Sample Size Configuration Research Articles

Joint Estimation of Binomial Proportions

Interval estimation of a binomial proportion has had a consistent presence in the statistical literature through the years. Many interval procedures have been developed for a single proportion as well as for the difference of two proportions. However, little work has been conducted on the joint estimation of two binomial proportions. In this paper, we construct four confidence regions for two binomial proportions based on three statistics: the Wald (W), adjusted Wald (W*), score (S), and likelihood ratio (LR) statistics. Once the regions have been established, we compare their coverage probabilities and average areas for different parameter and sample size configurations. For small-to-moderate sample sizes, this paper finds that the three regions based on the W*, S, and LR statistics have good coverage properties, with the score region usually having the smallest average area. Finally, we apply these four confidence regions to some real data in veterinary science and medicine for the joint estimation of important proportions.

Multiple assessments of non-inferiority trials with ordinal endpoints.

Non-inferiority (NI) trials are implemented when there is a practical demand to search for alternatives to standard therapies, such as to reduce side effects. An experimental treatment is considered non-inferior to the standard treatment when it exhibits clinically non-significant loss of efficacy. Ordinal categorical responses are frequently observed in clinical trials. It has been reported that responses measured using an ordinal scale produce more informative analysis than when responses collapse into binary outcomes. We study the NI trials using ordinal endpoints. We propose a latent variable model for ordinal categorical responses. Based on the proposed latent variable model, the mean efficacy of the different treatments is denoted by the corresponding mean parameter of the underlying continuous distributions. A two-step procedure is proposed for model identification and parameter estimation. A non-inferiority analysis can then be conducted based on the latent variable model and the corresponding estimation procedure. We also develop a method and an algorithm to produce an optimal sample size configuration based on the proposed testing procedure. Two clinical examples are provided for demonstrative purposes.

Radiomics Features Based on MRI-ADC Maps of Patients with Breast Cancer: Relationship with Lesion Size, Features Stability, and Model Accuracy.

Objective:To predict breast cancer molecular subtypes with neural networks based on magnetic resonance imaging apparent diffusion coefficient (ADC) radiomics and to detect the relation of lesion size with the stability of radiomics features.Methods:This retrospective study included 221 consecutive patients (224 lesions) with breast cancer imaged between January 2015 and January 2020. Three sample size configurations were identified based on tumor size (experiment 1: all cases, experiment 2: >1 cm3, and experiment 3: >2 cm3). The tumors were segmented by three observers based on diffusion-weighted imaging-registered ADC maps, and the volumetric agreement of these segmentations was evaluated using the Dice coefficient. Stability of radiomics features (n=851) was evaluated with intraclass correlation coefficient (ICC, >0.75) and coefficient of variation (CoV, <0.15). Feature selection was made with variance inflation factor (VIF, <10) and least absolute shrinkage and selection operator regression. Outcomes were identified as molecular subtypes (Luminal A, Luminal B, HER2-enriched, triple-negative). Neural network performance was presented as an area under the curve and accuracies.Results:Of the 851 radiomics features, 611 had ICC >0.75, and 37 remained stable in the first experiment, 49 in the second, and 59 in the third based on CoV and VIF analysis. High accuracy was demonstrated by the Luminal B, HER2-enriched, and triple-negative models in the first experiment (>80%), all models in the second experiment, and HER2-enriched and triple-negative models in the third experiment.Conclusions:A positive stability is indicated by an increased lesion size related to radiomics features. Neural networks may predict moleculer subtypes of breast cancers over 1 cm3 with high accuracy.

On the use of min-max combination of biomarkers to maximize the partial area under the ROC curve.

Evaluation of diagnostic assays and predictive performance of biomarkers based on the receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are vital in diagnostic and targeted medicine. The partial area under the curve (pAUC) is an alternative metric focusing on a range of practical and clinical relevance of the diagnostic assay. In this article, we adopt and extend the min-max method to the estimation of the pAUC when multiple continuous scaled biomarkers are available and compare the performances of our proposed approach with existing approaches via simulations. We conducted extensive simulation studies to investigate the performance of different methods for the combination of biomarkers based on their abilities to produce the largest pAUC estimates. Data were generated from different multivariate distributions with equal and unequal variance-covariance matrices. Different shapes of the ROC curves, false positive fraction ranges, and sample size configurations were considered. We obtained the mean and standard deviation of the pAUC estimates through re-substitution and leave-one-pair-out cross validation. Our results demonstrate that the proposed method provides the largest pAUC estimates under the following three important practical scenarios: (1) multivariate normally distributed data for non-diseased and diseased participants have unequal variance-covariance matrices; or (2) the ROC curves generated from individual biomarker are relative close regardless of the latent normality distributional assumption; or (3) the ROC curves generated from individual biomarker have straight-line shapes. The proposed method is robust and investigators are encouraged to use this approach in the estimation of the pAUC for many practical scenarios.

