Simulations

We compared the performance of models M2 with M4 and M3 with M5 by simulating a large number of trials from each model. An MCMC sampler based on the Metropolis-Hastings algorithm (Metropolis et al., 1953; Hastings, 1970) was devised to estimate features of the marginal posterior distribution of y . For each of the above four models, we simulated 5000 trials, each consisting of n = 30 patients. Comparisons of these models were based on the proportion of patients that were assigned dose levels higher than the MTD, the proportion of patients exhibiting DLT, the average bias and the estimated MSE. We found that on the average, fewer patients were overdosed under M4 compared to M2 whereas the proportions of patients exhibiting dose limiting toxicity were about the same under these two models. The efficiency of the estimated MTD as measured by the root mean square error was about the same on the average. Based on the above remarks, we recommend the use of model M4 with our proposed a priori correlation structure between p0 and y ; while the efficiency of the estimated MTD is about the same under the two models; fewer patients are overdosed under model M4. Under models M3 and M5, the prior distribution of the probability of dose-limiting toxicity at the initial dose is more concentrated toward zero. Since p0 and y are negatively correlated a priori under model M5, this resulted in more patients being overdosed and exhibiting DLT under this model compared to model M3. In other words, model M5 uses a more aggressive scheme in search of the MTD. On the other hand, model M5 performs much better in terms of the efficiency of the estimated MTD. Details on the above simulations can be found in Tighiouart et al. (2005).

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