Kung-Jong Lui

Sample Size Determination for Testing Equality in a Cluster Randomized Trial with Noncompliance

For administrative convenience or cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients rather than individual patients. Furthermore, because of ethical reasons or patients decision, it is not uncommon to encounter data in which there are patients not complying with their assigned treatments. Thus, the development of a sample size calculation procedure for a CRT with noncompliance is important and useful in practice. Under the exclusion restriction model, we have developed an asymptotic test procedure using a tanh−1(x) transformation for testing equality between two treatments among compliers for a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 − β at a nominal α level. We have employed Monte Carlo simulation to evaluate the finite-sample performance of the proposed test procedure with respect to type I error and the accuracy of the derived sample size calculation formula with respect to power in a variety of situations. Finally, we use the data taken from a CRT studying vitamin A supplementation to reduce mortality among preschool children to illustrate the use of sample size calculation proposed here.

Test non-inferiority and sample size determination based on the odds ratio under a cluster randomized trial with noncompliance.

Because the odds ratio (OR) possesses certain desirable statistical properties, the OR has been recommended elsewhere to measure the relative treatment effect in establishing non-inferiority. For cost efficiency, we may often employ a cluster randomized trial (CRT), in which randomized units are clusters of patients. Furthermore, it is not uncommon to encounter data in which there are patients not complying with their assigned treatment. Under the Dirichlet multinomial model, we have developed a test statistic for assessing non-inferiority based on the OR between two treatments under a CRT with noncompliance. We have further derived a sample size formula accounting for both noncompliance and the intraclass correlation for a desired power 1 − β of detecting non-inferiority with respect to the OR at a nominal α level. Using Monte Carlo simulation, we have evaluated the performance of the proposed test statistic and sample size formula. Finally, we use the CRT studying the effect of vitamin A supplementation on mortality among preschool children to illustrate the use of the sample size formula given here.

Test Equality between Three Treatments under an Incomplete Block Crossover Design

Under a random effects linear additive risk model, we compare two experimental treatments with a placebo in continuous data under an incomplete block crossover trial. We develop three test procedures for simultaneously testing equality between two experimental treatments and a placebo, as well as interval estimators for the mean difference between treatments. We apply Monte Carlo simulations to evaluate the performance of these test procedures and interval estimators in a variety of situations. We note that the bivariate test procedure accounting for the dependence structure based on the F-test is preferable to the other two procedures when there is only one of the two experimental treatments has a non-zero effect vs. the placebo. We note further that when the effects of the two experimental treatments vs. a placebo are in the same relative directions and are approximately of equal magnitude, the summary test procedure based on a simple average of two weighted-least-squares (WLS) estimators can outperform the other two procedures with respect to power. When one of the two experimental treatments has a relatively large effect vs. the placebo, the univariate test procedure with using Bonferroni’s equality can be still of use. Finally, we use the data about the forced expiratory volume in 1 s (FEV1) readings taken from a double-blind crossover trial comparing two different doses of formoterol with a placebo to illustrate the use of test procedures and interval estimators proposed here.

Hypothesis Testing and Estimation in Ordinal Data Under a Simple Crossover Design

Since each patient serves as his/her own control, the crossover design can be of use to improve power as compared with the parallel-groups design in studying noncurative treatments to certain chronic diseases. Although the research studies on the crossover design have been quite intensive, the discussions on analyzing ordinal data under such a design are truly limited. We propose using the generalized odds ratio (GOR) for paired sample data to measure the relative effect on patient responses for both treatment and period in ordinal data under a simple crossover trial. Assuming the treatment and period effects are multiplicative, we note that one can easily derive the maximum likelihood estimator (LE) in closed forms for the GOR of treatment and period effects. We develop asymptotic and exact procedures for testing treatment and period effects. We further derive asymptotic and exact interval estimators for the GOR of treatment and period effects. We use the data taken from a crossover trial to assess the clarity of leaflet instructions between two devices among asthma patients to illustrate the use of these test procedures and estimators developed here.

Notes on Testing Noninferiority in Ordinal Data Under the Parallel Groups Design

When testing the noninferiority of an experimental treatment to a standard (or control) treatment in a randomized clinical trial (RCT), we may come across the outcomes of patient response on an ordinal scale. We focus our discussion on testing noninferiority in ordinal data for an RCT under the parallel groups design. We develop simple test procedures based on the generalized odds ratio (GOR). We note that these test procedures not only can account for the information on the order of ordinal responses without assuming any specific parametric structural model, but also can be independent of any arbitrarily subjective scoring system. We further develop sample size determination based on the test procedure using the GOR. We apply Monte Carlo simulation to evaluate the performance of these test procedures and the accuracy of sample size calculation formula proposed here in a variety of situations. Finally, we employ the data taken from a trial comparing once-daily gatifloxican with three-times-daily co-amoxiclav in the treatment of community-acquired pneumonia to illustrate the use of these test procedures and sample size calculation formula.

