Exact-Permutation Based Sign Tests for Clustered Binary Data via Weighted and Unweighted Test Statistics.

Clustered binary data occur frequently in many application areas. When analyzing data of this form, ignoring key features, such as the intracluster correlation, may lead to inaccurate inference; e.g., inflated Type I error rates. For clustered binary data, Gerard and Schucany (2007) proposed an exact test for examining whether the marginal probability of a response differs from 0.5, which is the null hypothesis considered in the classic sign test. This new test maintains the specified Type I error rate and has more power, when compared to both the classic sign and permutation tests. The test statistic proposed by these authors equally weights the observed data from each cluster, regardless of whether the clusters are of equal size. To further improve the performance of the Gerard and Schucany test, a weighted test statistic is proposed and two weighting schemes are investigated. Seeking to further improve the performance of the proposed test, empirical Bayes estimates of the cluster level success probabilities are utilized. These adaptations lead to 5 new tests, each of which are shown through simulation studies to be superior to the Gerard and Schucany (2007) test. The proposed tests are further illustrated using data from a chemical repellency trial.

A robust distribution-free test for genetic association studies of quantitative traits.

In association studies of quantitative traits, the association of each genetic marker with the trait of interest is typically tested using the F-test assuming an additive genetic model. In practice, the true model is rarely known, and specifying an incorrect model can lead to a loss of power. For case-control studies, the maximum of test statistics optimal for additive, dominant, and recessive models has been shown to be robust to model misspecification. The approach has later been extended to quantitative traits. However, the existing procedures assume that the trait is normally distributed and may not maintain correct type I error rates and can also have reduced power when the assumption of normality is violated. Here, we introduce a maximum (MAX3) test that is based on ranks and is therefore distribution-free. We examine the behavior of the proposed method using a Monte Carlo simulation with both normal and non-normal data and compare the results to the usual parametric procedures and other nonparametric alternatives. We show that the rank-based maximum test has favorable properties relative to other tests, especially in the case of symmetric distributions with heavy tails. We illustrate the method with data from a real association study of symmetric dimethylarginine (SDMA).

Key properties of D-optimal designs for event-related functional MRI experiments with application to nonlinear models.

To properly formulate functional magnetic resonance imaging (fMRI) experiments with complex mental activity, it is advantageous to permit great flexibility in the statistical components of the design of these studies. The length of an experiment, the placement of various stimuli and the modeling approach used all affect the ability to detect mental activity. Major advances in understanding the implications of various designs of fMRI experiments have taken place over the last decade. Nevertheless, new and increasingly difficult issues relating to the modeling of hemodynamic responses and the detection of activated brain regions continue to arise because of the increasing complexity of the experiments. In this article, the D-optimality criterion is used in conjunction with a genetic algorithm to create probability-based design generators for the selection of designs in event-related fMRI experiments where the hemodynamic response function is modeled with a function that is nonlinear in the parameters. The designs produced by these generators are shown to perform well compared with locally D-optimal designs and provide insight into optimal design characteristics that investigators can utilize in the selection of interstimulus intervals. Designs with these characteristics are shown to be applicable to fMRI studies involving one or two stimulus types. The designs are also shown to be robust with respect to misspecification of an AR(1) error autocorrelation and compare favorably with a maximin procedure.

Sample Size Calculation for Clustered Binary Data with Sign Tests Using Different Weighting Schemes.

We propose a sample size calculation approach for testing a proportion using the weighted sign test when binary observations are dependent within a cluster. Sample size formulas are derived with nonparametric methods using three weighting schemes: equal weights to observations, equal weights to clusters, and optimal weights that minimize the variance of the estimator. Sample size formulas are derived incorporating intracluster correlation and the variability in cluster sizes. Simulation studies are conducted to evaluate a finite sample performance of the proposed sample size formulas. Empirical powers are generally close to nominal levels. The number of clusters required increases as the imbalance in cluster size increases and the intracluster correlation increases. The estimator using optimal weights yields the smallest sample size estimate among three estimators. For small values of intracluster correlation the sample size estimates derived from the optimal weight estimator are close to that derived from the estimator assigning equal weights to observations. For large values of intracluster correlation, the optimal weight sample size estimate is close to the sample size estimate assigning equal weights to clusters.

Power of genetic association studies with fixed and random genotype frequencies.

When estimating the power of genetic association studies, the allele and genotype frequencies are often assumed to be known, and the numbers of individuals with each genotype are set equal to their expectations under Hardy-Weinberg equilibrium. In fact, both allele and genotype frequencies are unknown and thus random. It has previously been suggested that ignoring uncertainty in these parameters could lead to inflated power expectations. To overcome the problem, one can average power estimates over the distributions of unknown frequencies. We investigate the power-averaging method and find that, despite the intuitive appeal, it may not improve accuracy in practice, while significantly increasing computational time. For a fixed allele frequency, we show that the amount of overestimation diminishes rapidly with sample size and is completely negligible for N > 200. For an unknown frequency, the result of averaging depends on the genetic model, and may not always provide a more conservative estimate of power. We explore the effect of uncertainty in the factors that determine statistical power of association studies and propose a more economical approach to the power analysis.

