Statistical Power

This dissertation is dedicated to my father, Claude P. Wightman, and mother, Kaye R. Wightman. Thank you for all your unconditional love, support, and guidance. iii ACKNOWLEDGEMENTS I vividly remember the day when I had my Ed.D. interview with the College of Education at Wayne State University. I was young, ambitious, and very anxious to do well. Because of this, I failed to realize that I was chewing a piece of gum. Needless to say, I entered the interview and endeavored to do my best. Now, I don't really recall what was specifically asked, what I said, or how well I did (due to the fact that this occurred many years ago), but I do recall that the interview panel noticed that I was chewing a piece of gum. When this occurred, one of the panel members asked me, -What would you think if a person showed up to an interview chewing gum?‖ With great embarrassment, I immediately stopped chewing the piece of gum, swallowed it whole, and responded by saying, -I would probably think that the person was very nervous and didn't realize he or she was chewing gum.‖ Everyone in the room paused for a moment and then suddenly began to laugh hysterically. Just then, Dr. Roney said, -We all know how you feel...‖ To Dr. Roney, my advisor, thank you for having a sense of humor and not giving up on me. Likewise, thank you for your encouragement, patience, and constant supervision throughout the time it has taken me to complete this study. To Dr. Addonizio, my cognate advisor, thank you for your knowledge, integrity, and level of professionalism. You have not only influenced me as an administrator, but also as a person. Much appreciation is also extended to Dr. Fahoome and Dr. Arya, committee members who provided me with valuable recommendations and advice for the completion of this study.

To obtain approval for the use vertebrate animals in research, an investigator must assure an ethics committee that the proposed number of animals is the minimum necessary to achieve a scientific goal. How does an investigator make that assurance? A power analysis is most accurate when the outcome is known before the study, which it rarely is. A 'pilot study' is appropriate only when the number of animals used is a tiny fraction of the numbers that will be invested in the main study because the data for the pilot animals cannot legitimately be used again in the main study without increasing the rate of type I errors (false discovery). Traditional significance testing requires the investigator to determine the final sample size before any data are collected and then to delay analysis of any of the data until all of the data are final. An investigator often learns at that point either that the sample size was larger than necessary or too small to achieve significance. Subjects...

The variable-criteria sequential stopping rule (SSR) allows an investigator to use a few subjects at a time to determine whether a planned experiment is worth pursuing without increasing the rate of false discoveries (type I errors). The SSR is appropriate whenever testing a null hypothesis if the experiment can be conducted in stages. The investigator adds a predetermined number of subjects at each stage and tests repeatedly for significance until the experiment is stopped because: (1) a significant effect is detected; (2) the effect is clearly not going to be significant; or (3) the predetermined maximal number of subjects has been reached. Two crucial features of the SSR are that it holds the probability of a type I error constant and maintains excellent power. The method is more efficient than is performing a typical significance test after a power analysis because SSR can require 30% fewer subjects to achieve the same power. The variable-criteria SSR provides a formal method fo...

In educational settings, researchers are likely to encounter multilevel data with cross-classified structure. However, due to the lack of familiarity and limitations of statistical software for cross-classified modeling, most researchers adopt less optimal approaches to analyze cross-classified multilevel data in testing measurement invariance. We conducted two Monte Carlo studies to investigate the performances of testing measurement invariance with cross-classified multilevel data when the noninvarinace is at the between-level: (a) the impact of ignoring crossed factor using conventional multilevel confirmatory factor analysis (MCFA) which assumes hierarchical multilevel data in testing measurement invariance and (b) the adequacy of the cross-classified multiple indicators multiple causes (MIMIC) models with cross-classified data. We considered two design factors, intraclass correlation (ICC) and magnitude of non-invariance. Generally, MCFA demonstrated very low statistical power ...

