Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Statnote 8: statistical power and sample size

Statistical software is now commonly available to calculate Power (P') and sample size (N) for most experimental designs. In many circumstances, however, sample size is constrained by lack of time, cost, and in research involving human subjects, the problems of recruiting suitable individuals. In addition, the calculation of N is often based on erroneous assumptions about variability and therefore such estimates are often inaccurate. At best, we would suggest that such calculations provide only a very rough guide of how to proceed in an experiment. Nevertheless, calculation of P' is very useful especially in experiments that have failed to detect a difference which the experimenter thought was present. We would recommend that P' should always be calculated in these circumstances to determine whether the experiment was actually too small to test null hypotheses adequately.

Sample size estimation and statistical power analyses

The concept of sample size and statistical power estimation is now something that Optometrists that want to perform research, whether it be in practice or in an academic institution, cannot simply hide away from. Ethics committees, journal editors and grant awarding bodies are now increasingly requesting that all research be backed up with sample size and statistical power estimation in order to justify any study and its findings. This article presents a step-by-step guide of the process for determining sample sizeand statistical power. It builds on statistical concepts presented in earlier articles in Optometry Today by Richard Armstrong and Frank Eperjesi.

Statistical properties of new neutrality tests against population growth.

A number of statistical tests for detecting population growth are described. We compared the statistical power of these tests with that of others available in the literature. The tests evaluated fall into three categories: those tests based on the distribution of the mutation frequencies, on the haplotype distribution, and on the mismatch distribution. We found that, for an extensive variety of cases, the most powerful tests for detecting population growth are Fu"s FS test and the newly developed R2 test. The behavior of the R2 test is superior for small sample sizes, whereas FS is better for large sample sizes. We also show that some popular statistics based on the mismatch distribution are very conservative. Key words: population growth, population expansion, coalescent simulations, neutrality tests

Regression-based techniques for statistical decision making in single-case designs

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions regarding intervention effectiveness in single-case designs. Ordinary least squares estimation is compared to two correction techniques dealing with general trend and one eliminating autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence. The results show that empirical Type I error rates do not approximate the nominal ones in presence of autocorrelation or general trend when ordinary and generalized least squares are applied. The techniques controlling trend show lower false alarm rates, but prove to be insufficiently sensitive to existing treatment effects. Consequently, the use of the statistical significance of the regression coefficients for detecting treatment effects is not recommended for short data series.

Are power calculations useful? A multicentre neuroimaging study

There are now many reports of imaging experiments with small cohorts of typical participants that precede large-scale, often multicentre studies of psychiatric and neurological disorders. Data from these calibration experiments are sufficient to make estimates of statistical power and predictions of sample size and minimum observable effect sizes. In this technical note, we suggest how previously reported voxel-based power calculations can support decision making in the design, execution and analysis of cross-sectional multicentre imaging studies. The choice of MRI acquisition sequence, distribution of recruitment across acquisition centres, and changes to the registration method applied during data analysis are considered as examples. The consequences of modification are explored in quantitative terms by assessing the impact on sample size for a fixed effect size and detectable effect size for a fixed sample size. The calibration experiment dataset used for illustration was a precursor to the now complete Medical Research Council Autism Imaging Multicentre Study (MRC-AIMS). Validation of the voxel-based power calculations is made by comparing the predicted values from the calibration experiment with those observed in MRC-AIMS. The effect of non-linear mappings during image registration to a standard stereotactic space on the prediction is explored with reference to the amount of local deformation. In summary, power calculations offer a validated, quantitative means of making informed choices on important factors that influence the outcome of studies that consume significant resources.

Nuclear power plants and childhood leukaemia: lessons from the past and future directions

In the 1980s, leukaemia clusters were discovered around nuclear fuel reprocessing plants in Sellafield and Dounreay in the United Kingdom. This raised public concern about the risk of childhood leukaemia near nuclear power plants (NPPs). Since then, the topic has been well-studied, but methodological limitations make results difficult to interpret. Our review aims to: (1.) summarise current evidence on the relationship between NPPs and risk of childhood leukaemia, with a focus on the Swiss CANUPIS (Childhood cancer and nuclear power plants in Switzerland) study; (2.) discuss the limitations of previous research; and (3.) suggest directions for future research. There are various reasons that previous studies produced inconclusive results. These include: inadequate study designs and limited statistical power due to the low prevalence of exposure (living near a NPP) and outcome (leukaemia); lack of accurate exposure estimates; limited knowledge of the aetiology of childhood leukaemia, particularly of vulnerable time windows and latent periods; use of residential location at time of diagnosis only and lack of data on address histories; and inability to adjust for potential confounders. We conclude that risk of childhood leukaemia around NPPs should continue to be monitored and that study designs should be improved and standardised. Data should be pooled internationally to increase the statistical power. More research needs to be done on other putative risk factors for childhood cancer such as low-dose ionizing radiation, exposure to certain chemicals and exposure to infections. Studies should be designed to allow examining multiple exposures.

