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PubMed2005

Small-sample performance of the robust score test and its modifications in generalized estimating equations.

The sandwich variance estimator of generalized estimating equations (GEE) may not perform well when the number of independent clusters is small. This could jeopardize the validity of the robust Wald test by causing inflated type I error and lower coverage probability of the corresponding confidence interval than the nominal level. Here, we investigate the small-sample performance of the robust score test for correlated data and propose several modifications to improve the performance. In a simulation study, we compare the robust score test to the robust Wald test for correlated Bernoulli and Poisson data, respectively. It is confirmed that the robust Wald test is too liberal whereas the robust score test is too conservative for small samples. To explain this puzzling operating difference between the two tests, we consider their applications to two special cases, one-sample and two-sample comparisons, thus motivating some modifications to the robust score test. A modification based on a simple adjustment to the usual robust score statistic by a factor of J/(J - 1) (where J is the number of clusters) reduces the conservativeness of the generalized score test. Simulation studies mimicking group-randomized clinical trials with binary and count responses indicated that it may improve the small-sample performance over that of the generalized score and Wald tests with test size closer to the nominal level. Finally, we demonstrate the utility of our proposal by applying it to a group-randomized clinical trial, trying alternative cafeteria options in schools (TACOS).

Adolescent↗
PubMed2005

Multiple comparisons between two groups on multiple Bernoulli outcomes while accounting for covariates.

The problem of adjusting for multiplicity when one has multiple outcome variables can be handled quite nicely by step-down permutation tests. More difficult is the problem when one wants an analysis of each outcome variable to be adjusted for some covariates and the outcome variables are Bernoulli. Special permutations can be used where the outcome vectors are permuted within each strata of the data defined by the levels of the (made discrete) covariates. This method is described and shown to control the familywise error rate at any prespecified level. The method is compared through simulation to a vector bootstrap approach, also using a step-down testing procedure. It is seen that the method using permutations within strata is superior to the vector bootstrap in terms of error control and power. The method is illustrated on a data set of 55 minor malformations of babies of diabetic and non-diabetic mothers.

Analysis of Variance↗
PubMed2007

Early stopping clinical trials of binomial response with an exact group sequential method.

In Phase II clinical trials much slower patient enrollment and intervening results of comparable trials can make it desirable to stop trials early when the data indicate no relevant effect. For a binomial response, we adopt an exact group sequential method as a decision tool to assess whether the trial could be stopped early or not. We have applied the exact group sequential method to a Phase II Tuberculosis clinical trial, and the results have been compared with that from error spending and conditional power approaches. We conclude that the exact group sequential method is more efficient for interim analysis in clinical trials than the error spending and conditional power approaches. Published in 2007 by John Wiley & Sons, Ltd.

Binomial Distribution↗
PubMed1989

Estimation of prevalence on the basis of screening tests.

Estimates of disease prevalence based on screening tests can be severely biased unless adjusted for the sensitivity and specificity of the screening test. One such adjusted estimate, the maximum likelihood estimator proposed by Levy and Kass, can yield an extreme estimate of zero or one that has undesirable characteristics such as a standard error of zero. We develop here a Bayesian estimator which always falls between zero and one. Users without specialized software can use the maximum likelihood estimate for most circumstances and, in special cases, such as a zero estimate of prevalence, turn to the Bayesian estimate. Others can use software to carry out a complete Bayesian solution. We have provided a method to obtain numerical values for the Bayesian estimate for those ranges of sample size (20-100), sensitivity (0.7-0.9) and specificity (0.7-0.9) for which the use of this estimator seems most practical.

Algorithms↗
PubMed1989

Analysis of epidemiologic case-base studies for binary data.