Notes on interval estimation of the generalized odds ratio under stratified random sampling.

It is not rare to encounter the patient response on the ordinal scale in a randomized clinical trial (RCT). Under the assumption that the generalized odds ratio (GOR) is homogeneous across strata, we consider four asymptotic interval estimators for the GOR under stratified random sampling. These include the interval estimator using the weighted-least-squares (WLS) approach with the logarithmic transformation (WLSL), the interval estimator using the Mantel-Haenszel (MH) type of estimator with the logarithmic transformation (MHL), the interval estimator using Fiellers theorem with the MH weights (FTMH) and the interval estimator using Fiellers theorem with the WLS weights (FTWLS). We employ Monte Carlo simulation to evaluate the performance of these interval estimators by calculating the coverage probability and the average length. To study the bias of these interval estimators, we also calculate and compare the noncoverage probabilities in the two tails of the resulting confidence intervals. We find that WLSL and MHL can generally perform well, while FTMH and FTWLS can lose either precision or accuracy. We further find that MHL is likely the least biased. Finally, we use the data taken from a study of smoking status and breathing test among workers in certain industrial plants in Houston, Texas, during 1974 to 1975 to illustrate the use of these interval estimators.

Prescott tests of equality in binary data under a three-treatment three-period crossover design

ABSTRACT Three test procedures accounting for patients with tied responses based on Prescott’s ideas are developed for comparing three treatments under a three-period crossover trial in binary data. Monte Carlo simulation is employed to evaluate the performance of these test procedures in a variety of situations. The test procedures proposed here are noted to have power larger than those procedures, which utilize only those patients with un-tied responses. The data taken from a three-period crossover trial comparing two different doses of an analgesic with placebo for the relief of primary dysmenorrhea are used to illustrate the use of the test procedures developed here.

Testing Equality and Interval Estimation in Binary Responses When High Dose Cannot Be Used First Under a Three-Period Crossover Design

When comparing two doses of a new drug with a placebo, we may consider using a crossover design subject to the condition that the high dose cannot be administered before the low dose. Under a random-effects logistic regression model, we focus our attention on dichotomous responses when the high dose cannot be used first under a three-period crossover trial. We derive asymptotic test procedures for testing equality between treatments. We further derive interval estimators to assess the magnitude of the relative treatment effects. We employ Monte Carlo simulation to evaluate the performance of these test procedures and interval estimators in a variety of situations. We use the data taken as a part of trial comparing two different doses of an analgesic with a placebo for the relief of primary dysmenorrhea to illustrate the use of the proposed test procedures and estimators.

Five interval estimators of the risk difference under stratified randomized clinical trials with noncompliance and repeated measurements.

We often employ stratified analysis to control the confounding effect due to centers in a multicenter trial or the confounding effect due to trials in a meta-analysis. On the basis of a general risk additive model, we focus discussion on interval estimation of the risk difference (RD) in repeated binary measurements under a stratified randomized clinical trial (RCT) in the presence of noncompliance. We develop five asymptotic interval estimators for the RD in closed form. These include the interval estimator using the weighted least-squares (WLS) estimator, the WLS interval estimator with tanh −1(x) transformation, the Mantel–Haenszel (MH) type interval estimator, the MH interval estimator with tanh −1(x) transformation, and the interval estimator using the idea of Fiellers theorem and a randomization-based variance. We employ Monte Carlo simulation to study and compare the finite-sample performance of these interval estimators in a variety of situations. We include an example studying the use of macrophage colony-stimulating factor to reduce the risk of febrile neutropenia events in acute myeloid leukaemia patients published elsewhere to illustrate the use of these estimators.

Estimation of the Risk Difference Under a Noncompliance Randomized Clinical Trial with Missing Outcomes

In a randomized clinical trial (RCT), we often come across the situations in which there are patients who do not comply with their assigned treatments or whose outcomes are missing due to their refusal or loss to follow-up. Because noncompliance and missing outcomes do not generally occur completely at random, analyzing data as treated or excluding patients with missing outcomes from our analysis can produce a biased estimate of a treatment effect. In this paper, we consider estimation of the risk difference (RD) in the presence of both noncompliance and missing outcomes under a RCT. On the basis of a constant risk additive model proposed elsewhere, we derive the maximum likelihood estimator (MLE) and develop three asymptotic interval estimators in closed form for the RD when we have outcome missing at random. We apply Monte Carlo simulation to evaluate and compare the performance of these estimators in a variety of situations. We note that all interval estimators developed here can perform well with respect to the coverage probability in all the situations considered here. We find that the interval estimator using tanh − 1 (x) transformation is generally more precise than the other two estimators with respect to the average length. Finally, we use the data taken from a randomized trial studying the association between flu vaccine and the risk of flu-related hospitalization to illustrate the practical use of these interval estimators.