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A clinical trial of an analgesic agent compares pain relief scores over time among groups of patients. All subjects experience the same painful procedure, but different subjects are given different randomly assigned doses of active agent or placebo when they first request it. The data are short individual time series of ordered categorical pain relief scores subsequent to dosing. Nonrandom right censoring may be present because patients can elect to remedicate with an active agent if their pain relief is insufficient. The trial is meant to address two questions: (a) Is there proof that the drug relieves pain? If so, (b) What dosage patterns should be investigated further, or recommended for use by a typical patient? Marginal models of human pharmacology are basically empirical models, and although an analysis of a study based on such a model can adequately address the first question, such is not the case for the second question, because this question requires extrapolation to untested dosing patt...

SUMMARY This bibliography lists all published methodological works (statistical methodology, implementation methodology, review papers, descriptions of software) in the area of population pharmacokinetics/ pharmacodynamics up to 1993 and all published works describing applications of population pharmacokinetics/pharmacodynamics up to 1992.

In a recent paper, Beal (1989, Biometrics 45, 969-977) considers the problem of determining the appropriate sample size when inference about a parameter theta is to be made on the basis of a confidence interval (CI). He suggests that the sample size should be chosen so that the probability that the length of the CI is less than a given value, conditional on the interval including the true theta, is greater than a specified level. In this note, in which we concentrate on two-sided intervals, this suggestion is examined, as is the effect of uncertainty in our knowledge of the population variance sigma 2 on estimates of sample size.

SUMMARY Use of the maximum likelihood method for parameter estimation in a general mixed effects model requires initial estimates for all the model parameters. When the model is complicated, it may not be easy to obtain such estimates, especially estimates of the variances and covariances. A computational strategy is given for obtaining initial estimates. It is based on a general formulation of the method of moments for mixed effects models which allows the variances and covariances to be estimated for fixed values of the regression parameters. A number of numerical algorithms has been proposed for obtaining maximum, or restricted maximum, likelihood estimates of the parameters of a linear mixed effects model (Hemmerle & Hartley, 1973; Jennrich & Sampson, 1976; Corbeil & Searle, 1976; Laird & Ware, 1982). The maximum likelihood method can also be used with a model in which some fixed effects enter nonlinearly, while all random effects enter linearly; see ? 2. With any of the algorithms it is important to have good initial estimates for all the model parameters. One computational strategy sometimes used for finding initial estimates is to first maximize the full likelihood or log likelihood function, referred to here as the objective function, over a mesh, or grid, of points covering the parameter space and then to use the mesh point corresponding to the maximum as the initial estimate. However, with a complicated mixed effects model the dimension of the parameter space can be large enough to make this strategy impractical. Also, this strategy implies that practical bounds can be placed on all variances and covariances of the model, and though this may be possible, it may not be easy to do, especially when the model is complicated. This paper presents a modification of this strategy. It makes use of a general formulation of the method of moments for mixed effects models which is applicable to obtaining estimates of the variances and covariances of such models for fixed values of the regression parameters. Thus initial estimates of the variances-covariances are obtained without recourse to a grid search over at least those dimensions of the parameter space corresponding to the variances and covariances. The method of moments formulation permits estimates to be obtained under various constraints which might be imposed on the variances and covariances. It is also applicable to multivariate mixed effects models, and

Consider a finite population, called here the target population, and consider two conditions, each of which we may imagine applying to all the units of this population. Suppose that under each condition, each population unit will exhibit some binary (0-1) response. The problem is to "compare" the set of responses of all the units under one condition with the set of responses of all the units under the second condition. We call these two sets the two population responses. In order to make the comparison, an experiment, in which some responses are actually obtained, must be performed. The population may be large enough to make it impractical to obtain an entire population response, and consequently, part of the experiment may entail determining a sample of units whose response under one or both conditions will be obtained. Also, in a real experiment it may be impossible in general to actually apply both conditions to a unit. (The actual application of a condition to a particular unit may result in altering the unit so that the other condition cannot be applied to it later). Consequently part of the experiment may entail choosing the conditions which shall be applied to particular experimental units. A common experimental design in these situations involves 1) obtaining a random sample from the target population, 2) randomly allocating the sample units to two experimental groups, and 3) applying one condition to the units of one group, while applying the other condition to the units of the other group. Even when both conditions may actually be applied to all units, this design may still be helpful since both groups may undergo experimentation during the same time period, and therefore, total experiment time may be reduced. Fisher's well known hypergeometric test (2,3,8) or a test which is approximate to Fisher's test, such as the chi-squared test with Yates correction (1,2,3,8), is usually used to analyze the responses obtained from an experiment with the above design. When the sample size, N, is sufficiently small compared to the size, M, of the target population, one may regard the responses of the first (second) group as being approximately a sequence of Bernoulli 0-1 outcomes, with probability m1!M (m2!M) for outcome 1, where mi = the number of I's in the ith population response. Thus Fisher's test may be regarded to be approximately testing the null hypothesis m1!M = m2!M (or ml = M2). In this article we explain that the appropriateness of using Fisher's test to test m1 = m2 may be examined without recourse to the Bernoulli approximation. Such examination is especially important when NIM is so large that it is not really meaningful to talk about Bernoulli outcomes. An important requirement of the inferential procedure is that the sample be random. The usual assumption that the sample is indeed random is often rather shaky in application. This is often the case in medical experiments where an accessible group of patients is used for a sample, rather than a group of patients chosen from either a well-defined target population or sampling frame, and where the inference is about some population of interest which is characterized after the sample is determined and which should be identified here with the target population. For a proper interpretation of the experimental result, one may need to redefine the target population in such a way that the randomness assumption becomes more tenable (or, as it is said, in such a way that the sample becomes more representative of the population). In so doing, one may well add restrictions to the original definition of the target population, thereby decreasing the population size. In fact, it may be necessary to define the target population to be, in effect, the set of units comprising the sample; the sample is then undoubtedly random. Of course, when the population is made less encompassing, it may lose some interest value with respect to the conclusion to be drawn about it. However, this loss is often necessary for a valid inference to result. While constricting the population, the ratio of sample size to population size may increase to the point where the inferential argument should not depend on the use of the Bernoulli approximation. These considerations motivated this author's inquiry into the role of Fisher's test in the inference problem to compare the population responses.