Another view on the analysis of cardiovascular morbidity/mortality trials

In many morbidity/mortality studies, composite endpoints are considered. Although the primary interest is to demonstrate that an invention delays death, the expected death rate is often that low that studies focussing on survival exclusively are not feasible. Components of the composite endpoint are chosen such that their occurrence is predictive for time to death. Therefore, if the time to non-fatal events is censored by death, censoring is no longer independent. As a consequence, the analysis of the components of a composite endpoint cannot be reasonably performed using classical methods for the analysis of survival times like Kaplan-Meier estimates or log-rank tests. In this paper we visualize the impact of disregarding dependent censoring during the analysis and discuss practicable alternatives for the analysis of morbidity/mortality studies. In the context of simulations we provide evidence that copula-based methods have the potential to deliver practically unbiased estimates of hazards of components of a composite endpoint. At the same time, they require minimal assumptions, which is important since not all assumptions are generally verifiable because of censoring. Therefore, there are alternative ways to analyze morbidity/mortality studies more appropriately by accounting for the dependencies among the components of composite endpoints. Despite the limitations mentioned, these alternatives can at minimum serve as sensitivity analyses to check the robustness of the currently used methods.     

Exact Statistical Tests for Heterogeneity of Frequencies Based on Extreme Values

Sophisticated statistical analyses of incidence frequencies are often required for various epidemiologic and biomedical applications. Among the most commonly applied methods is the Pearson's χ² test, which is structured to detect non specific anomalous patterns of frequencies and is useful for testing the significance for incidence heterogeneity. However, the Pearson's χ² test is not efficient for assessing the significance of frequency in a particular cell (or class) to be attributed to chance alone. We recently developed statistical tests for detecting temporal anomalies of disease cases based on maximum and minimum frequencies; these tests are actually designed to test of significance for a particular high or low frequency. The purpose of this article is to demonstrate merits of these tests in epidemiologic and biomedical studies. We show that our proposed methods are more sensitive and powerful for testing extreme cell counts than is the Pearson's χ² test. This feature could provide important and valuable information in epidemiologic or biomeidcal studies. We elucidated and illustrated the differences in sensitivity among our tests and the Pearson's χ² test by analyzing a data set of Langerhans cell histiocytosis cases and its hypothetical sets. We also computed and compared the statistical power of these methods using various sets of cell numbers and alternative frequencies. The investigation of statistical sensitivity and power presented in this work will provide investigators with useful guidelines for selecting the appropriate tests for their studies.     

Evaluating paired categorical data when the pairing is lost

We encountered a problem in which a study's experimental design called for the use of paired data, but the pairing between subjects had been lost during the data collection procedure. Thus we were presented with a data set consisting of pre and post responses but with no way of determining the dependencies between our observed pre and post values. The aim of the study was to assess whether an intervention called Self-Revelatory Performance had an impact on participant's perceptions of Alzheimer's disease. The participant's responses were measured on an Affect grid before the intervention and on a separate grid after. To address the underlying question in light of the lost pairing we utilized a modified bootstrap approach to create a null hypothesized distribution for our test statistic, which was the distance between the two Affect Grids' Centers of Mass. Using this approach we were able to reject our null hypothesis and conclude that there was evidence the intervention influenced perceptions about the disease.     

Relations among three parametric multiple testing methods for correlated tests

Multiple endpoints in clinical trials are usually correlated. To control the family-wise type I error rate, both Huque and Alosh's flexible fixed-sequence (FFS) testing method and Li and Mehrotra's adaptive α allocation approach (4A) have taken into account correlations among endpoints. I suggested a weighted multiple testing correction (WMTC) for correlated tests and compared it with FFS. However, the relationship between the 4A method and the FFS method or the relationship between the 4A method and the WMTC method has not been studied. In this paper, simulations are conducted to investigate these relationships. Tentative guidelines to help choosing an appropriate method are provided.     

How to avoid concerns with the interpretation of two primary endpoints if significant superiority in one is sufficient for formal proof of efficacy

Formal proof of efficacy of a drug requires that in a prospective experiment, superiority over placebo, or either superiority or at least non-inferiority to an established standard, is demonstrated. Traditionally one primary endpoint is specified, but various diseases exist where treatment success needs to be based on the assessment of two primary endpoints. With co-primary endpoints, both need to be “significant” as a prerequisite to claim study success. Here, no adjustment of the study-wise type-1-error is needed, but sample size is often increased to maintain the pre-defined power. Studies that use an at-least-one concept have been proposed where study success is claimed if superiority for at least one of the endpoints is demonstrated. This is sometimes also called the dual primary endpoint concept, and an appropriate adjustment of the study-wise type-1-error is required. This concept is not covered in the European Guideline on multiplicity because study success can be claimed if one endpoint shows significant superiority, despite a possible deterioration in the other. In line with Röhmel's strategy, we discuss an alternative approach including non-inferiority hypotheses testing that avoids obvious contradictions to proper decision-making. This approach leads back to the co-primary endpoint assessment, and has the advantage that minimum requirements for endpoints can be modeled flexibly for several practical needs. Our simulations show that, if planning assumptions are correct, the proposed additional requirements improve interpretation with only a limited impact on power, that is, on sample size.     

