Pooled Association Tests for Rare Genetic Variants: A Review and Some New Results

In the search for genetic factors that are associated with complex heritable human traits, considerable attention is now being focused on rare variants that individually have small effects. In response, numerous recent papers have proposed testing strategies to assess association between a group of rare variants and a trait, with competing claims about the performance of various tests. The power of a given test in fact depends on the nature of any association and on the rareness of the variants in question. We review such tests within a general framework that covers a wide range of genetic models and types of data. We study the performance of specific tests through exact or asymptotic power formulas and through novel simulation studies of over 10,000 different models. The tests considered are also applied to real sequence data from the 1000 Genomes project and provided by the GAW17. We recommend a testing strategy, but our results show that power to detect association in plausible genetic scenarios is low for studies of medium size unless a high proportion of the chosen variants are causal. Consequently, considerable attention must be given to relevant biological information that can guide the selection of variants for testing.Comment: Published in at http://dx.doi.org/10.1214/13-STS456 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Meta-analysis of safety data: approximation of arcsine transformation and application of mixture distribution modeling

Meta-analysis is frequently used in the analysis of safety data. In dealing with rare events, the commonly used risk measures, such as the odds ratio, or risk difference, or their variance, can become undefined when no events are observed in studies. The use of an arcsine transformation and arcsine difference (AD) as treatment effect were shown to have desirable statistical properties (Rucker, 2009). However, the interpretation of the AD remains challenging and this may hamper its utility. To convert the AD to a risk measure similar to the risk difference, two previously proposed linear approximation methods, along with new linear and non-linear methods were discussed and evaluated. The existing approximation methods generally provide satisfactory approximation when the event proportions are between 0.15 and 0.85. We propose a new linear approximation method, the modified rationalized arcsine unit (MRAU) which improves the approximation when proportions fall outside the range from 0.15 to 0.85. However, the MRAU can still lead to under- or over-estimation depending on the underlying proportion. We then proposed a non-linear approximation method, based on a Taylor series expansion (TRAUD), which shows the best approximation across the full range of risk levels. However, the variance for TRAUD is less easily estimated and requires bootstrap estimation. Results from simulation studies confirm these findings under a wide array of scenarios. In the second section, heterogeneity in meta-analysis is discussed along with current methods that address the issue. To provide an exploration of the nature of heterogeneity, finite mixture model methods (FMM) were presented, and their application in meta-analysis discussed. The estimates derived from the components in FMM indicate that even with a pre-specified protocol, the studies included in a meta-analysis may come from different distributions that can cause heterogeneity. The estimated number of components may suggest the existence of multiple sub-populations that a simple overall effect estimate will neglect. We propose that in the analysis of safety data, the estimates of the number of components and their respective means can provide valuable information for better patient care. In the final section, the application of the approximation methods and the use of FMM are demonstrated in the analysis of two published meta-analysis examples from the medical literature

Sample Size/power Calculation for Stratified Case-cohort Design and Generalized Stratified Case-cohort Design

Time to event is a commonly used endpoint in epidemiological and disease prevention trials in order to study the relationship between risk factors and the endpoints. Case-cohort design that consists of a sub-cohort randomly sampled from full cohort, and all subjects with event is often applied in studies where the disease is rare and the cost of collecting the event information is high. with the non-rare events, a generalized case-cohort design is advocated in which a subset of events instead of all events is sampled. Cai and Zeng have proposed the general log-rank tests and the corresponding sample size/power formulas to compare the hazard rates between two groups under the case-cohort and the generalized case-cohort designs, respectively. However, in many practical situations, the population is not homogenous and stratification is considered. While prequalification is increasingly commonly used in large cohorts, the stratified log-rank tests and the sample size and power estimation techniques have not been available even though these issues are critical to the study design. this dissertation is devoted to consider these issues and fulfill the availability. In addition to the development of the stratified general log-rank tests and the sample size/power formulae for both the stratified case-cohort design and the stratified generalized case-cohort design, simulation studies are to be conducted to examine the performance of the tests. Furthermore, optimal, proportional, and balanced sampling strategies are to be explored and recommendations are to be made. Two real epidemiological studies are to be presented to illustrate the sample size calculation under these sampling strategies

Transformations to additivity for binary data

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A new approach for sizing trials with composite binary endpoints using anticipated marginal values and accounting for the correlation between components

