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Repeated measures analyses require proper choice of the correlation model to ensure accurate inference and optimal efficiency. The linear exponent autoregressive (LEAR) correlation model provides a flexible two-parameter correlation structure that accommodates a variety of data types in which the correlation within-sampling unit decreases exponentially in time or space. The LEAR model subsumes three classic temporal correlation structures, namely compound symmetry, continuous-time AR(1), and MA(1), while maintaining parsimony and providing appealing statistical and computational properties. It also supplies a plausible correlation structure for power analyses across many experimental designs. However, no commonly used statistical packages provide a straightforward way to implement the model, limiting its use to those with the appropriate programming skills. Here we present a reparameterization of the LEAR model that allows easily implementing it in standard software for the special case of data with equally spaced temporal or spatial intervals.

Scientists often use a paired comparison of the areas under the receiver operating characteristic curves to decide which continuous cancer screening test has the best diagnostic accuracy. In the paired design, all participants are screened with both tests. Participants with unremarkable screening results enter a follow-up period. Participants with suspicious screening results and those who show evidence of disease during follow-up receive the gold standard test. The remaining participants are classified as non-cases, even though some may have occult disease. The standard analysis includes all study participants in the analysis, which can create bias in the estimates of diagnostic accuracy. If the bias affects the area under the curve for one screening test more than the other screening test, scientists may make the wrong decision as to which screening test has better diagnostic accuracy. We describe a weighted maximum likelihood bias correction method to reduce decision errors. We assessed the ability of the bias correction method to reduce decision errors via simulation studies. The simulations compared the Type I error rate and power of the standard analysis with that of the bias-corrected analysis. The performance of the bias correction method depends on characteristics of the screening tests and the disease, and on the percentage of study participants who receive the gold standard test. In studies with a large amount of bias in the difference in the full area under the curve, the bias correction method reduces the Type I error rate and improves power for the correct decision. In order to determine if bias correction is needed for a specific screening trial, we recommend the investigator conduct a simulation study using our free software., Comment: 32 pages, including 5 figures and 2 tables, submitted to BMC Medical Research Methodology March, 2013

Longitudinal imaging studies have moved to the forefront of medical research due to their ability to characterize spatio-temporal features of biological structures across the lifespan. Credible models of the correlations in longitudinal imaging require two or more pattern components. Valid inference requires enough flexibility of the correlation model to allow reasonable fidelity to the true pattern. On the other hand, the existence of computable estimates demands a parsimonious parameterization of the correlation structure. For many one-dimensional spatial or temporal arrays, the linear exponent autoregressive (LEAR) correlation structure meets these two opposing goals in one model. The LEAR structure is a flexible two-parameter correlation model that applies in situations in which the within-subject correlation decreases exponentially in time or space. It allows for an attenuation or acceleration of the exponential decay rate imposed by the commonly used continuous-time AR(1) structure. Here we propose the Kronecker product LEAR correlation structure for multivariate repeated measures data in which the correlation between measurements for a given subject is induced by two factors. We also provide a scientifically informed approach to assessing the adequacy of a Kronecker product LEAR model and a general unstructured Kronecker product model. The approach provides useful guidance for high dimension, low sample size data that preclude using standard likelihood based tests. Longitudinal medical imaging data of caudate morphology in schizophrenia illustrates the appeal of the Kronecker product LEAR correlation structure.

Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution function. The probability that these order statistics fall in disjoint, ordered intervals, and that of the smallest statistics, a certain number come from the first populations, are given in terms of the two distribution functions. The result is applied to computing the joint probability of the number of rejections and the number of false rejections for the Benjamini-Hochberg false discovery rate procedure., Comment: 10 pages

The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by Bapat and Beg. In the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations., Comment: 21 pages, 3 figures