Minimax powerful functional analysis of covariance tests with application to longitudinal genome-wide association studies

We model the Alzheimer's disease-related phenotype response variables observed on irregular time points in longitudinal Genome-Wide Association Studies as sparse functional data and propose nonparametric test procedures to detect functional genotype effects while controlling the confounding effects of environmental covariates. Our new functional analysis of covariance tests are based on a seemingly unrelated kernel smoother, which takes into account the within-subject temporal correlations, and thus enjoy improved power over existing functional tests. We show that the proposed test combined with a uniformly consistent nonparametric covariance function estimator enjoys the Wilks phenomenon and is minimax most powerful. Data used in the preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database, where an application of the proposed test lead to the discovery of new genes that may be related to Alzheimer's disease.     

A comparison of reweighting estimators of average treatment effects in real world populations

Regulatory agencies typically evaluate the efficacy and safety of new interventions and grant commercial approval based on randomized controlled trials (RCTs). Other major healthcare stakeholders, such as insurance companies and health technology assessment agencies, while basing initial access and reimbursement decisions on RCT results, are also keenly interested in whether results observed in idealized trial settings will translate into comparable outcomes in real world settings—that is, into so-called “real world” effectiveness. Unfortunately, evidence of real world effectiveness for new interventions is not available at the time of initial approval. To bridge this gap, statistical methods are available to extend the estimated treatment effect observed in a RCT to a target population. The generalization is done by weighting the subjects who participated in a RCT so that the weighted trial population resembles a target population. We evaluate a variety of alternative estimation and weight construction procedures using both simulations and a real world data example using two clinical trials of an investigational intervention for Alzheimer's disease. Our results suggest an optimal approach to estimation depends on the characteristics of source and target populations, including degree of selection bias and treatment effect heterogeneity.     

Rank aggregation using latent-scale distance-based models

Rank aggregation aims at combining rankings of a set of items assigned by a sample of rankers to generate a consensus ranking. A typical solution is to adopt a distance-based approach to minimize the sum of the distances to the observed rankings. However, this simple sum may not be appropriate when the quality of rankers varies. This happens when rankers with different backgrounds may have different cognitive levels of examining the items. In this paper, we develop a new distance-based model by allowing different weights for different rankers. Under this model, the weight associated with a ranker is used to measure his/her cognitive level of ranking of the items, and these weights are unobserved and exponentially distributed. Maximum likelihood method is used for model estimation. Extensions to the cases of incomplete rankings and mixture modeling are also discussed. Empirical applications demonstrate that the proposed model produces better rank aggregation than those generated by Borda and the unweighted distance-based models.

     

Predicting Turning Points Through the Integration of Multiple Models

A new method for forming composite turning-point (or other qualitative) forecasts is proposed. Rather than forming composite forecasts by the standard Bayesian approach with weights proportional to each model's posterior odds, weights are assigned to the individual models in proportion to the probability of each model's having the correct turning-point prediction. These probabilities are generated by logit models estimated with data on the models' past turning-point forecasts. An empirical application to gross national product/gross domestic product forecasting of 18 Organization for Economic Cooperation and Development countries demonstrates the potential benefits of the procedure     

Sample size determination for the weighted log‐rank test with the Fleming–Harrington class of weights in cancer vaccine studies

In recent years, immunological science has evolved, and cancer vaccines are available for treating existing cancers. Because cancer vaccines require time to elicit an immune response, a delayed treatment effect is expected. Accordingly, the use of weighted log‐rank tests with the Fleming–Harrington class of weights is proposed for evaluation of survival endpoints. We present a method for calculating the sample size under assumption of a piecewise exponential distribution for the cancer vaccine group and an exponential distribution for the placebo group as the survival model. The impact of delayed effect timing on both the choice of the Fleming–Harrington's weights and the increment in the required number of events is discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust extreme ranked set sampling

In this paper, a robust extreme ranked set sampling (RERSS) procedure for estimating the population mean is introduced. It is shown that the proposed method gives an unbiased estimator with smaller variance, provided the underlying distribution is symmetric. However, for asymmetric distributions a weighted mean is given, where the optimal weights are computed by using Shannon's entropy. The performance of the population mean estimator is discussed along with its properties. Monte Carlo simulations are used to demonstrate the performance of the RERSS estimator relative to the simple random sample (SRS), ranked set sampling (RSS) and extreme ranked set sampling (ERSS) estimators. The results indicate that the proposed estimator is more efficient than the estimators based on the traditional sampling methods.     

