Jerome Klotz

A phase III study comparing the clinical utility of four regimens of 5-fluorouracil: a preliminary report.

A clinical trial involving 462 colon, rectum, and breast cancer patients randomized among four different dosage regimens of 5‐FU (an intravenous loading course, a weekly intravenous schedule, a nontoxic schedule, and an oral schedule) has shown a significantly better response among colon‐rectum cancer patients for the intravenous loading course. In addition, duration of response and time to progression are also significantly better. Overall survival is approaching significance for the colon rectum group (p value .082). In contrast, breast cancer patients show little difference between treatments. Toxicity is somewhat higher for the loading course.

The Wilcoxon, Ties, and the Computer

Abstract In testing for equality of distribution in two unpaired samples with ordered categorical data or data with many ties, the two sample Wilcoxon average rank test is attractive. Unfortunately, the null distribution of the statistic depends upon the pattern of ties and is generally difficult to compute. In an attempt to improve existing approximations, moments through order four are derived. It is regretted that in small to moderate sample sizes, no consistent improvement over the simple normal approximation was found. The erratic nature of both the values of the statistic and the jumps of the distribution appears to rule out any good, smooth approximation in small samples. For calculation of the exact distribution, an algorithm is given to generate restricted compositions efficiently on a computer. The algorithm provides a useful means of obtaining exact probabilities in many cases.

One-Way Layout for Counts and the Exact Enumeration of the Kruskal-Wallis H Distribution with Ties

Abstract In a one-way layout situation in which the observations are counts corresponding to ordered categories, the attractive H test of Kruskal and Wallis is recommended. Because of the large number of ties, the variance-covariance correction factor for the chi-squared approximation is inaccurate in small samples, with approximate significance levels varying between overly conservative and overly optimistic values depending upon the tie configuration and the outcome. To overcome this problem, a computer algorithm and program are developed which calculate the exact small sample distribution. In addition, an exact Scheffe-type method of multiple comparisons is given.

Estimating Hot Numbers and Testing Uniformity for the Lottery

Abstract We consider the problem of estimating probabilities for the different numbers in a lottery when the winning numbers are selected sequentially without replacement. Numerical methods are developed to compute maximum likelihood estimates of the probabilities and their variance-covariance matrix based on observed outcomes. The generalized likelihood ratio statistic –2 ln(λ) for testing equiprobable numbers is also given. The methods are applied to a data set from the Lotto America lottery. The properties of the procedure are studied by simulation.

Combination Chemotherapy in Breast Cancer

A randomized clinical trial, involving approximately 100 patients, that compared two combination therapy regimens (5 FU, methotrexate, vincristine, cyclophosphamide with and without prednisone) in adv

Asymptotic Efficiency of the Two Sample Kolmogorov-Smirnov Test

Abstract A simple derivation of asymptotic efficiency for the two sample Kolmogorov-Smirnov statistic is given and evaluated for normal location and normal scale alternatives. Using equal samples to simplify the derivation, the limiting efficiency is obtained by letting the type I error α go to zero while the type II error goes to β, 0 < β < 1. For unimodal symmetric location alternatives, the efficiency is the same as that obtained for the Mood and Brown median test. Limits of relative efficiencies for alternatives which approach the null hypothesis are 2/π for normal location alternatives and (πe)−1 for normal scale alternatives.

Components of Variance Estimation for the Split-Plot Design

Abstract In the balanced two-way layout split-plot design, maximum likelihood estimators and restricted maximum likelihood estimators are compared with the commonly used minimum variance unbiased estimators of variance components. Consistency problems are noted for the maximum likelihood estimators and a theorem is proved showing that the mean square errors of the restricted maximum likelihood estimators are uniformly smaller than the minimum variance unbiased estimators.

Small sample relative performance of the spline smooth survival estimator

The spline smooth survival estimator of Klotz is compared by simulation with the Kaplan-Meier product limit estimator and the empirical Bayes estimator of Van Ryzin, Susarla, and Rai. Using integrated mean square error, the spline smooth estimator is seen to perform better than the Kaplan-Meier estimator for a variety of distributions and censoring percentages. The comparison with the estimator of Van Ryzin Susarla and Rai is less clear and is sometimes better and sometimes worse.

Microcomputer voice-response telephone entry for balanced clinical trial randomization

Simple randomization of patients to treatment regimens in clinical trials can result in inbalance among stratum categories. Procedures that produce balance may lack randomness. Systems that are not deterministic yet produce balance are often extremely complex and are not easily performed by randomization clerks. A microcomputer-based voice-response system has been implemented that permits clinic staff to easily randomize patients in clinical trials despite the complexity of the algorithm. Data entry is accomplished by the use of Touch-Tone® keys.§ Input prompts and regimen assignment are spoken by a commercially available voice synthesizer.

Truncated Geometric Response-Duration of Response Models for Clinical Trials

Abstract For treatment comparisons in clinical cancer trials, the data often indicate absence or presence of response along with duration of response when it occurs. Response length is frequently truncated by death, loss of followup information, study termination, or other causes, and is usually a discrete variable (days, weeks, or months). A mixture of a binomial and truncated geometric probability is studied as an appropriate statistical model. Maximum likelihood estimators are derived for parameters of the model and a likelihood ratio statistic (-2 InA) is given for testing equality of treatments. Noncentrality parameters are given for power approximations under contiguous alternatives.