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Many statistical methods have been developed that focus primarily on efficacy. Safety evaluation frequently involves many additional considerations. Randomized controlled trials, especially later phase 3 trials, are infrequently designed based on safety outcomes. Most of these trials are designed based on efficacy outcomes, and therefore have limited power to detect important differences in safety outcomes. Recently, there have been calls to design trials with sufficient power to address known safety concerns. When prevention trials introduce an experimental preventive intervention (e.g., a vaccine) to an otherwise healthy (although at-risk) population, safety considerations can substantially affect the benefit: risk ratio and thus the utility and acceptability of the intervention. Observation of safety outcomes is often less controlled than for efficacy outcomes, particularly for safety concerns that emerge during the course of the trial. When either safety or efficacy outcomes are missing, specific assumptions are required for analysis (e.g., missing completely at random, MCAR), but often these assumptions may not apply. The statistical methods that rely on these assumptions have largely been developed with a focus on efficacy outcomes. Illustrative examples, including meta-analyses, will be presented and the underdeveloped areas highlighted.

Few methods for cancer clinical trials have been proposed in the past decade to evaluate treatments on the basis of joint efficacy and toxicity endpoints. The primary goal of a new cancer treatment is to improve efficacy. Because of the antagonist relationship between efficacy and toxicity, a critical question is to achieve this improvement without increasing unacceptably the risk of a severe toxicity. In this paper, two methods due to Letierce et al. (2003) and Tubert-Bitter et al. (2005) are compared in a simulation study. They are both nonparametric and, besides the joint approach of efficacy and toxicity, they consider the cumulative doses at which efficacy and toxicity occur, with the idea that it is better for the patient to attain efficacy at a small dose and to experience toxicity, if it happens, at the highest dose possible. These methods are detailed in the same framework. For the simulation study, the two true correlated doses at which efficacy and toxicity occur are generated from a Clayton model with Weibull marginal distributions. A fixed censoring value is considered, corresponding to the total dose of drug received at the end of the trial by the patients. Treatment groups of size 50 and 100 patients were simulated with 50%, 65%, and 80% of efficacy and 20%, 35%, and 50% of toxicity. Two values for the correlation of the variables were considered. One thousand simulations were run to estimate the type I error rate and the power of the tests. A few features were observed depending on the sample size, the correlation of the variables, and whether the difference between the two simulated treatments concerned efficacy, toxicity, or both.

Pilot studies in clinical research settings frequently focus on estimating the frequency of occurrence of certain adverse events. When zero such events are observed, the question of legitimate inference on the true event rate arises. The relationship between binomial and geometric distributions’ confidence intervals yields two useful graphical displays and interpretations for the event rate inference in this circumstance. The interval is also closely related to the Bayesian credible interval when the prior distribution for the event rate is uniform. In addition, the simple algebraic expression for the confidence bound is seen to be useful in the context of planning studies.

In this article, we consider some up-and-down designs that are discussed in Ivanova et al. (2003) for estimating the maximum tolerated dose (MTD) in phase I trials: the biased coin design, k -in-a-row rule, Narayana rule, and continual reassessment method (CRM). A large-scale Monte Carlo simulation study, which is substantially more extensive than Ivanova et al. (2003), is conducted to examine the performance of these five designs for different sample sizes and underlying dose-response curves. For the estimation of MTD, we propose a modified maximum likelihood estimator (MMLE) in addition to those in Ivanova et al. (2003). The selection of different dose-response curves and their parameters allows us to evaluate the robustness features of the designs as well as the performance of the estimators. The results obtained, in addition to revealing that the new estimator performs better than others in many situations, enable us to make recommendations on designs.

This chapter is devoted to the investigation of multicentre clinical trials with random enrolment, where the patients enter the centres at random according to doubly stochastic Poisson processes. We consider two-arm trials and use a random-effects model to describe treatment responses. The time needed to complete the trial (recruitment time) and the variance of the estimator of the Expected Combined Response to Treatment (ECRT) are investigated for different enrolment scenarios, and closed-form expressions and asymptotic formulae are derived. Possible delays in initiating centres and dropouts of patients are also taken into account. The developed results lead to rather simple approximate formulae which can be used to design a trial.