Correspondence Analysis of Cumulative Frequencies Using a Decomposition of Taguchi's Statistic

Taguchi's statistic has long been known to be a more appropriate measure of association for ordinal variables than the Pearson chi-squared statistic. Therefore, there is some advantage in using Taguchi's statistic for performing correspondence analysis when a two-way contingency table consists of one ordinal categorical variable. This article will explore the development of correspondence analysis using a decomposition of Taguchi's statistic.     

Development of predictive signatures for treatment selection in precision medicine with survival outcomes

For survival endpoints in subgroup selection, a score conversion model is often used to convert the set of biomarkers for each patient into a univariate score and using the median of the univariate scores to divide the patients into biomarker‐positive and biomarker‐negative subgroups. However, this may lead to bias in patient subgroup identification regarding the 2 issues: (1) treatment is equally effective for all patients and/or there is no subgroup difference; (2) the median value of the univariate scores as a cutoff may be inappropriate if the sizes of the 2 subgroups are differ substantially. We utilize a univariate composite score method to convert the set of patient's candidate biomarkers to a univariate response score. We propose applying the likelihood ratio test (LRT) to assess homogeneity of the sampled patients to address the first issue. In the context of identification of the subgroup of responders in adaptive design to demonstrate improvement of treatment efficacy (adaptive power), we suggest that subgroup selection is carried out if the LRT is significant. For the second issue, we utilize a likelihood‐based change‐point algorithm to find an optimal cutoff. Our simulation study shows that type I error generally is controlled, while the overall adaptive power to detect treatment effects sacrifices approximately 4.5% for the simulation designs considered by performing the LRT; furthermore, the change‐point algorithm outperforms the median cutoff considerably when the subgroup sizes differ substantially.     

A convenient formula for sample size calculations in clinical trials with multiple co-primary continuous endpoints

The clinical efficacy of a new treatment may often be better evaluated by two or more co-primary endpoints. Recently, in pharmaceutical drug development, there has been increasing discussion regarding establishing statistically significant favorable results on more than one endpoint in comparisons between treatments, which is referred to as a problem of multiple co-primary endpoints. Several methods have been proposed for calculating the sample size required to design a trial with multiple co-primary correlated endpoints. However, because these methods require users to have considerable mathematical sophistication and knowledge of programming techniques, their application and spread may be restricted in practice. To improve the convenience of these methods, in this paper, we provide a useful formula with accompanying numerical tables for sample size calculations to design clinical trials with two treatments, where the efficacy of a new treatment is demonstrated on continuous co-primary endpoints. In addition, we provide some examples to illustrate the sample size calculations made using the formula. Using the formula and the tables, which can be read according to the patterns of correlations and effect size ratios expected in multiple co-primary endpoints, makes it convenient to evaluate the required sample size promptly.     

Asymptotic Properties of Adaptive Likelihood Weights by Cross-Validation

For clinical trials on neurodegenerative diseases such as Parkinson's or Alzheimer's, the distributions of psychometric measures for both placebo and treatment groups are generally skewed because of the characteristics of the diseases. Through an analytical, but computationally intensive, algorithm, we specifically compare power curves between 3- and 7-category ordinal logistic regression models in terms of the probability of detecting the treatment effect, assuming a symmetric distribution or skewed distributions for the placebo group. The proportional odds assumption under the ordinal logistic regression model plays an important role in these comparisons. The results indicate that there is no significant difference in the power curves between 3-category and 7-category response models where a symmetric distribution is assumed for the placebo group. However, when the skewness becomes more extreme for the placebo group, the loss of power can be substantial.     

Bayesians Should Not Resample a Prior Sample to Learn about the Posterior

It is argued in a Bayesian context in which a set of parameter values is simulated from a prior distribution, that the sampling importance resampling algorithm should not be used to resample these values so as to obtain an approximate sample from the posterior. Rather, the whole set of prior values, along with their appropriate weights, can be more gainfully employed.     