Authors have highlighted for decades that sample size justification through power analysis is the exception rather than the rule. Even when authors do report a power analysis, there is often no justification for the smallest effect size of interest, or they do not provide enough information for the analysis to be reproducible. We argue one potential reason for these omissions is the lack of a truly accessible introduction to the key concepts and decisions behind power analysis. In this tutorial targeted at complete beginners, we demonstrate a priori and sensitivity power analysis using jamovi for two independent samples and two dependent samples. Respectively, these power analyses allow you to ask the questions: "How many participants do I need to detect a given effect size?", and "What effect sizes can I detect with a given sample size?". We emphasise how power analysis is most effective as a reflective process during the planning phase of research to balance your inferential goals with your resources. By the end of the tutorial, you will be able to understand the fundamental concepts behind power analysis and extend them to more advanced statistical models.

Three possible sampling designs for monitoring programmes were compared for both bias and variance of the associated estimators of year-to-year change. The statistical power of the accompanying univariate analysis of variance models was also analysed. The analysis was based on species abundance data from monitoring programmes for soft-bottom marine benthos in The Netherlands. The first design, with random selection of stations in each year, revealed larger variance and smaller power than the second design, in which stations are sampled randomly in the first year and revisited in succeeding years. The third design, with fixed non-randomly selected stations, yielded the largest power, but gives biased estimates of the year-to-year changes. These results suggest the following rule-of-thumb for monitoring programmes focusing on the abundance of marine benthic species: revisit many randomly selected stations, and make little effort per station.

Science is based on developing empirically testable theories or hypotheses. This implies that research can provide evidence about whether a scientific theory or hypothesis is true or false. However, past research practices in psychology have focused on finding evidence that a hypothesis is true with little attention to the methods for evidence that the hypothesis may be false. The statistical methods for conducting falsifiable research are not well known in the social sciences. The purpose of this article is to bring together various concepts and methods to form a useful framework for conducting research that can provide evidence that a scientific hypothesis is false as well as true. For falsifiable research, scientists must prespecify a study outcome or magnitude of effect that would be considered evidence that the hypothesis is not true. If any obtained effect, no matter how close to zero, could be considered evidence supporting the hypothesis, the hypothesis is not falsifiable—and therefore is of questionable scientific value. Power analysis or operating characteristics are used to design studies that can provide evidence that a hypothesis is true or false. These study design practices are needed for Bayesian analyses as well as for traditional frequentist statistical analysis. Preregistered confirmatory research with a prespecified minimum effect size for study design and appropriate power analysis are required for falsifiable scientific theories or hypotheses. Studies with more than 1,000 subjects will often be needed.

Background Mixed effects logistic models have become a popular method for analyzing multicenter clinical trials with binomial data. However, the statistical properties of these models for testing homogeneity of odds ratios under various conditions, such as within-center and among-centers inequality, are still unknown and not yet compared with those of commonly used tests of homogeneity. Methods We evaluated the effect of within-center and among-centers inequality on the empirical power and type I error rate of the three homogeneity tests of odds ratios including likelihood ratio (LR) test of a mixed logistic model, DerSimonian-Laird (DL) statistic and Breslow-Day (BD) test by simulation study. Moreover, the impacts of number of centers (K), number of observations in each center and amount of heterogeneity were investigated by simulation. Results As compared with the equal sample size design, the power of the three tests of homogeneity will decrease if the same total sample size, whi...

