressions and expressions (For the shrinkage estimator, we take The shrinkage estimates show slightly bigger treatment effects than the naive estimates (in Table 