Conditional analysis of mixed Poisson processes with baseline counts: implications for trial design and analysis

Abstract

The design of clinical trials is typically based on marginal comparisons of a primary response under two or more treatments. The considerable gains in efficiency afforded by models conditional on one or more baseline responses has been extensively studied for Gaussian models. The purpose of this article is to present methods for the design and analysis of clinical trials in which the response is a count or a point process, and a corresponding baseline count is available prior to randomization. The methods are based on a conditional negative binomial model for the response given the baseline count and can be used to examine the effect of introducing selection criteria on power and sample size requirements. We show that designs based on this approach are more efficient than those proposed by McMahon et al. (1994).

Non‐inferiority trial design for recurrent events

“…Cook and Wei [31,32] studied the impact of selection criteria in clinical trials based on mixedPoisson processes. Specifically, if n i0 is a count of the number of clinical events experienced by subject i over a previous time period, then individual i may be eligible if n i0 >C where C is a threshold count.…”

“…Specifically, if n i0 is a count of the number of clinical events experienced by subject i over a previous time period, then individual i may be eligible if n i0 >C where C is a threshold count. If the baseline count and prospectively observed event times are correlated through a shared random effect [32], then when historical event counts are used to select individuals for 4574 R. J. COOK, K.-A. LEE AND H. LI inclusion into a study, efficiency gains may be realized.…”

Mixture Models for Mixed Poisson Processes with Baseline Counts in Randomized Controlled Trials

“…With γ0 = γ1 = δ = 0, (1) is identical to the model from which Cook and Wei developed their methods (Cook and Wei, 2002;Cook and Wei, 2003). If the lengths of periods differ by patient, we may replace τt in (1) by the patient specific value τit.…”

“…Following the analysis done in Cook and Wei (2003), we analyze the data as coming from prepost design with patient screening by c = 5 and period lengths of τ0 = τ1 = 8 (weeks); the total numbers of seizures during whole 8 weeks before and after the random allocation are regarded as baseline and response value of the endpoint variable, respectively. In the following, first we apply our models without covariate effect parameter; although Thall and Vail treated patient's age as a covariate(1990), its clinical meaning is not very clear (we could not find any description about the age effect in the original paper of Leppik et al, 1987).…”

The Statistical Analysis of Recurrent Events

“…[Section 2.6; Cook and Wei, 2003] 2.15. Suppose that the intensity function in (2.55) is specified in terms of a parameter θ. Estimation of θ can be based on a product of likelihood contributions L(θ), of the form (2.55), across independent event processes.…”