Thomas W. O'Gorman

A Monte Carlo investigation of homogeneity tests of the odds ratio under various sample size configurations.

Epidemiologic data for case-control studies are often summarized into K 2 x 2 tables. Given a fixed number of cases and controls, the degree of sparseness in the data depends on the number of strata, K. The effect of increasing stratification on size and power of seven tests of homogeneity of the odds ratio is studied using Monte Carlo methods. In all the designs considered here, the numbers of cases and controls per stratum are the same. Considering both size and power in non-sparse-data settings, we recommend the Breslow-Day statistic (1980, Statistical Methods in Cancer Research, 1. The Analysis of Case-Control Studies, p. 142; Lyon: International Agency for Research on Cancer) for general use. In sparse-data settings the T4 statistic of Liang and Self (1985, Biometrika 72, 353-358) performs the best when all tables, regardless of sample size, have odds ratios generated from the same distribution. In sparse-data settings characterized by a large table with an odds ratio of 1 and many small tables with odds ratios greater than 1, the T5 statistic of Liang and Self (1985) performs the best. One of the most important results of this study is the generally low power for all homogeneity tests especially when the data are sparse.

Variable Selection to Discriminate between Two Groups: Stepwise Logistic Regression or Stepwise Discriminant Analysis?

Abstract Monte Carlo methods were used to compare the stepwise variable selection procedure in discriminant analysis with the stepwise procedure using logistic regression. In these studies four of the candidate variables were related to group membership and four were not. The data sets were generated from normal, lognormal, and Bernoulli distributions. Several sample sizes, mean vectors, and covariance matrices were used. In most situations there was little difference between stepwise logistic regression and discriminant analysis in the probability of selecting the related variables. In some situations stepwise discriminant analysis gave a greater probability of selecting the related variables.

The Performance of Randomization Tests that Use Permutations of Independent Variables

ABSTRACT In this article we evaluate the performance of a randomization test for a subset of regression coefficients in a linear model. This randomization test is based on random permutations of the independent variables. It is shown that the method maintains its level of significance, except for extreme situations, and has power that approximates the power of another randomization test, which is based on the permutation of residuals from the reduced model. We also show, via an example, that the method of permuting independent variables is more valuable than other randomization methods because it can be used in connection with the downweighting of outliers.

An adaptive permutation test procedure for several common tests of significance

An adaptive weighted least-squares test procedure is proposed that increases the power of the most commonly used tests of significance. This test is shown to have high power if the number of observations is at least 20. The proposed adaptive method is a modification of weighted least squares with the weights determined from the order statistics of the residuals of the model specified by the null hypothesis. The weights are then used with a weighted least-squares regression to compute a test statistic. To insure that the test maintains its size, a permutation method is used to compute the observed significance level. To evaluate the performance of the test, Monte Carlo simulations were used to estimate the power for two-independent samples, for one-way layouts, for paired comparisons, and for the slope in a simple linear regression. In these simulations the proposed adaptive weighted least-squares method maintained its size and often had greater power than the common parametric and nonparametric tests. For the study designs investigated in this paper, the proposed adaptive weighted least-squares method is recommended if the number of observations is at least 20.

A COMPARISON OF TWO METHODS OF ESTIMATING A COMMON RISK DIFFERENCE IN A STRATIFIED ANALYSIS OF A MULTICENTER CLINICAL TRIAL

In this paper, we compare two methods of estimating the difference between the proportion of adverse events in a test treatment group and the proportion of adverse events in a control treatment group in a multicenter clinical trial. We used simulated data to compare the bias and mean squared error of the weighted least squares estimator to the bias and mean squared error of the Cochran-Mantel-Haenszel estimator. We also computed the coverage probabilities for confidence intervals derived from these estimators. We found that the weighted least squares method was often seriously biased. The coverage probabilities for the Cochran-Mantel-Haenszel estimators were often closer to their nominal values than were the coverage probabilities for the weighted least squares estimators. It also was found that these methods require a larger sample size to maintain coverage probabilities near their nominal values when unequal numbers of persons are assigned to the test and control treatments.

A comparison of an adaptive two-sample test to the t-test and the rank-sum test

A two-sample test is proposed which has greater power than the commonly used tests for several stochastically ordered alternatives, including the shift alternative. The proposed test is an adaptive test which uses the order statistics within the two samples to determine a suitable score function for a rank test. This test is shown, by Monte Carlo studies, to maintain its significance level for many distributions and sample size configurations. The proposed test had the highest power or was within 5% of the highest power among the tests considered for 90.4% of the simulations. The corresponding percentages were 39.6% for the pooled t-test, 65.7% for the rank-sum test, 78.8% for the normal scores test, and 78.7% for the adaptive test of Hogg, Fisher, and Randies. These simulations also showed that Welchs t-test often failed to maintain its significance level.

An adaptive two-sample test based on modified wilcoxon scores

An adaptive two-sample test is proposed which uses the tail lengths of the empirical distribution to determine the appropriate rank scores. The tail lengths are functions of the sample percentiles that are estimated from the combined samples. Monte Carlo methods were used to estimate the size and power of the proposed test and several other tests. Fifteen distributions having five levels of skewness and three levels of kurtosis were used in these simulations. Sample sizes varied from 12 to 800 in each group. The proposed test has greater power than the t-test, the Wilcoxon test, and the normal scores test for skewed data, and has power that is approximately equal to those tests for symmetric data.

The effect of category choice on the odds ratio and several measures of association in case-control studies

In many case-control studies the risk factors are categorized in order to clarify the analysis and presentation of the data. However, inconsistent categorization of continuous risk factors may make interpretation difficult. This paper attempts to evaluate the effect of the categorization procedure on the odds ratio and several measures of association. Often the risk factor is dichotomized and the data linking the risk factor and the disease is presented in a 2 x 2 table. We show that the odds ratio obtained from the 2x2 table is usually considerably larger than the comparable statistic that would have been obtained had a large number of outpoints been used. Also, if 2 x 2, 2 x 3, or 2 x 4 tables are obtained by using a few outpoints on the risk factor, the measures of association for these tables are usually greater than the measure that would have been obtained had a large number of cntpoints been used. We propose an odds ratio measure that more closely approximates the odds ratio between the continuous ...

The effect of unequal variances on the power of several two–sample tests

In consulting situations it is often difficult to select the most appropriate two-sample test for a particular situation. The objective of this research was to determine which two-sample test procedures were the most powerful when there were small differences in variability between the populations. A variety of skewed and symmetric distributions with unequal and equal variances were used in a Monte Carlo study to estimate the size and power of these tests. The tests maintained their size for the parameters used in this simulation. Those tests that were sensitive to location and scale shift alternatives were more powerful than the t-test and rank-sum test when there were small differences in variability between the groups

Using Kendall's tau b correlations to improve variable selection methods in case-control studies.

In this manuscript we evaluate the performance of a variable selection procedure that could be used in case-control studies. This method is based on selection statistics computed from a matrix of Kendall tau b correlation coefficients. A simulation study was performed to compare the performance of this method to logistic regression, discriminant analysis, and the rank-transformed versions of these methods. For most of the situations studied the method based on Kendall tau b correlation coefficients correctly selected the variables that were related to case-control status more often than any of the other methods. We discuss the implications of the results of this study for epidemiologic research.