Outcome-dependent randomisation schemes for clinical trials with fluctuations in patient characteristics
A clinical trial is considered in which two treatments are to be compared. Treatment allocation schemes are usually designed to assign approximately equal numbers of patients to each treatment. The purpose of this thesis is to investigate the efficiency of estimation and the effect of instability in the response variable for allocation schemes which are aimed at reducing the number of patients who receive the inferior treatment. The general background to outcome-dependent allocation schemes is described in Chapter 1. A discussion of ethical and practical problems associated with these methods is presented together with brief details of actual trials conducted. In Chapter 2, the response to treatment is Bernoulli and the trial size is fixed. A simple method for estimating the treatment difference is proposed. Simulation results for a selection of allocation schemes indicate that the effect of instability upon the performance of the schemes can sometimes be substantial. A decision-theory approach is taken in Chapter 3. The trial is conducted in a number of stages and the interests of both the patients in the trial and those who will be treated after the end of the trial are taken into account. Using results for conditional normal distributions, analytical results are derived for estimation of the treatment difference for both a stable and an unstable normal response variable for three allocation schemes. Some results for estimation are also given for other responses. The problem of sequential testing is addressed in Chapter 4. With instability in the response variable, it is shown that the error probabilities for the test for a stable response variable can be approximately preserved by using a modified test statistic with appropriately-widened stopping boundaries. In addition, some recent results for estimation following sequential tests are outlined. Finally, the main conclusions of the thesis are highlighted in Chapter 5.