Seven studies have now been published pertaining to the acute effect of iv administration of glucagon-like peptide-1 (7-36) amide on ad libitum energy intake. In four of these studies energy intake was significantly reduced following the glucagon-like peptide-1 infusion compared with saline. In the remaining studies, no significant effect of glucagon-like peptide-1 could be shown. Lack of statistical power or low glucagon-like peptide-1 infusion rate may explain these conflicting results. Our aim was to examine the effect of glucagon-like peptide-1 on subsequent energy intake using a data set composed of subject data from previous studies and from two as yet unpublished studies. Secondly, we investigated whether the effect on energy intake is dose dependent and differs between lean and overweight subjects. Raw subject data on body mass index and ad libitum energy intake were collected into a common data set (n ‫؍‬ 115), together with study characteristics such as infusion rate, duration of infusion, etc. From four studies with comparable protocol the following subject data were included if available: plasma concentrations of glucagon-like peptide-1, subjective appetite measures, well-being, and gastric emptying rate of a meal served at the start of the glucagon-like peptide-1 infusion. Energy intake was reduced by 727 kJ (95% confidence interval , 548-908 kJ) or 11.7% during glucagon-like peptide-1 infusion. Although the absolute reduction in energy intake was higher in lean (863 kJ) (634-1091 kJ) compared with overweight subjects (487 kJ) (209-764 kJ) (P ‫؍‬ 0.05), the relative reduction did not differ between the two groups (13.2% and 9.3%, respectively). Stepwise regression analysis showed that the glucagon-like peptide-1 infusion rate was the only independent predictor of the reduction in energy intake during glucagon-like peptide-1 (7-36) amide infusion (r ‫؍‬ 0.4, P < 0.001). Differences in mean plasma glucagon-like peptide-1 concentration on the glucagon-like peptide-1 and placebo day (n ‫؍‬ 43) were related to differences in feelings of prospective consumption (r ‫؍‬ 0.40, P < 0.01), fullness (r ‫؍‬ 0.38, P < 0.05), and hunger (r ‫؍‬ 0.26, P ‫؍‬ 0.09), but not to differences in ad libitum energy intake. Gastric emptying rate was significantly lower during glucagon-like peptide-1 infusion compared with saline. Finally, well-being was not influenced by the glucagon-like peptide-1 infusion. Glucagon-like peptide-1 infusion reduces energy intake dose dependently in both lean and overweight subjects. A reduced gastric emptying rate may contribute to the increased satiety induced by glucagon-like peptide-1. (

Dr Nick Martin has made enormous contributions to the field of behavior genetics over the past 50 years. Of his many seminal papers that have had a profound impact, we focus on his early work on the power of twin studies. He was among the first to recognize the importance of sample size calculation before conducting a study to ensure sufficient power to detect the effects of interest. The elegant approach he developed, based on the noncentral chi-squared distribution, has been adopted by subsequent researchers for other genetic study designs, and today remains a standard tool for power calculations in structural equation modeling and other areas of statistical analysis. The present brief article discusses the main aspects of his seminal paper, and how it led to subsequent developments, by him and others, as the field of behavior genetics evolved into the present era.

Nutritional intervention studies, like those with pre-and probiotics, are often hampered by low effect sizes, reducing the power to demonstrate potential efficacy. Here, we perform computer simulations of a hypothetical clinical trial using such an intervention in order to elucidate determining factors that can be influenced in order to optimise the statistical power. Our simulations demonstrate that steering the study population towards a low intraindividual variation dramatically improves statistical power. A more than 10-fold decrease of number-to-treat could be reached. Also, a careful balancing between the number of subjects and measurements per subject, in combination with possible stratification of the subjects into responders and non-responders, based on inherent intraindividual variation, improves the likelihood to reach statistically significant results. Our results also show that traditional dogmas, with respect to clinical trials, i.e. aiming at low interindividual variation and a high number (n) of study participants, should be re-evaluated in favour of reducing intraindividual variation. This reduction in intraindividual variation could be achieved by maintaining a steady lifestyle, including dietary habits among others, within the timeframe of the intervention study.

In this work we propose an eective solution to the main challenges of behavioral power modeling: the generation of models for the power dissipation of technology-independent soft macros and the strong dependence o f p ower from input pattern statistics. Our methodology is based on a fast characterization performed by simulating the gate-level implementation of instances of soft macros within the behavioral description of the complete design. Once characterization has been completed, the backannotated b ehavioral model replaces the gate-level representation, thus allowing fast but accurate power estimates in a fully behavioral context. Our power characterization procedure is a very ecient process that can be e asily embedded in synthesisbased design ows. No additional eort is required f r om the designer, since p ower characterization merges seamlessly with a natural top-down design methodology with iterative improvement. After characterization, the behavioral power simulation produces accurate average and instantaneous power estimates (with errors around 7% and 25%, respectively, from accurate gate-level power simulation).