Approximate one-sided tolerance limits in random effects model and in some mixed models and comparisons

An approximate closed-form one-sided tolerance limit (TL) in a general mixed model is proposed. One-sided TLs for the distribution of observable random variable and for the distribution of unobservable random variable in one-way random model are obtained as special cases from the one for the general mixed model. Applications to a two-way nested random model are also given. The merits of the TLs are evaluated using Monte Carlo simulation and compared with the existing ones. Our comparison studies indicate that the approximate TLs are quite satisfactory for all parameter and sample size configurations, and better than the existing ones in some cases. Approximate confidence intervals for exceedance probabilities in one-way random effects model are also proposed. The procedures are illustrated using three examples.

Multi-regional clinical trial design and consistency assessment of treatment effects

We can apply both fixed and random effects models to multi-regional clinical trial (MRCT) design and data analysis. Thoroughly, understanding the features of these models in an MRCT setting will help assessing their applicability to an MRCT. In this paper, we discuss the interpretations of trial results from these models. We also evaluate the impact of the number of regions and the sample size configuration across the regions on the required total sample size for the overall treatment effect assessment. For quantifying treatment effects of individual regions, the empirical shrinkage estimator and the James-Stein type shrinkage estimator associate with smaller variability compared with the regular sample estimator. We conduct computation and simulation to compare the performance of these estimators when they are applied to assess consistency of treatment effects across regions. We use a multinational trial example to illustrate the application of these methods.

Bayesian clustering analyses for genetic assignment and study of hybridization in oaks: effects of asymmetric phylogenies and asymmetric sampling schemes

Bayesian clustering methods have been widely used for studying species delimitation and genetic introgression. In order to test the effect of phylogenetic relationships and sampling scheme on the inferred clustering solution and on the performance of Bayesian clustering analysis, I simulated genotypes of the interfertile oak species Quercus robur, Quercus petraea, and Quercus pubescens and I run analyses using two popular software programs, STRUCTURE and BAPS. First, based on purebred simulations, I compared clustering solutions resulting from different sample size configurations. While clustering solution generally reflected the taxonomic relationships when equal samples of each species were included, spurious partition was inferred by STRUCTURE when some species were represented by larger and others by smaller samples. In very unbalanced configurations, STRUCTURE failed to identify the three species, even if three subpopulations were assumed. By contrast, BAPS could properly identify the three species under any sampling scheme. Second, based on simulations of purebreds and hybrids, I tested the performance of individual assignments with variable number of loci. This analysis showed that STRUCTURE can detect introgressed individuals more efficiently than BAPS. However, BAPS could assign purebreds more efficiently with a lower number of loci. Method performance also depended on phylogenetic relationships. In the case of Q. petraea, Q. pubescens, and their hybrids, method performance was lower due to their phylogenetic affinity. Inclusion of three instead of two species into the analysis led to reduction of performance, and to misclassification of hybrids, which often reflected the phylogenetic affinity between Q. petraea and Q. pubescens.

Extension of three‐arm non‐inferiority studies to trials with multiple new treatments

Non-inferiority (NI) trials are becoming increasingly popular. The main purpose of NI trials is to assert the efficacy of a new treatment compared with an active control by demonstrating that the new treatment maintains a substantial fraction of the treatment effect of the control. Most of the statistical testing procedures in this area have been developed for three-arm NI trials in which a new treatment is compared with an active control in the presence of a placebo. However, NI trials frequently involve comparisons of several new treatments with a control, such as in studies involving different doses of a new drug or different combinations of several new drugs. In seeking an adequate testing procedure for such cases, we use a new approach that modifies existing testing procedures to cover circumstances in which several new treatments are present. We also give methods and algorithms to produce the optimal sample size configuration. In addition, we also discuss the advantages of using different margins for the assay sensitivity test between the active control and the placebo and the NI test between the new treatments and the active control. We illustrate the new approach by using data from a clinical trial.

Bayesian Inference for a Correlated 2 × 2 Table with a Structural Zero

We develop a new Bayesian approach to interval estimation for both the risk difference and the risk ratio for a 2 x 2 table with a structural zero using Markov chain Monte Carlo (MCMC) methods. We also derive a normal approximation for the risk difference and a gamma approximation for the risk ratio. We then compare the coverage and interval width of our new intervals to the score-based intervals over various parameter and sample-size configurations. Finally, we consider a Bayesian method for sample-size determination.

