Model Assisted Statistics and Applications

In some clinical trials, more than one primary endpoints are used for efficacy evaluation, and the drug is considered efficacious as long as a large enough subset of the endpoints meet some 'success' criteria. In this paper, we study the type I error rate and power under this subset decision rule. We demonstrate that the type I error rate can be inflated when each endpoint is tested at the nominal level. Particularly, when the endpoints are conditionally unbiased, this inflation is maximized when the number of endpoints that truly carry the drug effect is exactly one less than that in the subset. We study two methods in adjusting the type I error rate: modified Bonferroni method and Hochberg method. With mutually independent endpoints, when the number of endpoints in the subset is pre-fixed (due to the requirement of regulatory agency or a established criteria), we recommend that the total number of endpoints specified should be as close as possible to that of the subset to avoid excessive loss in power with adjustment procedures. Discussion for the situation of correlated endpoints and improvement for decision rule are also provided.

When mean treatment difference is not considered valid to quantify treatment effect for endpoints measured in continuous or ordinal scales in clinical trials because small treatment gains may not be clinically relevant, data on individuals are often dichotomized into responder versus non-responder. Thus, differences in responder rates between treatments are used to quantify the treatment effect, without incorporating the sizes of treatment gains in responders. Sizes of treatment gains provide information on how good the treatment is in responders, while the sizes in non-responders are clinically irrelevant. It is therefore important to incorporate information on treatment gains in responders when assessing the treatment difference. In this article, we propose a new way of quantifying the treatment effect, referred to as weighted responder mean, by making complete use of the information available in responders. Tests for treatment differences using weighted responder means are proposed. Examples of using this weighted responder mean analysis are illustrated.

The traditional fixed margin approach for evaluating an experimental treatment through an active-controlled noninferiority trial is simple and straightforward. However its utility is highly dependent on the ability of the experimental data to satisfy the constancy assumption. If the constancy assumption is violated, other approaches must be used. One such approach is the recently described covariate-adjustment methodology. This approach permits more flexibility and improved discriminatory capacity compared to the fixed margin approach. However, the absence of a declared pre-determined noninferiority margin during the planning stage can lead to data analysis disputes between clinical trial sponsors and regulatory agencies. In this article, we present an adaptive noninferiority margin and sample size adjustment strategy implementing the covariate adjustment approach. We will demonstrate that the covariate-adjusted approach not only provides improved decision making quality, but also maintains implementation simplicity.

The linear rank test statistic has been an important test statistic in the area of nonparametrics. In this study, new test statistics based on the linear rank test are derived and applied to compare two length biased distributions. Through a series of size and power simulations, it is found that the new tests adjust for length biasing so efficiently that they behave similarly to the corresponding linear rank tests without length biasing. In practice, these new test procedures can be utilized as a proper tool to adjust length bias, which enables us to analyze a length biased sample.

Correlated survival data analysis techniques were utilized to determine the efficacy of such techniques to analyze correlated airway responsiveness data. When the survival data are correlated, standard maximum likelihood estimates of the regression coefficients obtained by using the Cox’s model are consistent, but the estimates of standard errors may not be valid or consistent due to within-subject dependencies and hence give rise to wrong interpretations. We used jackknife, bootstrap and the method proposed by Wei, Lin and Weissfeld (WLW) to obtain robust estimates for the standard errors. The data analyzed in this report were obtained from a longitudinal study conducted to investigate the respiratory health effects of initial exposure to grain dust among workers commencing employment in the grain industry in the province of Saskatchewan, Canada. Bronchial responsiveness was determined by histamine inhalation test administered at four different time points. The provocation concentration ( PC 20 ) of inhaled histamine that produced 20% fall in the lung function parameter forced expired volume in one second ( FEV 1 ) was used as an indicator of bronchial responsiveness. Failure was defined as the dose of histamine at which a 20% fall in FEV 1 occurred. In provocation tests, censored data may occur due to the failure to reach a determined end point. Censoring occurred when a subject did not have 20% fall in FEV 1 with the maximum histamine dose of 8 mg. Significant predictors of bronchial responsiveness were FEV 1 , wheezing and height. The estimates of standard errors were similar for jackknife, bootstrap, and WLW, but different from those obtained using standard maximum likelihood method.

An important application of microarray analysis is to identify a subset of differentially expressed genes as biomarkers. Microarray experiments are often performed with few replicates and data are obtained from a limited sample size. To overcome the impact of small sample size on gene marker identification, we used a new approach to validate the candidate gene markers. In this study, candidate genes were first identified based on the statistically significant p-value levels and the biologically significant levels of fold-change from original microarray data. Multiple new, perturbed datasets were then generated from the original dataset by introducing artificial errors at different levels. Subsequently, the performance of candidate genes in the new perturbed datasets was evaluated using t-test at various statistical significance levels. Based on the stability of candidate genes in the perturbed datasets at different error levels, a subset of candidate genes can be selected as potential target biomarkers. Perturbed artificial datasets provide a new opportunity to validate candidate target genes identified by microarray experiments with a limited sample size.

Unexpected and unplanned events like lab errors can occur during scientific experiments or measurements. When they occur, a model that ignores them can be very inaccurate. Two diagnostic tools are compared. One is improb which equals the sum of the probabilities of all outcomes as likely as or less likely than the actual outcome. The second is a rarity index which is newer and equals the probability of the actual outcome divided by the probability of the most probable outcome. Serial dilution experiments are the motivating example and will be discussed extensively, although both methods may apply more generally.