Genetic analyses of complex traits in wheat (Triticum aestivum L.) are facilitated by the availability of unique genetic tools such as chromosome substitution lines and recombinant inbred chromosome lines (RICLs) which allow the effects of genes on single chromosomes to be studied individually. Chromosome 3A of ‘Wichita’ is known to contain alleles at quantitative trait loci (QTLs) that influence variation in grain yield and agronomic performance traits relative to alleles of ‘Cheyenne’. To determine the number, location, and environmental interactions of genes related to agronomic performance on chromosome 3A, QTL and QTL × environment analyses of 98 RICLs‐3A were conducted in seven locations across Nebraska from 1999 through 2001. QTLs were detected for seven of eight agronomic traits measured and generally localized to three regions of chromosome 3A. QTL × environment interactions were detected for some QTLs and these interactions were caused by changes in magnitude and crossover...

Target detection of RADAR deals with different and manifold problems over few decades. The detection capability is one of the most significant factors in RADAR system. The main aim of detection is to increase probability of detection while decreasing rate of false alarm. The threshold of detection is modified as a function of the receiver noise level to keep a fixed rate of false alarm. Constant False Alarm Rate (CFAR) processors are used to maintain the amount of false alarm under supervision in a diverse background of interference. In Signal to Noise Ratio (SNR) level, a loss can be occurred due to CFAR processor. Gamma function is used to determine the probability of false alarm. It is assumed in adaptive CFAR that the interference distribution is familiar here. This type of CFAR also approximates the unknown parameters connected with various interference distributions. CFAR loss depends on gamma function. Incomplete gamma function plays an important role in maintaining threshold voltage as well as probability of detection. Changing the value of gamma function can improve the probability of detection for various Swerling Models which are proposed here. This paper has also proposed a technique to compare various losses due to CFAR in terms of different gamma function in presence of different number of pulses for four Swerling Models.

Abstract: Fisheries can cause major impacts on ecosystems, but the goal of managing them sustainably requires more and different information than we now have. Few fisheries have the legal mandate for ecosystem-based management or to apply precautionary management when information is lacking, so fishermen have little incentive to demand improved information. The California Marine Life Management Act of 1998 requires the maintenance of ecosystem health and diversity in California&#x27;s complex nearshore ...

Categorical variables identifying microscopic features of cut marks produce high accuracy in discrimination of bone surface modifications, but are vulnerable to variable degrees of inter-analyst subjectivity. Metric analyses of cut mark width and depth are presented by as a more objective method of identifying cut marks. However, this uni(bi)variate method has shown very high rates of mark classification error when structurally similar marks are compared. Furthermore, within-sample comparison carried out via subsampling shows that different datasets of metric values, obtained with the same type of tool and raw material, are subject to such a high degree of variability that significant differences of homogeneous subsamples are repeatedly obtained, thus preventing any useful analogs to be made. Additionally, this much higher stochastic variability depends on limited knowledge of the contextual processes that intervene in cut mark metric properties, as well as on a mismatch between theoretical premises on the immanent-configurational process-trace dynamics and their confusion during experimental praxis. The selection of specific contextual variables and disregard of others, in addition to the combination of different tool types and raw materials, distorts the resulting cut mark properties. This indicates that even when attempting to use exclusively metric numeric variables, subjectivity is a conditioning factor in analyzing and interpreting cut marks. Assumption 1. Lack of replication and poor sample qualities. Merrit et al.