Some c-sample rank tests of homogeneity against umbrella alternatives with unknown peak

The c-sample location problem with umbrella alternatives is investigated. The umbrella peak l is assumed to be unknown. All test statistics are maxima of substatistics which are constructed for the case of a known peak l. These substatistics are based on ranks. Arbitrary scores and arbitrary sample size configurations are allowed. As special cases we have tests of Chen and Wolfe [Chen, Y.I. and Wolfe, D.A., 1990, A study of distribution-free tests for umbrella alternatives. Biometrical Journal, 32, 47–57.], Hettmansperger and Norton [Hettmansperger, T.P. and Norton, R.M., 1987, Tests for patterned alternatives in k-sample problems. Journal of the American Statistical Association, 82, 292–299.] and Shi [Shi, N.-Z., 1988, Rank test statistics for umbrella alternatives. Communications in Statistics, Theory and Methods, 17, 2059–2073.]. We compute the asymptotic power functions of the constructed tests. For the cases of three or four treatments, some figures give an impression of the asymptotic power functions for various setups. Simulation studies show that the asymptotic results can also be used for moderate sample sizes. In average, over all setups, the Hettmansperger–Norton-type test performs best densely followed by the Chen–Wolfe-type test and the Shi-type test.

Statistical Considerations on Bridging Strategy through Joining a Multi-regional Study

For bridging clinical data, a study is additionally conducted in new region to demonstrate some similarity in treatment effects between two regions. An alternative bridging strategy is that new region participates in a multi-regional study as one site. This paper focuses on a possibility of bridging through joining multi-regional study, and statistical inference for an interaction term between treatment and region to detect non-similarity of treatment effects among regions/countries. Applying a logistic model with the terms of treatment effect, regional effect and their interaction to dichotomous response data, a simulation study is performed to investigate statistical power to detect significant treatment-by-region interaction, and treatment effect for a variety of sample size configurations. The result suggests that moderate or large sample sizes are required in new region to achieve sufficient power, if a substantial (qualitative or quantitative) interaction exists.

A comparison of an adaptive two-sample test to the t-test and the rank-sum test

A two-sample test is proposed which has greater power than the commonly used tests for several stochastically ordered alternatives, including the shift alternative. The proposed test is an adaptive test which uses the order statistics within the two samples to determine a suitable score function for a rank test. This test is shown, by Monte Carlo studies, to maintain its significance level for many distributions and sample size configurations. The proposed test had the highest power or was within 5% of the highest power among the tests considered for 90.4% of the simulations. The corresponding percentages were 39.6% for the pooled t-test, 65.7% for the rank-sum test, 78.8% for the normal scores test, and 78.7% for the adaptive test of Hogg, Fisher, and Randies. These simulations also showed that Welch's t-test often failed to maintain its significance level.

On the conservatism of the Tukey-Kramer multiple comparison procedure

Asymptotically correct confidence intervals for the Tukey-Kramer procedure are given for a limiting sample size configuration. It is conjectured that the procedure is the ‘most conservative’ for this configuration.

A Monte Carlo Investigation of Homogeneity Tests of the Odds Ratio under Various Sample Size Configurations

Epidemiologic data for case-control studies are often summarized into K 2 x 2 tables. Given a fixed number of cases and controls, the degree of sparseness in the data depends on the number of strata, K. The effect of increasing stratification on size and power of seven tests of homogeneity of the odds ratio is studied using Monte Carlo methods. In all the designs considered here, the numbers of cases and controls per stratum are the same. Considering both size and power in non-sparse-data settings, we recommend the Breslow-Day statistic (1980, Statistical Methods in Cancer Research, 1. The Analysis of Case-Control Studies, p. 142; Lyon: International Agency for Research on Cancer) for general use. In sparse-data settings the T4 statistic of Liang and Self (1985, Biometrika 72, 353-358) performs the best when all tables, regardless of sample size, have odds ratios generated from the same distribution. In sparse-data settings characterized by a large table with an odds ratio of 1 and many small tables with odds ratios greater than 1, the T5 statistic of Liang and Self (1985) performs the best. One of the most important results of this study is the generally low power for all homogeneity tests especially when the data are sparse.

A Method of Obtaining an Exact Confidence Interval for the Common Mean of Several Normal Populations

A linear combination T of Student's t statistics is proposed as a practical method of obtaining confidence intervals for the common mean, and the distribution function of T is conveniently approximated for the general case. Exact percentage points of T are compared with those based on this approximation for two populations and various sample size configurations.