Nonparametric Sample Size Estimation for Sensitivity and Specificity with Multiple Observations per Subject.

We propose a sample size calculation approach for the estimation of sensitivity and specificity of diagnostic tests with multiple observations per subjects. Many diagnostic tests such as diagnostic imaging or periodontal tests are characterized by the presence of multiple observations for each subject. The number of observations frequently varies among subjects in diagnostic imaging experiments or periodontal studies. Nonparametric statistical methods for the analysis of clustered binary data have been recently developed by various authors. In this paper, we derive a sample size formula for sensitivity and specificity of diagnostic tests using the sign test while accounting for multiple observations per subjects. Application of the sample size formula for the design of a diagnostic test is discussed. Since the sample size formula is based on large sample theory, simulation studies are conducted to evaluate the finite sample performance of the proposed method. We compare the performance of the proposed sample size formula with that of the parametric sample size formula that assigns equal weight to each observation. Simulation studies show that the proposed sample size formula generally yields empirical powers closer to the nominal level than the parametric method. Simulation studies also show that the number of subjects required increases as the variability in the number of observations per subject increases and the intracluster correlation increases.

Abnormal brain response to cholinergic challenge in chronic encephalopathy from the 1991 Gulf War.

Several case definitions of chronic illness in veterans of the 1991 Persian Gulf War have been linked epidemiologically with environmental exposure to cholinesterase-inhibiting chemicals, which cause chronic changes in cholinergic receptors in animal models. Twenty-one chronically ill Gulf War veterans (5 with symptom complex 1, 11 with complex 2, and 5 with complex 3) and 17 age-, sex- and education-matched controls, underwent an 99mTc-HMPAO-SPECT brain scan following infusion of saline and >48 h later a second scan following infusion of physostigmine in saline. From each SPECT image mean normalized regional cerebral blood flow (nrCBF) from 39 small blocks of correlated voxels were extracted with geostatistical spatial modeling from eight deep gray matter structures in each hemisphere. Baseline nrCBF in symptom complex 2 was lower than controls throughout deep structures. The change in nrCBF after physostigmine (challenge minus baseline) was negative in complexes 1 and 3 and controls but positive in complex 2 in some structures. Since effects were opposite in different groups, no finding typified the entire patient sample. A hold-out discriminant model of nrCBF from 17 deep brain blocks predicted membership in the clinical groups with sensitivity of 0.95 and specificity of 0.82. Gulf War-associated chronic encephalopathy in a subset of veterans may be due to neuronal dysfunction, including abnormal cholinergic response, in deep brain structures.

Testing the ratio of two poisson rates.

In this paper we compare the properties of four different general approaches for testing the ratio of two Poisson rates. Asymptotically normal tests, tests based on approximate p -values, exact conditional tests, and a likelihood ratio test are considered. The properties and power performance of these tests are studied by a Monte Carlo simulation experiment. Sample size calculation formulae are given for each of the test procedures and their validities are studied. Some recommendations favoring the likelihood ratio and certain asymptotic tests are based on these simulation results. Finally, all of the test procedures are illustrated with two real life medical examples.

Using a white matter reference to remove the dependency of global signal on experimental conditions in SPECT analyses.

Proportional scaling models are often used in functional imaging studies to remove confounding of local signals by global effects. It is generally assumed that global effects are uncorrelated with experimental conditions. However, when the global effect is estimated by the global signal, defined as the intracerebral average, incorrect inference may result from the dependency of the global signal on preexisting conditions or experimental manipulations. In this paper, we propose a simple alternative method of estimating the global effect to be used in a proportional scaling model. Specifically, by defining the global signal with reference strictly to a white matter region within the centrum semiovale, the dependency is removed in experiments where white matter is unaffected by the disease effect or experimental treatments. The increase in the ability to detect changes in regional blood flow is demonstrated in a SPECT study of healthy and ill Gulf War veterans in whom it is suspected that brain abnormalities influence the traditional calculation of the global signal. Controlling for the global effect, ill veterans have significantly lower intracerebral averages than healthy controls (P = 0.0038), evidence that choice of global signal has an impact on inference. Scaling by the modified global signal proposed here results in an increase in sensitivity leading to the identification of several regions in the insula and frontal cortex where ill veterans have significantly lower SPECT emissions. Scaling by the traditional global signal results in the loss of sensitivity to detect these regional differences. Advantages of this alternative method are its computational simplicity and its ability to be easily integrated into existing analysis frameworks such as SPM.

Improved agreement between Talairach and MNI coordinate spaces in deep brain regions.

Disagreement between the Talairach atlas and the stereotaxic space commonly used in software like SPM is a widely recognized problem. Others have proposed affine transformations to improve agreement in surface areas such as Brodmann's areas. This article proposes a similar transformation with the goal of improving agreement specifically in the deep brain region. The task is accomplished by finding an affine transformation that minimizes the mean distance between the surface coordinates of the lateral ventricles in the Talairach atlas and the MNI templates. The result is a transformation that improves deep brain agreement over both the untransformed Talairach coordinates and the surface-oriented transformation. While the transformation improves deep brain agreement, surface agreement is generally made worse. For areas near the lateral ventricle, the transformation presented herein is valuable for applications such as region of interest (ROI) modeling.