Composite binary endpoints are increasingly used as primary endpoints in clinical trials. When designing a trial, it is crucial to determine the appropriate sample size for testing the statistical differences between treatment groups for the primary endpoint. As shown in this work, when using a composite binary endpoint to size a trial, one needs to specify the event rates and the effect sizes of the composite components as well as the correlation between them. In practice, the marginal parameters of the components can be obtained from previous studies or pilot trials, however, the correlation is often not previously reported and thus usually unknown. We first show that the sample size for composite binary endpoints is strongly dependent on the correlation and, second, that slight deviations in the prior information on the marginal parameters may result in underpowered trials for achieving the study objectives at a pre-specified significance level. We propose a general strategy for calculating the required sample size when the correlation is not specified, and accounting for uncertainty in the marginal parameter values. We present the web platform CompARE to characterize composite endpoints and to calculate the sample size just as we propose in this paper. We evaluate the performance of the proposal with a simulation study, and illustrate it by means of a real case study using CompARE

Design and Analysis of Multi-Arm Trials with a Common Control Using Order Restrictions

PhDTrials for comparing I treatments with a control are considered, where the aim is to identify one treatment (if at least one exists) which is better than control. Tests are developed which use all of the data simultaneously, rather than combining separate tests of a single arm versus control. The null hypothesis H0 : i 0 is tested against H1 : i > 0 for at least one i, where i represents the scaled di erence in response between treatment i and the control, i = 1; : : : ; I, and, if rejected, the best treatment is selected. A likelihood ratio test (LRT) is developed using order restricted inference, a family of tests is de ned and it is shown that the LRT and Dunnett-type tests are members of this family. Tests are compared by simulation, both under normality and for binary data, an exact test being developed for the latter case. The LRT compares favourably with other tests in terms of power and a simple loss function. Proportions of subjects on the control close to ( p I 1)=(I 1) are found to maximise the power and minimise the expected loss. Two-stage adaptive designs for comparing two experimental arms with a control are developed, in which the trial is stopped early if the di erence between the best treatment and the control is less than C1; otherwise, it continues, with one arm if one experimental treatment is better than the other by at least C2, or with both arms otherwise. Values of the constants C1 and C2 are compared and the adaptive design is found to be more powerful than the xed design. The new tests can make a contribution to improving the analysis of multi-arm clinical trials and further research in their application is recommended

Asymptotic properties of randomized clinical trials designs

Nowadays, we are witnessing changes in the traditional clinical trial landscape: many methods have been proposed as a compromise between uncontrolled trials and randomized trials and a large number of adaptive randomization procedures have been developed for various studies, including multi-arm trials, dose-finding trials and platform trials. Adaptive designs often require time-consuming and computationally intensive Monte Carlo simulations to establish operating characteristics, particularly type I error probability and power. These statistical properties should be thoroughly investigated in order that the designs achieve regulatory approval. In particular, the estimated operating characteristics need to cover different scenarios, varying key parameters, such as enrollment rates and treatment effects. This makes routine applications of adaptive designs challenging. Also, at present new data sources are becoming available that can supplement data generated in standard randomized clinical trials. Externally-controlled clinical trials designs incorporate existing data about the control treatment available from external sources as external controls. So far, these designs have been evaluated mainly according to qualitative arguments or simulation studies. In the first part of this PhD thesis, we focus on asymptotic properties of the designs of response-adaptive clinical trials, that is characteristics of these designs obtained under the assumption that the number of patients enrolled in the studies is large. Approximations of the operating characteristics, beyond simulations, leveraging asymptotic properties, could allow a fast comparison of designs across plausible scenarios. In the second part of this PhD thesis, we investigate the statistical properties of externally-controlled randomized clinical trial designs, adopting a quantitative approach, and question whether these designs could shorten study length and benefit more patients being treated with a better treatment. The aims of our research are threefold: to determine appropriate methodology that can be used in the assessment of asymptotic properties of the designs of response-adaptive clinical trials; to develop a quantitative framework to compare externally-controlled randomized clinical trial designs to standard randomized clinical trial designs; and finally to examine the identified methods and verify our results via simulation studies, across a variety of scenarios and endpoints. The key contributions of our work are: proposing a novel methodology to derive asymptotic results for the randomization probabilities and allocation proportions of patients to various arms in a broad class of Bayesian response-adaptive randomized clinical trials designs, by combining tools from the classical foundations of statistical inference and probability theory with mathematical techniques such as stochastic approximation; showing that asymptotic analyses of adaptive procedures simplify the design of clinical trials and reduce the need for time-consuming simulations to evaluate operating characteristics across potential trial scenarios; proving that externally-controlled clinical trials can increase power compared to randomized clinical trials by leveraging additional information from outside the trial rather than committing resources to an internal control