Multivariate Markov models for the conditional probability of toxicity in phase II trials

In addition to getting a preliminary assessment of efficacy, phase II trials can also help to determine dose(s) that have an acceptable toxicity profile over repeated cycles as well as identify subgroups with particularly poor toxicity profiles. Correct modeling of the dose-toxicity relationship in patients receiving multiple cycles of the same dose in oncology trials is crucial. A major challenge lies in taking advantage of the conditional nature of data collection, that is each cycle is observed conditional on having no previous toxicities on earlier cycles. We develop a novel and parsimonious model for the probability of toxicity during a kth cycle of therapy, conditional on not seeing toxicity in any of the k-1 previous cycles using a Markov model, hereafter we refer to these probabilities as conditional probabilities of toxicity. Our model allows the conditional probability of toxicity to depend on randomized dose group, cumulative dose from prior cycles, a measure of how consistently a patient responds to the same dose exposure and individual risk factors influencing the ability to tolerate the treatment regimen. Simulations studying finite sample properties of the model are given. Finally, the approach is demonstrated in a phase II trial studying two dose levels of ifosfamide plus doxorubicin and granulocyte colony-stimulating factor in soft tissue sarcoma patients over four cycles. The Markov model provides correct estimates of the probabilities of toxicity in finite sample simulations. It also correctly models the data from the phase II clinical trial, and identifies particularly high cumulative toxicity in females.