Precise definitions of some terminology for longitudinal clinical trials: subjects,patient populations,analysis sets,intention to treat,and related terms

Biostatisticians recognize the importance of precise definitions of technical terms in randomized controlled clinical trial (RCCT) protocols, statistical analysis plans, and so on, in part because definitions are a foundation for subsequent actions. Imprecise definitions can be a source of controversies about appropriate statistical methods, interpretation of results, and extrapolations to larger populations. This paper presents precise definitions of some familiar terms and definitions of some new terms, some perhaps controversial. The glossary contains definitions that can be copied into a protocol, statistical analysis plan, or similar document and customized. The definitions were motivated and illustrated in the context of a longitudinal RCCT in which some randomized enrollees are non‐adherent, receive a corrupted treatment, or withdraw prematurely. The definitions can be adapted for use in a much wider set of RCCTs. New terms can be used in place of controversial terms, for example, subject. We define terms specifying a person's progress through RCCT phases and that precisely define the RCCT's phases and milestones. We define terms that distinguish between subsets of an RCCT's enrollees and a much larger patient population. ‘The intention‐to‐treat (ITT) principle’ has multiple interpretations that can be distilled to the definitions of the ‘ITT analysis set of randomized enrollees’. Most differences among interpretations of ‘the’ ITT principle stem from an RCCT's primary objective (mainly efficacy versus effectiveness). Four different ‘authoritative’ definitions of ITT analysis set of randomized enrollees illustrate the variety of interpretations. We propose a separate specification of the analysis set of data that will be used in a specific analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

AN INVENTORY PROBLEM APPLIED TO A RENTAL SITUATION

An inventory problem, applied to a rental situation business, has been considered. If no item is in stock when a demand occurs, the company borrows the units from other concerns in the same line of business. The profit function has been calculated and it has been shown how the inventory level increases with penalty cost. A review of the literature on inventory control reveals that not much work has been done in holding inventories of rental items. In a recent paper, Tainiter (1964) considered the situation in which a company rents out items such as cars, trucks, farm equipment, books, furniture, etc., and obtained the profit function by taking “rental-out” time as a negative exponential and demand as a general random variable. The model is equally applicable to companies which rent out “service personnel”, repair men, taxi cabs, etc. “We consider a company renting out items to customers. The company starts its business by purchasing a total number of M items in the inventory. The term inventory, defined by Arrow, Earlin and Scarf (1958) as the stock of goods which is kept for future sale or production, is applicable here. Whenever a demand occurs the item is rented out immediately, if it is available in the stock. But if the inventory is zero, i.e. all the items are rented out, the demand will be satisfied by borrowing items from other companies which are dealing in the same line of business. For example, a manufacturer of refrigerators maintains and repairs his product at the customer's house after sale. If a complaint arrives when no repairmen are available, the company will “borrow” repairmen from elsewhere and will attend to the complaint immediately. The borrowing cost may be negative or positive, representing a penalty or a profit. On the other hand if the company does not borrow and the customer has to wait (and such situations occur very often) the loss of the customer's goodwill may occur. It is also not possible to keep large numbers of items because of the storage costs and tied up capital. The problem is then to devise an optimal policy such that the profits of the company are maximized.     

Aspects of two group concordance

A definition of concordance is derived from Rao's concept of a perfect diversity measure in order to identify aspects about which two populations of judges agree. In the case where each judge independently ranks a fixed set of items, the class of concordance measures based on the marginal distributions of the ranks is characterized by bi-affine similarity functions that measure how well pairs of judges tend to agree. This class contains population versions of several familiar indices of concordance, including Kendall's W. Concordance between two populations, refered to as intergroup concordance, is also scaled against its corresponding intragroup measures. Small sample properties of estimators of the ratio of inter-to-intra group concordance are investigated in a Monte Carlo study. An example is given to illustrate components of concordance attributable to subsets of items, and to contrast the proposed methods with previous analyses.     

A structured brain‐wide and genome‐wide association study using ADNI PET images

A multistage variable selection method is introduced for detecting association signals in structured brain‐wide and genome‐wide association studies (brain‐GWAS). Compared to conventional methods that link one voxel to one single nucleotide polymorphism (SNP), our approach is more efficient and powerful in selecting the important signals by integrating anatomic and gene grouping structures in the brain and the genome, respectively. It avoids resorting to a large number of multiple comparisons while effectively controlling the false discoveries. Validity of the proposed approach is demonstrated by both theoretical investigation and numerical simulations. We apply our proposed method to a brain‐GWAS using Alzheimer's Disease Neuroimaging Initiative positron emission tomography (ADNI PET) imaging and genomic data. We confirm previously reported association signals and also uncover several novel SNPs and genes that are either associated with brain glucose metabolism or have their association significantly modified by Alzheimer's disease status.