Lipsitz et al. (1998, Biometrics 54, 148-160) discussed testing the homogeneity of the risk difference for a series of 2 x 2 tables. They proposed and evaluated several weighted test statistics, including the commonly used weighted least squares test statistic. Here we suggest various important improvements on these test statistics. First, we propose using the one-sided analogues of the test procedures proposed by Lipsitz et al. because we should only reject the null hypothesis of homogeneity when the variation of the estimated risk differences between centers is large. Second, we generalize their study by redesigning the simulations to include the situations considered by Lipsitz et al. (1998) as special cases. Third, we consider a logarithmic transformation of the weighted least squares test statistic to improve the normal approximation of its sampling distribution. On the basis of Monte Carlo simulations, we note that, as long as the mean treatment group size per table is moderate or large (> or = 16), this simple test statistic, in conjunction with the commonly used adjustment procedure for sparse data, can be useful when the number of 2 x 2 tables is small or moderate (< or = 32). In these situations, in fact, we find that our proposed method generally outperforms all the statistics considered by Lipsitz et al. Finally, we include a general guideline about which test statistic should be used in a variety of situations.

Study Objectives Fast frequency sleep spindles are reduced in aging and Alzheimer’s disease (AD), but the mechanisms and functional relevance of these deficits remains unclear. The study objective was to identify AD biomarkers associated with fast sleep spindle deficits in cognitively unimpaired older adults at risk for AD. Methods Fifty-eight cognitively unimpaired, β-amyloid negative, older adults (mean±SD; 61.4±6.3 years, 38 female) enriched with parental history of AD (77.6%) and apolipoprotein E (APOE) ε4 positivity (25.9%) completed the study. Cerebrospinal fluid (CSF) biomarkers of central nervous system (CNS) inflammation, β-amyloid and tau proteins, and neurodegeneration were combined with polysomnography (PSG) using high density electroencephalography and assessment of overnight memory retention. Parallelized serial mediation models were used to assess indirect effects of age on fast frequency (13—&lt;16Hz) sleep spindle measures through these AD biomarkers. Results Glial activation was associated with prefrontal fast frequency sleep spindle expression deficits. While adjusting for sex, APOE ε4 genotype, apnea-hypopnea index (AHI), and time between CSF sampling and sleep study, serial mediation models detected indirect effects of age on fast sleep spindle expression through microglial activation markers and then tau phosphorylation and synaptic degeneration markers. Sleep spindle expression at these electrodes was also associated with overnight memory retention in multiple regression models adjusting for covariates. Conclusions These findings point toward microglia dysfunction as associated with tau phosphorylation, synaptic loss, sleep spindle deficits, and memory impairment even prior to β-amyloid positivity, thus offering a promising candidate therapeutic target to arrest cognitive decline associated with aging and AD.

Perceptual decision making has several underlying components including stimulus encoding, perceptual categorization, response selection, and response execution. Evidence accumulation is believed to be the underlying mechanism of decision-making and plays a decisive role in determining response time. Previous studies in animals and humans have shown parietal cortex activity that exhibits characteristics of evidence accumulation in tasks requiring difficult perceptual categorization to reach a decision. In this study, we made use of a task where the challenge for the participants is to identify the stimulus and then from memory apply an abstract rule to select one of two possible actions. The task was designed so that stimulus identification was easy but response selection required cognitive computations and working memory. In simultaneous EEG recordings, we find a one-to-one relationship between the duration of the readiness potential observed prior to the response over motor areas, and decision-making time estimated by a drift-diffusion model of the response time distribution. This close relationship implies that the readiness potential reflects an evidence accumulation process for response selection, and supports the notion that evidence accumulation is a general neural implementation of decision-making. The evidence accumulation process that captures variability in decision-making time will depend on the location of the bottleneck in information processing.