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In ophthalmologic or otolaryngologic studies, bilateral correlated data often arise when observations involving paired organs (e.g., eyes, ears) are measured from each subject. Based on Donner's model , in this paper, we focus on investigating the relationship between the disease probability and covariates (such as ages, weights, gender, and so on) via the logistic regression for the analysis of bilateral correlated data. We first propose a new minorization-maximization (MM) algorithm and a fast quadratic lower bound (QLB) algorithm to calculate the maximum likelihood estimates of the vector of regression coefficients, and then develop three large-sample tests (i.e., the likelihood ratio test, Wald test, and score test) to test if covariates have a significant impact on the disease probability. Simulation studies are conducted to evaluate the performance of the proposed fast QLB algorithm and three testing methods. A real ophthalmologic data set in Iran is used to illustrate the proposed methods.

In a parallel group study comparing a new treatment with a standard of care, missing data often occur for various reasons. When the outcome is binary, the data from such studies can be summarized into a 2 × 3 contingency table, with the missing observations in the last column. When the missingness is neither related to the outcome of interest nor related to other outcomes from the study but it is covariate dependent with the sole covariate being treatment, this type of missing data mechanism is considered as missing at random. In 2016, Tian et al.  proposed three statistics to test the hypothesis that the response rate is equivalent for a parallel group study with missing data. The asymptotic limiting distributions of these test statistics were used for statistical inference. However, asymptotic approaches for testing proportions generally do not have satisfactory performance with regard to type I error rate control for a clinical trial with the sample size from small to medium. For this reason, we consider an exact approach based on maximization to provide valid and efficient statistical inference for a parallel group study with missing data. Exact approaches can guarantee the type I error rate and they are computationally feasible in this setting. We conduct extensive numerical studies to compare the performance of the exact approach based on the three statistics for a one-sided hypothesis testing problem. We conclude that the exact approach based on the likelihood ratio statistic is more powerful than the exact approach based on the other two statistics. Two real clinical trial data sets are used to illustrate the application of the proposed exact approach.

In stratified bilateral studies, responses from two paired body parts are correlated. Confidence intervals (CIs), which reveal various features of the data, should take the correlations into account. In this article, five CI methods (sample-size weighted naïve Maximum likelihood estimation (MLE)-based Wald-type CI, complete MLE-based Wald-type CI, profile likelihood CI, MLE-based score CI and pooled MLE-based Wald-type CI) are derived for proportion ratios under the assumption of equal correlation coefficient within each stratum. Monte Carlo simulation shows that the complete MLE-based Wald-type CI approach generally produces the shortest mean interval width and satisfactory empirical coverage probability with close form solution; while the profile likelihood CI and the MLE-based score CI provide preferred ratio of non coverage probability and are more symmetric. Two real examples are used to demonstrate the performance of the proposed methods.

Matched-pair design is often used in clinical trials to increase the efficiency of establishing equivalence between two treatments with binary outcomes. In this article, we consider such a design based on rate ratio in the presence of incomplete data. The rate ratio is one of the most frequently used indices in comparing efficiency of two treatments in clinical trials. In this article, we propose 10 confidence-interval estimators for the rate ratio in incomplete matched-pair designs. A hybrid method that recovers variance estimates required for the rate ratio from the confidence limits for single proportions is proposed. It is noteworthy that confidence intervals based on this hybrid method have closed-form solution. The performance of the proposed confidence intervals is evaluated with respect to their exact coverage probability, expected confidence interval width, and distal and mesial noncoverage probability. The results show that the hybrid Agresti-Coull confidence interval based on Fieller's theorem performs satisfactorily for small to moderate sample sizes. Two real examples from clinical trials are used to illustrate the proposed confidence intervals.

The study of drug combinations has become important in drug development due to its potential for efficacy at lower, less toxic doses and the need to move new therapies rapidly into clinical trials. The goal is to identify which combinations are additive, synergistic, or antagonistic. Although there exists statistical framework for finding doses and sample sizes needed to detect departure from additivity, e.g., the power maximized F-test, different classes of drugs of different does-response shapes require different derivation for calculating sample size and finding doses. Motivated by two anticancer combination studies that we are involved with, this article proposes dose-finding and sample size method for detecting departures from additivity of two drugs with linear and log-linear single dose-response curves. The first study involves combination of two drugs, where one single drug dose-response curve is linear and the other is log-linear. The second study involves combinations of drugs whose single drug dose-response curves are linear. The experiment had been planned with the common fixed ratio design before we were consulted, but the resulting data missed the synergistic combinations. However, the experiment based on the proposed design was able to identify the synergistic combinations as anticipated. Thus we shall summarize the analysis of the data collected according to the proposed design and discuss why the commonly used fixed ratio method failed and the implications of the proposed method for other combination studies.

In cancer drug development, demonstrated anticancer activity in animal models is an important step to bring a promising compound to clinic. Proper design and analysis of experiments using laboratory animals have received increasing attention recently. These experiments involve informatively censored longitudinal data with small samples. The problem is further complicated because of order constraints due to the intrinsic growth of control tumors without treatment. This article proposes a Bayesian hierarchical model to analyze informatively censored longitudinal data while accounting for the parameter constraints and providing valid small sample inference. We adopt a noniterative sampling approach, the inverse Bayes formulae (IBF) sampler, to generate independent posterior samples, which avoids convergence problems associated with Markov chain Monte-Carlo methods. To effectively deal with the restricted parameter problem, we use a linear transformation to simplify the constraints and exploit the IBF method to generate random samples from truncated multivariate normal distributions. Because diffuse priors are used, the posterior modes approximate the maximum likelihood estimates well, and the hierarchical model can be considered as an extended mixed-effects model. A real xenograft experiment on a new treatment is analyzed by using the proposed method.

A series of N-protected peptide alcohols were synthesized using amino alcohols with unprotected hydroxy groups as amino components by the catalysis of subtilisin or alpha-chymotrypsin in organic solvents. N-protected aromatic amino acid esters were more suitable as acyl donors for subtilisin. The influences of different N-protecting groups, organic solvents, and content of water on synthesis of N-protected peptide alcohols were systematically studied.