Morris Meisner

Testing Whether an Identified Treatment Is Best

We consider the problem of testing whether an identified treatment is better than each of K treatments. Suppose there are univariate test statistics Si that contrast the identified treatment with treatment i for i = 1, 2,...., K. The min test is defined to be the alpha-level procedure that rejects the null hypothesis that the identified treatment is not best when, for all i, Si rejects the one-sided hypothesis, at the alpha-level, that the identified treatment is not better than the ith treatment. In the normal case where Si are t statistics the min test is the likelihood ratio test. For distributions satisfying mild regularity conditions, if attention is restricted to test statistics that are monotone nondecreasing functions of Si, then regardless of their covariance structure the min test is an optimal alpha-level test. Tables of the sample size needed to achieve power .5, .8, .90, and .95 are given for the min test when the Si are Students t and Wilcoxon.

Optimal crossover designs in the presence of carryover effects.

Under either the random patient-effect model with sequence effects or the fixed patient-effect model, the usual two-period, two-treatment crossover design, AB,BA, cannot be used to estimate the contrast between direct treatment effects when unequal carryover effects are present. If baseline observations are available, the design AB,BA can validly be used to estimate a treatment contrast. However, the design AB,BA,AA,BB with baseline observations is more efficient. In fact, we show that this design is optimal whether or not baseline observations are available. For experiments with more than two periods, universally optimal designs are found for both models, with and without carryover effects. It is shown that uncertainty about the presence of carryover effects is of little or no consequence, and the addition of baseline observations is of little or no added value for designs with three or more periods; however, if the experiment is limited to only two periods the investigator pays a heavy penalty.

Statistical inference for cost-effectiveness ratios.

Methods for statistical inference for cost-effectiveness (C/E) ratios for individual treatment and for incremental cost-effectiveness (delta C/ delta E) ratios when two treatments are compared are presented. In a lemma, we relate the relative magnitude of two C/E ratios to the delta C/ delta E ratio. We describe a statistical procedure to test for dominance, or admissibility, that can be used to eliminate an inferior treatment. The one-sided Bonferronis confidence interval procedure is generalized to the two-sided case. The method requires only that two confidence intervals be available, one for cost and one for effectiveness. We describe Fieller-based confidence intervals and show them to be shorter than Bonferroni intervals. When distribution assumptions hold and variance and covariance estimates are available, Fieller intervals are preferable. However, Bonferroni intervals can be applied in more diverse situations and are easier to calculate. A simple Bonferroni based technique, and a likelihood ratio statistic given by Siegel, Laska and Meisner, for testing the null hypothesis that the C/E ratios of two treatments are equal is presented. The approaches are applied to the data from a phase II clinical trial of a new treatment for sepsis considered previously by others.

Nonparametric estimation and testing in a cure model.

Nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship. One-, two-, and K-sample likelihood ratio tests for inference on the cure rates are developed. In the two-sample case its power is compared to the power of several alternatives, including the log-rank and Gray and Tsiatis (1989, Biometrics 45, 899-904) tests. Implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed.

Oral analgesic studies: Pentazocine hydrochloride, codeine, aspirin, and placebo and their influence on response to placebo

In an analgesic study of 244 patients with postsurgical pain, doses of placebo, 600 mg. aspirin, 60 mg. codeine, and 35 and 50 mg. of pentazocine were compared. Two drug presentations were used, the second one always placebo, in this “double unknowns” design. Pentazocine, 50 mg., was found to be equivalent to 60 mg. of codeine in analgesic potency; 600 mg. aspirin was superior to the 35 mg. dose of pentazocine. The analgesic potency of placebo as a second dose was functionally dependent on the preceding medication. When placebo followed placebo, responses were identical. This finding is interpreted to be a serious drawback to crossover designs in clinical trials of analgesics.

A Variational Approach to Optimal Two-Treatment Crossover Designs: Application to Carryover-Effect Models

Abstract A variational method is used to obtain sufficient conditions for an optimal two-treatment, p-period design, given a repeated-measures model with arbitrary within-subject covariance. The design minimizes the variance of the estimator of treatment differences over all possible allocations of N subjects to the 2 p possible treatment sequences. The method is applied to a model that includes carryover effects. When subject effects are random with equicorrelated observations, designs are optimal if they are (a) strongly balanced; (b) uniform on the rows; and (c) either uniform on the subjects p is even and greater than 2, or uniform on the first p — 1 periods if p is odd. For two periods the optimal design is AB, BA, AA, BB. The same designs are optimal when baseline measurements are obtained in each period. Baseline observations improve efficiency considerably for p = 2, only slightly for p odd, and are of no help for p even and greater than 2. A second model of errors in which a subjects response ha...

MATCHED-PAIRS STUDY OF RESERPINE USE AND BREAST CANCER

This paper reports on an analysis of psychiatric population. 55 female patients with breast cancer were matched with non-cancer patients on age, year of admission, psychiatric diagnosis, race, and religion. Reserpine use was examined for yearly use by each year preceding the diagnosis of breast cancer, by cumulative yearly use, and by other defined time periods. Regardless of the definition of reserpine user, there were no significant increased relative risks of breast cancer for those women on reserpine. There was a fairly low proportion of patients from each group who were on the drug in any given year, and a fairly wide range of total dosage received. Over half of the women used reserpine at some time during their hospital stay.

A bioassay computer program for analgesic clinical trials

A Fortran program to calculate estimates of relative potency of a test to a standard analgesic is described. The program considers, at the option of the users, four distinct populations: completers, all of those patients who have completed a full crossover round of medication; two‐rounders, patients who have completed two or more rounds of medication; incompleters, patients who have not completed one or more rounds of medication; and first dose only patients, the initial administration received by all patients in the study whether or not they have dropped out. Up to six observations plus the initial reading for pain intensity scores and pain relief scores may be processed separately. The program also creates several summary variables including: SPID, an estimate of the area under the reciprocal of the pain intensity curve; TOTAL, an estimate of the area under the pain relief curve; and estimates of onset and duration as measured by relief scores and by pain intenSity scores. The program automatically performs calculations‐ for the analysis of variance and produces F values when appropriate for testing linearity of the log dose relationship, parallelism of the two curves for test and standard, and so forth. The paper discusses the rationale behind the approach adopted in the program.

Simple Designs and Model-free Tests for Synergy

Current statistical designs for studying whether two or more agents in combination act synergistically nearly always require the study of several doses of many dose ratios. The analysis is usually based on an assumed parametric model of the dose-response surface. In this paper, for both quantal and quantitative response variables, sufficient conditions are given for establishing synergy at a dose of the combination without the need to specify the model. This enables the use of simple designs with few doses even when there is sparse knowledge of the dose-response curves of the individual agents. The Min test, used for testing whether an identified treatment is best, may be used for testing synergy. Power issues are discussed.

Analgesic studies of indomethacin as analyzed by computer techniques

A method of evaluating oral analgesics in a general hospital is presented. The competition between crossover studies and single dose studies has led us to compare a basic crossover design with a single dose design, and a computer program was developed from both paints of view. The patients included in this study had moderate or severe postoperative or fracture pain, and received indomethacin, aspirin, and a placebo on a random complete crossover basis. This study indicated that single dose data only yielded more reliable information and probably a more efficient design than the crossover technique. Furthermore, placebo varied in its effect, depending on its position in the study, and appeared more effective when administered as a second test medication. Fifty milligrams of indomethacin appeared to be an effective oral analgesic equivalent to approximately 600 mg. of aspirin.