The information obtained as a result of research in natural sciences should have a high statistical power, that is also valid for the field of aquaculture. The sample size needs to be increased in order to increase the statistical power of a scientific study. However, studying on large sample size may not always be possible. Therefore, many experimental designs have been developed for data collection purposes to keep the sample size minimum. Group sequential designs have been enhanced for the data entered sequentially to the trial most of the time in medicine, production, economy etc. With these designs, the studies can be early terminated and results can also be obtained the results based on with high statistical power with smaller sample size. These experimental designs are specifically applied to survival data. In the survival analysis used in the field of aquaculture, all of the samples are included at the beginning. One of the important risk in this method is the loss of most or all of the samples due to unexpected effects. If this occurs, the trial must be discontinued or repeated and procedure then becomes time consuming and expensive. To minimize these risks the use of group sequential test methods is proposed in our study. It can be done by a standard treatment (or survival etc.) group and a (or more) new treatment (or survival etc.) group(s). For this approach, 450 rainbow trout were divided into three sequential groups including 1. Control, 2. Aeromonas hyrophilia infected group and 3. Yersinia ruckeri infected group. The survival-time of each sequential run was evaluated by means of four interim analyses via a retrospective trial design. By entering new samples during the trial, both unexpected risks were minimized and continuous data was provided. After the third interim analysis, it was determined that the survival times of the three groups were significantly different from each other and the early termination of the trial was approved.

Genetic modification of plants may result in unintended effects causing potentially adverse effects on the environment. A comparative safety assessment is therefore required by authorities, such as the European Food Safety Authority, in which the genetically modified plant is compared with its conventional counterpart. Part of the environmental risk assessment is a comparative field experiment in which the effect on non-target organisms is compared. Statistical analysis of such trials come in two flavors: difference testing and equivalence testing. It is important to know the statistical properties of these, for example, the power to detect environmental change of a given magnitude, before the start of an experiment. Such prospective power analysis can best be studied by means of a statistical simulation model. This paper describes a general framework for simulating data typically encountered in environmental risk assessment of genetically modified plants. The simulation model, avai...

Mutual information (MI) quantifies the statistical dependency between a pair of random variables and plays a central role in signal processing and data analysis. Recent advances in machine learning have enabled the estimation of MI from a dataset using the expressive power of neural networks. In this study, we conducted a comparative experimental analysis of several existing neural estimators of MI between random vectors that model power spectrum features. We explored alternative models of power spectrum features by leveraging information-theoretic data processing inequality and bijective transformations. Empirical results demonstrated that each neural estimator of MI covered in this study has its limitations. In practical applications, we recommend the collective use of existing neural estimators in a complementary manner for the problem of estimating MI between power spectrum features.

Telemetry is a key, widely used tool to understand marine megafauna distribution, habitat use, behavior, and physiology; however, a critical question remains: “How many animals should be tracked to acquire meaningful data sets?” This question has wide‐ranging implications including considerations of statistical power, animal ethics, logistics, and cost. While power analyses can inform sample sizes needed for statistical significance, they require some initial data inputs that are often unavailable. To inform the planning of telemetry and biologging studies of marine megafauna where few or no data are available or where resources are limited, we reviewed the types of information that have been obtained in previously published studies using different sample sizes. We considered sample sizes from one to &gt;100 individuals and synthesized empirical findings, detailing the information that can be gathered with increasing sample sizes. We complement this review with simulations, using re...

Background: Statistical power calculations are a critical part of any study design for gene mapping. Most calculations assume that the locus of interest is biallelic. However, there are common situations in human genetics such as X-linked loci in males where the locus is haploid. The purpose of this work is to mathematically derive the biometric model for haploid loci, and to compute power for QTL mapping when the loci are haploid. Results: We have derived the biometric model for power calculations for haploid loci and have developed software to perform these calculations. We have verified our calculations with independent mathematical methods. Conclusion: Our results fill a need in power calculations for QTL mapping studies. Furthermore, failure to appropriately model haploid loci may cause underestimation of power.

