Multinomial N-mixture models for removal sampling.

Multinomial -mixture models are commonly used to fit data from a removal sampling protocol. If the mixing distribution is negative binomial, the distribution of the counts does not appear to have been identified, and practitioners approximate the requisite likelihood by placing an upper bound on the embedded infinite sum. In this paper, the distribution which underpins the multinomial -mixture model with a negative binomial mixing distribution is shown to belong to the broad class of multivariate negative binomial distributions.

Maximum likelihood estimation for N-mixture models.

The focus of this article is on the nature of the likelihood associated with N-mixture models for repeated count data. It is shown that the infinite sum embedded in the likelihood associated with the Poisson mixing distribution can be expressed in terms of a hypergeometric function and, thence, in closed form. The resultant expression for the likelihood can be readily computed to a high degree of accuracy and is algebraically tractable.

Start-up designs for response-adaptive randomization procedures with sequential estimation.

Response-adaptive randomization procedures are appropriate for clinical trials in which two or more treatments are to be compared, patients arrive sequentially and the response of each patient is recorded before the next patient arrives. However, for those procedures that involve sequential estimation of model parameters, start-up designs are commonly required in order to provide initial estimates of the parameters. In this paper, a suite of such start-up designs for two treatments and binary patient responses are considered and compared in terms of the numbers of patients required in order to give meaningful parameters estimates, the number of patients allocated to the better treatment, and the bias in the parameter estimates.

Sequential designs for ordinal phase I clinical trials.

Sequential designs for phase I clinical trials which incorporate maximum likelihood estimates (MLE) as data accrue are inherently problematic because of limited data for estimation early on. We address this problem for small phase I clinical trials with ordinal responses. In particular, we explore the problem of the nonexistence of the MLE of the logistic parameters under a proportional odds model with one predictor.

Sequential designs for logistic phase I clinical trials.

Both parametric and nonparametric sequential designs and estimation methods are implemented in phase I clinical trials. In this article, we take a systematic approach, consisting of a start-up design, a follow-on design, a sequential dose-finding design, and an estimation method, to find an efficient estimate of the maximum tolerated dose under the assumption that the dose-response curve has a true underlying logistic distribution. In particular, for the problem of the nonexistence of the maximum likelihood estimates of the logistic parameters, a constraint on the probability of an undetermined maximum likelihood estimator (MLE) is incorporated into the parametric sequential designs.

Bayesian optimal designs for Phase I clinical trials.

A broad approach to the design of Phase I clinical trials for the efficient estimation of the maximum tolerated dose is presented. The method is rooted in formal optimal design theory and involves the construction of constrained Bayesian c- and D-optimal designs. The imposed constraint incorporates the optimal design points and their weights and ensures that the probability that an administered dose exceeds the maximum acceptable dose is low.

Competing designs for phase I clinical trials: a review.

Phase I clinical trials are typically small, uncontrolled studies designed to determine a maximum tolerated dose of a drug which will be used in further testing. Two divergent schools have developed in designing phase I clinical trials. The first defines the maximum tolerated dose as a statistic computed from data, and hence it is identified, rather than estimated.