Recent developments in statistical methods for epidemiology have revived the application of sampling techniques in the design and analysis of cohort studies. The 'case-base' design involves sampling of both the cases and the cohort base of the study. This paper reviews some data-analytic imperfections of the approaches to risk ratio estimation, and modifies and advances a consistent likelihood-based procedure-analogous to Miettinen and Nurminen's proposal for a full cohort design--for interval estimation (and also point estimation and significance testing) in the context of binary case-base data. First, the procedure avoids the use of Taylor-series approximations to derive variance estimators for non-linear functions of parameters. Second, the asymptotic condition effects a simple computational expression for the chi-square function of risk ratios that is universally applicable to small samples. The statistical modelling underlying the method allows inferences about risk ratios without the assumption of rare disease either for the general population or for a particular base. The paper also extends the analysis to encompass stratified data. Finally, a numerical evaluation evinced the accurate small-sample properties of the proposed method.

Binomial Distribution↗
PubMed1990

Test statistics and sample size formulae for comparative binomial trials with null hypothesis of non-zero risk difference or non-unity relative risk.

When it is required to establish a materially significant difference between two treatments, or, alternatively, to show that two treatments are equivalent, standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply. This paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non-zero difference or non-unity relative risk. Methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine.

Analysis of Variance↗
PubMed1990

Statistical methods for determining risk factors of chronic otitis media with effusion.

We use logistic regression with paired Bernouilli outcomes to analyse data on subjects who have either one or two organs (e.g. ears) each of which may develop disease. In this model, subject-specific covariates are related to the probability of developing disease. The proposed method is applied to determine risk factors for chronic otitis media with effusion.

Analysis of Variance↗
PubMed1991

Monitoring a randomized clinical trial for futility: the north-Norwegian lidocaine intervention trial.

Randomized clinical trials of acute disease are usually designed as single-look, fixed sample size trials. This methodological study compares the conventional approach with a multiple-look, group sequential design with stopping rules for both treatment efficacy and for an inconclusive trial outcome, called trial futility. An ongoing trial on pre-hospital prophylaxis of sudden death in acute myocardial infarction forms the basis of the analysis. The effects of introducing multiple looks (or interim analyses) and tests for futility were obtained by binomial simulation. The introduction of four looks (that is, three interim and a final analysis) resulted in a modest increase in the maximal number of patients required. This was, however, fully compensated for by the high probability of early termination in case of treatment efficacy. The addition of futility tests, enabling termination at half the maximum trial size when there is no treatment difference, resulted in only a negligible reduction of overall power. We conclude that multiple-look, group sequential designs testing for both treatment efficacy and trial futility may improve the cost-effectiveness of randomized trials of acute disease.

Binomial Distribution↗
PubMed1991

A quasi-exact test for comparing two binomial proportions.

The use of the Fisher exact test for comparing two independent binomial proportions has spawned an extensive controversy in the statistical literature. Many critics have faulted this test for being highly conservative. Partly in response to such criticism, some statisticians have suggested the use of a modified, non-randomized version of this test, namely the mid-P-value test. This paper examines the actual type I error rates of this test. For both one-sided and two-sided tests, and for a wide range of sample sizes, we show that the actual levels of significance of the mid-P-test tend to be closer to the nominal level as compared with various classical tests. The computational effort required for the mid-P-test is no more than that needed for the Fisher exact test. Further, the basis for its modification is a natural adjustment for discreteness; thus the test easily generalizes to r x c contingency tables and other discrete data problems.

Binomial Distribution↗
PubMed1992

Monitoring clinical trials with a conditional probability stopping rule.

Conditional probability procedures offer a flexible means of performing sequential analysis of clinical trials. Since these procedures are not based on repeated significance test, the number and schedule of the interim analyses is less important than with group sequential procedures. Their main disadvantage is that the magnitude of their effect on the significance level is difficult to assess. This paper describes a conditional probability procedure which attempts to maintain the overall significance level by balancing the probabilities of false early rejection and false early acceptance. Monte Carlo sampling results suggest that this procedure can achieve a large reduction in expected sample size without greatly affecting either the significance level or power of the trial.