In big data analysis for detecting rare and weak signals among n features, some grouping-test methods such as Higher Criticism test (HC), Berk-Jones test (B-J), and φ-divergence test share the similar asymptotical optimality when n → ∞. However, in practical data analysis n is frequently small and moderately large at most. In order to properly apply these optimal tests and wisely choose them for practical studies, it is important to know how to get the p-values and statistical power of them. To address this problem in an even broader context, this paper provides analytical solutions for a general family of goodness-of-fit (GOF) tests, which covers these optimal tests. For any given i.i.d. and continuous distributions of the input test statistics of the n features, both p-value and statistical power of such a GOF test can be calculated. By calculation we compared the finite-sample performances of asymptotically optimal tests under the normal mixture alternative. Results show that HC is the best choice when signals are rare, while B-J is more robust over various signal patterns. In the application to a real genome-wide association study, results illustrate that the p-value calculation works well, and the optimal tests have potentials for detecting novel disease genes with weak genetic effects. The calculations have been implemented in an R package SetTest and published on the CRAN.

We estimated reader-dependent variability of region of interest (ROI) analysis and evaluated its impact on preclinical quantitative molecular imaging. To estimate reader variability, we used five independent image datasets acquired each using microPET and multispectral fluorescence imaging (MSFI). We also selected ten experienced researchers who utilize molecular imaging in the same environment that they typically perform their own studies. Nine investigators blinded to the data type completed the ROI analysis by drawing ROIs manually that delineate the tumor regions to the best of their knowledge and repeated the measurements three times, non-consecutively. Extracted mean intensities of voxels within each ROI are used to compute the coefficient of variation (CV) and characterize the inter- and intra-reader variability. The impact of variability was assessed through random samples iterated from normal distributions for control and experimental groups on hypothesis testing and comput...

A new method for instantaneous temperature field measurements based on LIF studies of OH, 02, and H 2 0 in an open atmospheric flame with a tunable excimer laser is suggested. In this method the crucial problem of quenching at higher pressures is almost completely eliminated by excitation to a fast predissociating state. The various possible excitation and fluorescence processes that can be induced in the narrow tuning range of the KrF laser are characterized experimentally by excitation and dispersion spectra for the three molecules OH, 02, and H 2 0. Of particular importance is the large power of the KrF laser, which allows efficient excitation of even weak transitions. The fast predissociation of these molecules in connection with the powerful excitation laser suggests that instantaneous temperature field measurements should be possible at higher pressures.

Background: Structural brain MRI measures are frequently examined in both healthy and clinical groups, so an understanding of how these measures vary over time is desirable. Purpose: To test the stability of structural brain MRI measures over time. Population: In all, 112 healthy volunteers across four sites. Study Type: Retrospective analysis of prospectively acquired data. Field Strength/Sequence: 3 T, magnetization preparedrapid gradient echo, and single-shell diffusion sequence. Assessment: Diffusion, cortical thickness, and volume data from the sensorimotor network were assessed for stability over time across 3 years. Two sites used a Siemens MRI scanner, two sites a Philips scanner. Statistical Tests: The stability of structural measures across timepoints was assessed using intraclass correlation coefficients (ICC) for absolute agreement, cutoff ≥0.80, indicating high reliability. Mixed-factorial analysis of variance (ANOVA) was used to examine between-site and between-scanner type differences in individuals over time. Results: All cortical thickness and gray matter volume measures in the sensorimotor network, plus all diffusivity measures (fractional anisotropy plus mean, axial and radial diffusivities) for primary and premotor cortices, primary somatosensory thalamic connections, and the cortico-spinal tract met ICC. The majority of measures differed significantly between scanners, with a trend for sites using Siemens scanners to produce larger values for connectivity, cortical thickness, and volume measures than sites using Phillips scanners. Data Conclusion: Levels of reliability over time for all tested structural MRI measures were generally high, indicating that any differences between measurements over time likely reflect underlying biological differences rather than inherent methodological variability. Level of Evidence: 4. Technical Efficacy Stage: 1.

