Therapeutic Innovation & Regulatory Science

This paper describes a conceptual empirical Bayes framework for random effects modeling and estimation of population kinetic/dynamic parameters. Using this framework, one can easily see that the random effects formulation does not require unique parameter estimates for each individual based strictly on data for that individual. This approach is particularly useful in situations involving sparse data. A general solution to the estimation problem via the EM algorithm is presented and compared with other methods including those used in the NONMEM (Nonlinear Mixed Effects Modeling) package. Key areas that need further investigation, such as model validation and identification of design limitations, are pointed out.

Dose-response studies often form integral parts of pharmacological investigations of drug activity and efficacy and of toxicological investigations of drug and chemical safety. Standardized dose-response study protocols, statistical models, model fitting techniques, and computer programs are widely available for such applications. Many studies however, require nonstandard models and model fitting procedures to adequately describe the resulting data. Maximum likelihood analysis can accommodate a wide variety of model structures in a unified manner. This presentation illustrates how general purpose nonlinear regression analysis routines, such as those that are available in SAS or in BMDP, can be used to obtain maximum likelihood model solutions and associated error analyses for nonstandard model fitting situations. This reduces the need for special purpose computer programs for individual modeling applications. Methodological considerations in the application of nonlinear regression modeling procedures to maximum likelihood estimation are discussed. The methodology is illustrated with several modeling situations.

This paper is intended as a commentary on some statistical and scientific issues arising from current practices in new drug development. We wish to provoke thought concerning the question, “How can we better utilize the results of early development studies to obtain better understanding of the potential usefulness of a new drug before committing to a narrowly-focused, resource-intensive, Phase III program?” The role of hypothesis generation and exploratory data analysis is discussed in the context of the “research continuum” of drug development.

This paper describes a Bayesian approach to the design and analysis of clinical trials, with special reference to Phase III drug trials. The focus is on two rather general areas that are important in clinical trials: (1) monitoring trials with the possibility of changing the trial's design, and (2) combining various sources of information concerning the effect of the drug. Topics covered include survival analysis, analysis of trials in which the patients have different prognoses, multicenter trials and meta-analysis.

Procedures are presented for incorporating external information into inferences about outcomes from clinical and other trials. The objective is to use findings from trials that did include placebo to construct predictive distributions for evaluating the likelihood of a significant active-placebo difference in active-controlled trials that include no or few placebo controls. Information about differences between active controls and placebo from other trials also can be incorporated. The predictive distributions allow for random between-study variation in the variances as well as in the means. The calculations are summarized with simple graphical displays.

Agreement on appropriate ways of presenting Bayesian analyses of clinical trials is essential if these methods are to obtain more widespread use and not fall into disrepute. Using an example based upon a trial currently in progress, two aspects of reporting are proposed. Using noninformative priors gives standardized likelihoods from which point and interval estimates, and probabilities associated with adverse effects, can be obtained with numerically similar values to classical estimates, confidence intervals, and p-values. Standardized likelihoods are therefore a useful means of introducing Bayesian analyses into trial reports and emphasizing the change in interpretation to quantifying beliefs. The second important use of Bayesian analyses is to illustrate strength of evidence coming from a trial by showing the sensitivity of the conclusions drawn to choice of prior distribution made. This can be achieved by employing other well–defined priors, notably that based on previous trial results and that reflecting investigators' opinions. However, this may not be sufficient to convince clinicians in general of an effect and so produce a real change in clinical practice. A method which relates the strength of evidence for a beneficial effect to the degree of prior scepticism in no effect is therefore proposed to address this.

The combination of studies is described, with particular attention to the objectives, databases, methods, and results of a combination. Two fallacies in the use of p-values as the sole summaries of studies are described. Four examples are discussed: (1) an overview of trials of some new formulations of a drug; (2) an overview of the effects of placebo; (3) the discovery of argon; and (4) an overview of fibrinolytic therapy. In conclusion, recommendations are made concerning the combination of studies.

The trough/peak ratio, the ratio of mean trough effect to mean peak effect, has been recently proposed as a measure for evaluating sustained release formulations of antihypertensive medications. This paper gives a method for constructing exact confidence intervals for the true trough/peak ratio of parallel, placebo–controlled, clinical trials. The confidence interval procedure, which can also be used to test hypotheses about the trough/peak ratio, is based on a transformation from bivariate to univariate responses. Moreover, it can be shown that this method is identical to an extension of Fieller's method of confidence interval construction. The method is demonstrated with data from a clinical trial which compared an antihypertensive agent to placebo.

A chronology of populations of patients eligible for analysis in clinical trials is discussed. A practical definition of the intention–to–treat population is given and its role relative to the efficacy analyzable population discussed for both parallel groups and crossover trials. Sensitivity analyses are proposed to address dilemmas as to which population of patients is appropriate for the final analysis of the trial. Associated issues regarding multiple comparisons, exclusion analyses, and post hoc analyses are discussed in the context of the intention–to–treat approach to statistical analysis. Examples for analgesia, intermittent claudication, anxiety or depression, and duodenal ulcers are given to illustrate the points discussed.

In a separate paper we have pointed out that in addition to safety concerns which strongly suggest the use of concentration-controlled trials (CCTs) for drugs with narrow therapeutic windows, sample size considerations favor the choice of CCTs in many situations. In this paper, we consider ways in which CCTs can be utilized to streamline the drug development process. In particular, a randomized concentration-controlled titration design is proposed for Phase II of drug development. Such a design would facilitate an assessment of efficacy early in drug development, while providing information on concentration-response for a rational choice of dose or concentration in Phase III-Alternative schemes are considered for comparison. Data analysis and dose selection based on CCTs are also discussed.

While not required for every adverse event, inferential statistical methods can be used both formally and informally to help characterize the safety profile of a new drug and help guide the resulting inferences to the broader population. Examples of probability statements will be shown when used both formally and informally. The particular setting or phase of clinical drug development dictates to some degree whether description with or without formal inference is appropriate.

When a new drug is being developed for market approval, clinical trials are intended to assess efficacy and safety. Typically, however, individual trials are designed vis a vis one (or a few) efficacy parameters. This is because there is usually inadequate information to specify the safety endpoints, and to characterize the population at risk. Also, the cost of studying any specific adverse event definitively in a single study is usually prohibitive. Thus, safety information is monitored throughout the efficacy trials and then the safety profile of the new drug is described across trials. The manner in which safety information is collected implies that formal statistical inference is invalid. Several descriptive techniques for displaying safety information accumulated during clinical trials will be presented.

Accompanying this article are two very succinct reviews, one authored by Enas and the other by Huster. They present important and timely information on methods of analysis of adverse event data and the alternative benefits and shortcomings of such analyses. I was originally asked to provide a medical perspective of the information presented by Enas and Huster. In preparing this perspective, it became clear that some improvement in the recognition of various roles of adverse event data was desirable. This paper is an attempt to delineate a classification of adverse event data.