When testing for a treatment effect or a difference among groups, the distributional assumptions made about the response variable can have a critical impact on the conclusions drawn. For example, controversy has arisen over transformations of the response (Keene). An alternative approach is to use some member of the family of generalized linear models. However, this raises the issue of selecting the appropriate member, a problem of testing non-nested hypotheses. Standard model selection criteria, such as the Akaike information criterion (AIC), can be used to resolve problems. These procedures for comparing generalized linear models are applied to checking for difference in T4 cell counts between two disease groups. We conclude that appropriate model selection criteria should be specified in the protocol for any study, including clinical trials, in order that optimal inferences can be drawn about treatment differences.

SUMMARYWhen testing for a treatment effect or a difference among groups, the distributional assumptions made about the response variable can have a critical impact on the conclusions drawn. For example, controversy has arisen over transformations of the response (Keene). An alternative approach is to use some member of the family of generalized linear models. However, this raises the issue of selecting the appropriate member, a problem of testing non-nested hypotheses. Standard model selection criteria, such as the Akaike information criterion (AIC), can be used to resolve problems. These procedures for comparing generalized linear models are applied to checking for difference in T cell counts between two disease groups. We conclude that appropriate model selection criteria should be specified in the protocol for any study, including clinical trials, in order that optimal inferences can be drawn about treatment differences.

Phase I trials to study the pharmacokinetic properties of a new drug generally involve a restricted number of healthy volunteers. Because of the nature of the group involved in such studies, the appropriate distributional assumptions are not always obvious. These model assumptions include the actual distribution but also the ways in which the dispersion of responses is allowed to vary over time and the fact that small concentrations of a substance are not easily detectable and hence are left censored. We propose that a reasonably wide class of generalized nonlinear models allowing for left censoring be considered now that this is feasible with current computer power and sophisticated statistical packages. These modelling strategies are applied to a Phase I study of the drug flosequinan and its metabolite. This drug was developed for the treatment of heart failure. Because the metabolite also exhibits an active pharmacologic effect, study of both the parent drug and the metabolite is of interest.

A fundamental assumption underlying pharmacokinetic compartment modelling is that each subject has a different individual curve. To some extent this runs counter to the statistical principle that similar individuals will have similar curves, thus making inferences to a wider population possible. In population pharmacokinetics, the compromise is to use random effects. We recommend that such models also be used in data rich situations instead of independently fitting individual curves. However, the additional information available in such studies shows that random effects are often not sufficient; generally, an autoregressive process is also required. This has the added advantage that it provides a means of tracking each individual, yielding predictions for the next observation. The compartment model curve being fitted may also be distorted in other ways. A widely held assumption is that most, if not all, pharmacokinetic concentration data follow a log-normal distribution. By examples, we show that this is not generally true, with the gamma distribution often being more suitable. When extreme individuals are present, a heavy-tailed distribution, such as the log Cauchy, can often provide more robust results. Finally, other assumptions that can distort the results include a direct dependence of the variance, or other dispersion parameter, on the mean and setting non-detectable values to some arbitrarily small value instead of treating them as censored. By pointing out these problems with standard methods of statistical modelling of pharmacokinetic data, we hope that commercial software will soon make more flexible and suitable models available.

Pharmacokinetic studies of drug and metabolite concentrations in the blood are usually conducted as crossover trials, especially in phases I and II. A longitudinal series of measurements is collected on each subject within each period. However, much of the dependence among such observations, within and between periods, is generally ignored in analyzing this type of data. Usually, only a random coefficient model is fitted for the parameters in the nonlinear mean function, along with allowing the variance to depend on the mean so that it changes over time. Here, we develop models to allow more fully for the structure of the crossover study. We introduce two levels of variance components, for the subjects and for the periods within subjects, and also an autocorrelation within periods. We also retain the time-varying variance, using a separate variance function for this, different from that for the mean. We apply this model to a phase I study of the drug flosequinan and its metabolite. This drug was developed for the treatment of heart failure. Because the metabolite also exhibits an active pharmacologic effect, study of both the parent drug and the metabolite is of interest. We find that the autocorrelation is the element in the covariance structure that most improves the fit of the model but that two levels of variance components can also be necessary.