Binomial Distribution↗
PubMed1992

Clustering in sparse data and an analysis of rhabdomyosarcoma incidence.

Time series of epidemiologic events often contain periods of atypically low or high frequency. Correspondingly, for quite rate diseases there occur instances of long vacuous durations interrupted noticeably by periods of some disease activity. A recent community-based observation of the incidence of rhabdomyosarcoma (RMS), and an investigation of it, yielded sparse data of this general description. We introduce a combinatorial test for patchy time series and apply it to the RMS data. We comment on the prevalent practice of post hoc data analysis of alleged clusters, and on scale effects.

Adolescent↗
PubMed1992

Exact unconditional tables for significance testing in the 2 x 2 multinomial trial.

This paper presents tables analogous to T-tables for use in the 2 x 2 multinomial trial, where the continuity corrected Z-statistic is used to make exact unconditional inference. This is the first solution of a discrete exact unconditional inference problem involving a multivariate nuisance parameter for which no ancillary statistic exists.

Bias↗
PubMed1992

The use of cusums and other techniques in modelling continuous covariates in logistic regression.

The assessment of continuous covariates singly as possible predictors in a multivariable logistic regression model is an important first step in the analysis. An approach to plotting which uses a cusum (cumulative sum) of the binary response variable is described. Extreme-deviation statistics associated with the cusum may be used to detect monotonic and non-monotonic trends. Probability plots of the covariate in the two groups defined by the response variable may help to determine the appropriate scale (transformation) of the covariate and to anticipate possible problems with the logistic fit. The ratio of the variances in the response/non-response groups is informative about the need for a quadratic term in the logistic model. Smoothed scatterplots of the response are valuable in displaying the observed and fitted values. The techniques are illustrated with two data sets.

Binomial Distribution↗
PubMed1992

On the sample size for studies based upon McNemar's test.

When computing the sample size for studies using McNemar's test, one needs to know the probability of discordance and the odds ratio to be detected. In many studies, the investigator is unable to specify the probability of discordance, but can state, at least approximately, the marginal probabilities of each variable. This information leads to restrictions on the possible values of the cell probabilities and provides a range of admissible values for the off-diagonal cells. We compute the sample size needed in these circumstances and compare them to the results cited by Schlesselman and Connett et al. These sample sizes for the method are quite close to those found in the Monte Carlo study of Connett et al.

Antibodies, Monoclonal↗
PubMed1993

Sample size and power for prospective analysis of relative risk.

In a placebo-controlled vaccine efficacy trial or a trial of equivalence of vaccines, one may wish to show that relative risk of disease is less than a specified value R0, not equal to one. This paper compares three methods for estimating relative risk in the binomial setting, based on a logarithmic transformation, likelihood scores, and a Poisson approximation. Exact power and size of test are calculated by enumeration of possible binomial outcomes, and power is approximated from asymptotic formulations. Although the score method is generally preferable, for most studies of practical interest the log and score methods are comparable, and the Poisson method is also appropriate for small risks, up to about 0.05. When true and null relative risks are less than one, unequal allocation of study individuals can increase power, and the asymptotic formula for the log method may substantially underestimate power; in such a study the power approximation for the score method is more reliable, even if the log method is used in analysis. Exact power calculations are helpful in planning studies. The log and Poisson methods, but not the score method, apply readily in the case of unequal follow-up.

Binomial Distribution↗
PubMed1993

Exact conditional and unconditional sample size for pair-matched studies with binary outcome: a practical guide.

Tables of sample sizes for pair-matched studies with binary outcome are presented. They are based on conditional and unconditional approaches using the 'exact' (binomial) test. An approximate procedure is suggested to estimate the sample size for parameter values that do not correspond exactly with table entries. The procedure utilizes a minor modification of the large-sample formula given by Connett et al. A practical strategy for estimating the overall sample size in the presence of a nuisance parameter (the proportion of discordant pairs) is recommended. An example from a proposed clinical trial is given.

Binomial Distribution↗