ObjectiveThe identification of sensitive biomarkers is essential to validate therapeutics for Huntington disease (HD). We directly compare structural imaging markers across the largest collective imaging HD dataset to identify a set of imaging markers robust to multicenter variation and to derive upper estimates on sample sizes for clinical trials in HD.MethodsWe used 1 postprocessing pipeline to retrospectively analyze T1‐weighted magnetic resonance imaging (MRI) scans from 624 participants at 3 time points, from the PREDICT‐HD, TRACK‐HD, and IMAGE‐HD studies. We used mixed effects models to adjust regional brain volumes for covariates, calculate effect sizes, and simulate possible treatment effects in disease‐affected anatomical regions. We used our model to estimate the statistical power of possible treatment effects for anatomical regions and clinical markers.ResultsWe identified a set of common anatomical regions that have similarly large standardized effect sizes (&gt;0.5) bet...

Background: Polymorphisms within the insulin gene can influence insulin expression in the pancreas and especially in the thymus, where self-antigens are processed, shaping the T cell repertoire into selftolerance, a process that protects from β-cell autoimmunity. Methods: We investigated the role of the-2221Msp(C/T) and-23HphI(A/T) polymorphisms within the insulin gene in patients with a monoglandular autoimmune endocrine disease [patients with isolated type 1 diabetes (T1D, n = 317), Addison's disease (AD, n = 107) or Hashimoto's thyroiditis (HT, n = 61)], those with a polyglandular autoimmune syndrome type II (combination of T1D and/or AD with HT or GD, n = 62) as well as in healthy controls (HC, n = 275). Results: T1D patients carried significantly more often the homozygous genotype "CC"-2221Msp(C/T) and "AA"-23HphI(A/T) polymorphisms than the HC (78.5% vs. 66.2%, p = 0.0027 and 75.4% vs. 52.4%, p = 3.7 × 10-8 , respectively). The distribution of insulin gene polymorphisms did not show significant differences between patients with AD, HT, or APS-II and HC. Conclusion: We demonstrate that the allele "C" of the-2221Msp(C/T) and "A"-23HphI(A/T) insulin gene polymorphisms confer susceptibility to T1D but not to isolated AD, HT or as a part of the APS-II. Background Type 1 diabetes (T1D) has a multifactorial pathogenesis, partly caused by environment but also by genetic predisposition. The association of the MHC class II genes with T1D is well known, but there are also non-MHC genes

For the analysis of rare-variant data in population-based designs, we propose a method to detect study subjects that may create population substructure in the study sample. Our approach is computationally fast and simple, permitting applications to whole-genome sequencing studies. The method does not require the variants to be in linkage equilibrium and can be applied to all the genetic loci that are available in the study. For both rare and common variants, we assess the performance of our approach by its application to the 1000 Genome Project data, and in simulation studies. The results are compared to the commonly used outlier detection algorithm based on principal component analysis (PCA). The statistical power of both approaches to detect outliers are comparable in most of the scenarios, but the power of PCA to detect outliers is lower than the novel approach in the presence of linkage disequilibrium and for subpopulations that are genetically similar. The data analysis and the simulation studies suggest that the number of falsepositive results appears to be different for the two approaches. Our approach maintains the type I error rate while the outlier detection approach based on PCA does not. Taking additionally into account the minimal computational requirements of our approach and the ability to incorporate all the marker information, the proposed method will have important application in sequencing studies and genome-wide association studies.

IntroductionDiffusion tensor imaging (DTI) can be used to map disease progression in amyotrophic lateral sclerosis (ALS) and therefore is a promising candidate for a biomarker in ALS. To this end, longitudinal study protocols need to be optimized and validated regarding group sizes and time intervals between visits. The objective of this study was to assess the influences of sample size, the schedule of follow-up measurements, and measurement uncertainties on the statistical power to optimize longitudinal DTI study protocols in ALS.Patients and methodsTo estimate the measurement uncertainty of a tract-of–interest-based DTI approach, longitudinal test-retest measurements were applied first to a normal data set. Then, DTI data sets of 80 patients with ALS and 50 healthy participants were analyzed in the simulation of longitudinal trajectories, that is, longitudinal fractional anisotropy (FA) values for follow-up sessions were simulated for synthetic patient and control groups with dif...