This chapter reviews recently developed methodology for designs that combine clinical trial phases II and III in a single trial. The designs enable both selection of the best of a number of experimental treatments and comparison of this treatment with a control treatment, and allow the trial to be stopped early if the best experimental treatment is insufficiently promising or is clearly superior to the control. The stopping rules are constructed to preserve the overall type I error rate for the trial. Two-stage designs are reviewed briefly and two multistage methods based, respectively, on the adaptive and group-sequential approaches are described in detail. The latter are illustrated by a trial to compare three doses of a new drug for the treatment of Alzheimer’s disease.

A sequential clinical trial is designed with given significance level and power to detect a certain difference in the parameter of interest and the trial will be stopped early when data collected at an early stage of the trial have produced enough, in one sense or another, evidence for the conclusion of the hypotheses. Different sequential test designs are available for a same requirement of significance level and power. On the other hand, a same set of observed data can be interpreted as outcomes of different sequential designs with the same significance level and power. Therefore for same observed data, the conclusion of a test may be significant by one sequential design but insignificant by another sequential test design. This phenomenon may lead to the question of whether applying sequential test design to clinical trials is rational. Withstanding this challenge, the sequential conditional probability ratio test (SCPRT) offers a special feature such that a conclusion made at an early stopping is unlikely to be reversed if the trial were not stopped but continued to the planned end. The SCPRT gives a sound reason to stop a trial early; that is, if the trial were not stopped as it should, then adding more data and continuing the trial by the planned end would not change the conclusion. With an SCPRT procedure, a sequential clinical trial is designed not only with given significance level and power, but also with a given probability of discordance which controls the chance that conclusion at an early stage would differ from that at the final stage of the trial. In particular, the SCPRT procedure based on Brownian motion on information time is simple to use and can be applied to clinical trials with different endpoints and different distributions.

Biosurveillance systems for infectious diseases typically deal with nonlinear time series. This nonlinearity is due to the non-Gaussian and nonstationary nature of an outcome process. Infectious diseases (ID), waterborne and foodborne enteric infections in particular, are typically characterized by a sequence of sudden outbreaks, which are often followed by long low endemic levels. Multiple outbreaks occurring within a relatively short time interval form a seasonal pattern typical for a specific pathogen in a given population. Seasonal variability in the probability of exposure combined with a partial immunity to a pathogen adds to the complexity of seasonal patterns. Although seasonal variation is a well-known phenomenon in the epidemiology of enteric infections, simple analytical tools for examination, evaluation, and comparison of seasonal patterns are limited. This obstacle also limits analysis of factors associated with seasonal variations. The objectives of this paper are to outline the notion of seasonality, to define characteristics of seasonality, and to demonstrate tools for assessing seasonal patterns and the effects of environmental factors on such patterns. To demonstrate these techniques, we conducted a comparative study of seasonality in Salmonella cases as reported by the state surveillance system in relation to seasonality in ambient temperature, and found that the incidence in Salmonella infection peaked two weeks after a peak in temperature. The results suggest that ambient temperature can be a potential predictor of Salmonella infections at a seasonal scale.

Generalized linear models with a Poisson distribution are often used to model cancer registry data stratified by sex, age, year, and little geographical units. We compare three different approaches which take into account possible spatial correlation among neighbouring units, using lung cancer incidence data. Inference is fully Bayesian and uses Markov chain Monte Carlo techniques. Comparison between models is based on the Deviance Information Criterion (DIC).

The first aim of this work is to clearly present a very popular semiparametric methodology often used to estimate the association between death or hospital counting data and pollution data and to estimate short-term effects of ambient air pollution on infant bronchiolitis hospital consultations. Infant bronchiolitis is a frequent infectious disease caused by a virus, the syncethial respiratory virus (RSV). Normally, contact with this virus is responsible for a cold, but in infant and in some circumstances, especially at the beginning of winter, the virus can be responsible for a severe respiratory disease which can lead to numerous hospital consultations and hospitalizations. A critical comparison of its practical application using S-Plus, R, or SAS Proc Gam is performed. It appears that more work is needed to get a satisfactory implementation of the Schwartz method in SAS with similar results to those in S-Plus or R.