Notes on Hypothesis Testing under a Single-Stage Design in Phase II Trial

A primary objective of a phase II trial is to determine future development is warranted for a new treatment based on whether it has sufficient activity against a specified type of tumor. Limitations exist in the commonly-used hypothesis setting and the standard test procedure for a phase II trial. This study reformats the hypothesis setting to mirror the clinical decision process in practice. Under the proposed hypothesis setting, the critical points and the minimum required sample size for a desired power of finding a superior treatment at a given α -level are presented. An example is provided to illustrate how the power of finding a superior treatment by accounting for a secondary endpoint may be improved without inflating the given Type I error

Interval Estimation of Risk Difference in Simple Compliance Randomized Trials

Consider the simple compliance randomized trial, in which patients randomly assigned to the experimental treatment may switch to receive the standard treatment, while patients randomly assigned to the standard treatment are all assumed to receive their assigned treatment. Six asymptotic interval estimators for the risk difference in probabilities of response among patients who would accept the experimental treatment were developed. Monte Carlo methods were employed to evaluate and compare the finite-sample performance of these estimators. An example studying the effect of vitamin A supplementation on reducing mortality in preschool children was included to illustrate their practical use

Notes on Use of the Composite Estimator: an Improvement of the Ratio Estimator

This article discusses use of the composite estimator with the optimal weight to reduce the variance (or the mean-squared-error, MSE) of the ratio estimator. To study the practical usefulness of the proposed composite estimator, a Monte Carlo simulation is performed comparing the bias and MSE of composite estimators (with estimated optimal weight and with known optimal weight) with those of the simple expansion and the ratio estimators. Two examples, one regarding the estimation of dead fir trees via an aerial photo and the other regarding the estimation of the average sugarcane acres per county, are included to illustrate the use of the composite estimator developed here

Notes on interval estimation of risk difference in stratified noncompliance randomized trials: A Monte Carlo evaluation

When comparing an experimental treatment with a standard treatment in a randomized clinical trial (RCT), we often use the risk difference (RD) to measure the efficacy of an experimental treatment. In this paper, we have developed four asymptotic interval estimators for the RD in a stratified RCT with noncompliance. These include an asymptotic interval estimator based on the weighted-least-squares (WLS) estimator of the RD, an asymptotic interval estimator using tanh-1(x) transformation with the WLS optimal weight, an asymptotic interval estimator derived from Fieller's Theorem, and an asymptotic interval estimator using a randomization-based approach. Based on Monte Carlo simulations, we have compared these four asymptotic interval estimators with the asymptotic interval estimator recently proposed elsewhere. We have found that when the probability of compliance is high, the interval estimator using a randomization-based approach is probably more accurate than the others, especially when the stratum size is not large. When the probability of compliance is moderate, the interval estimator using tanh-1(x) transformation is likely to be the best among all interval estimators considered here. We note that the interval estimator proposed elsewhere can be of use when the underlying RD is small, but lose accuracy when the RD is large. We also note that when the number of patients per assigned treatment is large, the four asymptotic interval estimators developed here are essentially equivalent; they are all appropriate for use. Finally, to illustrate the use of these interval estimators, we consider the data taken from a large field trial studying the effect of a multifactor intervention program on reducing the mortality of coronary heart disease in middle-aged men.

INTERVAL ESTIMATION OF TREATMENT EFFECTS IN DOUBLE CONSENT RANDOMIZED DESIGN

Abstract: The double consent randomized design, in which the physician and the patient know exactly what treatment the patient receives, has been proposed to alleviate the concern in carrying out a conventional randomized trial. In the latter, the assignment of patients to treatments after obtaining patients' informed consents depends completely on a chance mechanism. We develop four interval estimators, two using the delta method or the principle of Fieller's Theorem calculated over the pooled samples of eligible patients, and two calculated over the samples excluding patients who have treatment preference. Using Monte Carlo simulation, we evaluate and compare the performance of these estimators in a variety of situations. We note that the estimators using the principle of Fieller's Theorem outperform those derived from the delta method with respect to both coverage probability and average length in almost all situations considered here. We further note that when the expected number of patients who have no treatment preference is moderate or large (say ≥ 25) per treatment, the interval estimator using Fieller's Theorem calculated over the restricted samples is generally more efficient than those calculated over the entire pooled samples without much loss of accuracy as measured by coverage probability. On the other hand, when the expected number of patients who have no treatment preference is small, the coverage probability for the estimators calculated over the restricted samples tends to be less than the desired confidence level, while the coverage probability of the estimator using Fieller's Theorem on the pooled samples may still agree with the desired confidence level