Seung-Ho Kang

Rank-based estimating equations with general weight for accelerated failure time models: an induced smoothing approach

The induced smoothing technique overcomes the difficulties caused by the non-smoothness in rank-based estimating functions for accelerated failure time models, but it is only natural when the estimating function has Gehans weight. For a general weight, the induced smoothing method does not provide smooth estimating functions that can be easily evaluated. We propose an iterative-induced smoothing procedure for general weights with the estimator from Gehans weight initial value. The resulting estimators have the same asymptotic properties as those from the non-smooth estimating equations with the same weight. Their variances are estimated with an efficient resampling approach that avoids solving estimating equations repeatedly. The methodology is generalized to incorporate an additional weight to accommodate missing data and various sampling schemes. In a numerical study, the proposed estimators were obtained much faster without losing accuracy in comparison to those from non-smooth estimating equations, and the variance estimators provided good approximation of the variation in estimation. The methodology was applied to two real datasets, the first one from an adolescent depression study and the second one from a cancer study with missing covariates by design. The implementation is available in an R package aftgee.

Strength of evidence of non-inferiority trials-The adjustment of the type I error rate in non-inferiority trials with the synthesis method.

In non-inferiority trials that employ the synthesis method several types of dependencies among test statistics occur due to sharing of the same information from the historical trial. The conditions under which the dependencies appear may be divided into three categories. The first case is when a new drug is approved with single non-inferiority trial. The second case is when a new drug is approved if two independent non-inferiority trials show positive results. The third case is when two new different drugs are approved with the same active control. The problem of the dependencies is that they can make the type I error rate deviate from the nominal level. In order to study such deviations, we introduce the unconditional and conditional across-trial type I error rates when the non-inferiority margin is estimated from the historical trial, and investigate how the dependencies affect the type I error rates. We show that the unconditional across-trial type I error rate increases dramatically as does the correlation between two non-inferiority tests when a new drug is approved based on the positive results of two non-inferiority trials. We conclude that the conditional across-trial type I error rate involves the unknown treatment effect in the historical trial. The formulae of the conditional across-trial type I error rates provide us with a way of investigating the conditional across-trial type I error rates for various assumed values of the treatment effect in the historical trial.

Strength of Evidence of Noninferiority Trials with the Two Confidence Interval Method with Random Margin

This article deals with the dependency(ies) of noninferiority test(s) when the two confidence interval method is employed. There are two different definitions of the two confidence interval method. One of the objectives of this article is to sort out some of the confusion in these two different definitions. In the first definition the two confidence interval method is considered as the fixed margin method that treats a noninferiority margin as a fixed constant after it is determined based on historical data. In this article the method is called the two confidence interval method with fixed margin. The issue of the dependency(ies) of noninferiority test(s) does not occur in this case. In the second definition the two confidence interval method incorporates the uncertainty associated with the estimation for the noninferiority margin. In this article the method is called the two confidence interval method with random margin. The dependency(ies) occurs, because the two confidence interval method(s) with random margin shares the same historical data. In this article we investigate how the dependency(ies) affects the unconditional and conditional across-trial type I error rates.

The Adjustment of the Type I Error Rate in Noninferiority Trials with λ-Margin Approach: Each of Two Different New Drugs is Approved with Two Independent Trials with the Same Active Control

A regulatory agency usually requires two independent positive trials of the same new drug for approval. If two different new drugs are approved with the λ-margin approach by using the same active control, it implies that four noninferiority trials share the same active control. Sharing the same active control generates dependencies among trials. In this paper we investigate how much such dependencies inflate the unconditional and conditional across-trial type I error rates, and we propose a new procedure to adjust the inflated unconditional across-trial type I error rates.

Sample Size of Thorough QTc Clinical Trial Adjusted for Multiple Comparisons

A thorough QT trial is typically designed to test for two sets of hypotheses. The primary set of hypotheses is for demonstrating that the test treatment will not prolong QT interval. The second set of hypotheses is to demonstrate the assay sensitivity of the positive control treatment in the study population. Both analyses require multiple comparisons by testing the treatment difference measured repeatedly at multiple selected time points. Tsong and Zhong (2010) indicated that for prolongation testing, this involves an intersection-union test that leads to the reduction of study power. It requires type II error rate adjustment in order to maintain proper sample size and power of the test. Tsong et al. (2010) indicated also that the assay sensitivity analysis is carried out using a union-intersection test that leads to the inflation of the family-wise type I error rate. Type I error rate adjustment is required to control the family-wise type I error rate. Zhang and Machado (2008) proposed the sample size calculation of test-placebo QT response difference based on simulation with a multivariate normal distribution model. Even though the results are generally used as guidance for sample size determination for balanced arm TQT trials, they are limited in generalization to various advanced and adaptive designs of TQT trials (Zhang, 2011; Tsong, 2013). In this article, we propose a power equation based on multivariate normal distribution of TQT trials. Sample sizes of various TQT designs can be obtained through numerical iteration of the equation.

Sample Size Calculations for the Development of Biosimilar Products Based on Binary Endpoints

It is important not to overcalculate sample sizes for clinical trials due to economic, ethical, and scientific reasons. Kang and Kim (2014) investigated the accuracy of a well-known sample size calculation formula based on the approximate power for continuous endpoints in equivalence trials, which has been widely used for Development of Biosimilar Products. They concluded that this formula is overly conservative and that sample size should be calculated based on an exact power. This paper extends these results to binary endpoints for three popular metrics: the risk difference, the log of the relative risk, and the log of the odds ratio. We conclude that the sample size formulae based on the approximate power for binary endpoints in equivalence trials are overly conservative. In many cases, sample sizes to achieve 80% power based on approximate powers have 90% exact power. We propose that sample size should be computed numerically based on the exact power.

Statistical Assessment of Biosimilarity based on the Relative Distance between Follow-on Biologics in the (k + 1)-Arm Parallel Design

A three-arm parallel design has been proposed to assess the biosimilarity between a biological product and a reference product using relative distance (Kang and Chow, 2013). The three-arm parallel design consists of two arms for the reference product and one arm for the biosimilar product. This paper extended the three-arm parallel design to a (k + 1)-arm parallel design composed of k () arms for the reference product and one arm for the biosimilar product. A new relative distance was defined based on Euclidean distance; consequently, a corresponding test procedure was developed based on asymptotic distribution. Type I error rates and powers were investigated both theoretically and empirically.

Statistical Methods in Non-Inferiority Trials - A Focus on US FDA Guidelines -

The effect of a new treatment is proven through the comparison of a new treatment with placebo; however, the number of parent non-inferiority trials tends to grow proportionally to the number of active controls. In a non-inferiority trial a new treatment is approved by proof that the new treatment is not inferior to an active control; however, both additional assumptions and historical trials are needed to show (through the comparison of the new treatment with the active control in a non-inferiority trial) that the new treatment is more efficacious than a putative placebo. The two different methods of using the historical data: frequentist principle method and meta-analytic method. This paper discusses the statistical methods and different Type I error rates obtained through the different methods employed.

The Comparison of the Unconditional and Conditional Exact Power of Fisher`s Exact Tes

Abstract Since Fisher’s exact test is conducted conditional on the observed value of the margin, there are two kindsof the exact power, the conditional and the unconditional exact power. The conditional exact power iscomputed at a given value of the margin whereas the unconditional exact power is calculated by incorpo-rating the uncertainty of the margin. Although the sample size is determined based on the unconditionalexact power, the actual power which Fisher’s exact test has is the conditional power after the experimentis nished. This paper investigates di erences between the conditional and unconditional exact power ofFisher’s exact test. We conclude that such discrepancy is a disadvantage of Fisher’s exact test. Keywords: Conditional test, sample size determination, homogeneity, binomial. 1. Introduction In this paper we focus on testing the homogeneity of two independent binomial proportions whenthe sample size is small. When the sample size is large enough, the normal approximation to thebinomial distribution may be employed. However, when the sample size is small, such approximationmay not be valid and Fisher’s exact test is often employed as an alternative. The main advantageof exact tests (including Fisher’s exact test) is that it is guaranteed to control type I error ratesunder the nominal level.A key feature of Fisher’s exact test is that the test is conducted conditional on the observed valueof the margin. Therefore, there are two kinds of the exact power, the conditional and unconditionalexact power. The conditional exact power is computed at a given value of the margin whereas theunconditional exact power is calculated by incorporating the uncertainty of the margin. The samplesize should be determined based on the unconditional exact power, because a value of the margin isnot observed yet before an experiment is conducted. However, after the experiment is nished, theactual power which Fisher’s exact test has is the conditional power, because the test is a conditionaltest. Since in general the conditional exact power is not as same as the unconditional exact power,the actual power (the conditional exact power) which Fisher’s exact test has after the experiment

New Confidence Intervals for the Proportion of Interest in One-Sample Correlated Binary Data

Correlated binary data is obtained in many fields of biomedical research. When constructing a confidence interval for the proportion of interest, asymptotic confidence intervals have already been developed. However, such asymptotic confidence intervals are unreliable in small samples. To improve the performance of asymptotic confidence intervals in small samples, we obtain the Edgeworth expansion of the distribution of the studentized mean of beta-binomial random variables. Then, we propose new asymptotic confidence intervals by correcting the skewness in the Edgeworth expansion in one direct and two indirect ways. New confidence intervals are compared with the existing confidence intervals in simulation studies.