Coronary events and exposure to environmental tobacco smoke: a case-control study from Australia and New Zealand

Objectives-To estimate the relative risk of coronary heart disease (CHD) associated with exposure to environmental tobacco smoke (ETS). Design-Population-based case-control study. Subjects-Cases were 953 people identified in a population register of coronary events, and controls were 3189 participants in independent community-based risk factor prevalence surveys from the same study populations. Setting-Newcastle, Australia and Auckland, New Zealand. Main outcome measures-Acute myocardial infarction or coronary death. Results-After adjusting for the effects of age, education, history of heart disease, and body mass index, women had a statistically significant increased risk of a coronary event associated with exposure to ETS (relative risk (RR) = 1.99; 95% confidence interval (CI)= 1.40-2.81). There was little statistical evidence of increased risk found in men (RR = 1.02, 95% CI = 0.81-1.28). Conclusion-Our study found evidence for the adverse effects of exposure to ETS on risk of coronary heart disease among women, especially at home. For men the issue is unclear according to the data from our study. Additional studies with detailed information on possible confounders and adequate statistical power are needed. Most importantly, they should use methods for measuring exposure to ETS that are sufficiently accurate to permit the investigation of dose-response relationships.

An fMRI study indicating increased cortical recruitment during a cognitive interference task in Huntington's disease patients

We used an event related fMRI design to study the BOLD response in Huntington’s disease (HD) patients during performance of a Simon interference task. We hypothesised that HD patients will demonstrate significantly slower RTs than controls, and that there will be significant differences in the pattern of brain activation between groups. Seventeen HD patients and 15 age and sex matched controls were scanned using 3T GE scanner (FOV = 24 cm2; TE = 40 ms; TR = 3 s; FA = 60°; slice thickness = 6 mm; in-plane resolution = 1.88x1.88 mm2). The task involved two activation conditions, namely congruent (for example, left pointing arrow appearing on the left side of the screen) and incongruent (for example, left pointing arrow appearing on the right side of the screen), and a baseline condition. Each stimulus was presented for 2500 ms followed by a blank screen for 500 ms. Subjects were instructed to press a button using the same hand as indicated by the direction of the arrow head and were given 3000 ms to respond. Data analysis was performed using SPM2 with a random effects analysis model. For each subject parameter estimates for combined task conditions (congruent and incongruent combined) were calculated. Comparisons such as these, based on block designs, have superior statistical power for detecting subtle changes in the BOLD response anywhere in the brain. The activations reported are significant at PFDR_corr

Long-term safety and efficacy of percutaneous coronary intervention with stenting and coronary artery bypass surgery for multivessel coronary artery disease - A meta-analysis with 5-year patient-level data from the ARTS, ERACI-II, MASS-II, and SoS trials

Background-Randomized trials that studied clinical outcomes after percutaneous coronary intervention (PCI) with bare metal stenting versus coronary artery bypass grafting (CABG) are underpowered to properly assess safety end points like death, stroke, and myocardial infarction. Pooling data from randomized controlled trials increases the statistical power and allows better assessment of the treatment effect in high-risk subgroups. Methods and Results-We performed a pooled analysis of 3051 patients in 4 randomized trials evaluating the relative safety and efficacy of PCI with stenting and CABG at 5 years for the treatment of multivessel coronary artery disease. The primary end point was the composite end point of death, stroke, or myocardial infarction. The secondary end point was the occurrence of major adverse cardiac and cerebrovascular accidents, death, stroke, myocardial infarction, and repeat revascularization. We tested for heterogeneities in treatment effect in patient subgroups. At 5 years, the cumulative incidence of death, myocardial infarction, and stroke was similar in patients randomized to PCI with stenting versus CABG (16.7% versus 16.9%, respectively; hazard ratio, 1.04, 95% confidence interval, 0.86 to 1.27; P = 0.69). Repeat revascularization, however, occurred significantly more frequently after PCI than CABG (29.0% versus 7.9%, respectively; hazard ratio, 0.23; 95% confidence interval, 0.18 to 0.29; P<0.001). Major adverse cardiac and cerebrovascular events were significantly higher in the PCI than the CABG group (39.2% versus 23.0%, respectively; hazard ratio, 0.53; 95% confidence interval, 0.45 to 0.61; P<0.001). No heterogeneity of treatment effect was found in the subgroups, including diabetic patients and those presenting with 3-vessel disease. Conclusions-In this pooled analysis of 4 randomized trials, PCI with stenting was associated with a long-term safety profile similar to that of CABG. However, as a result of persistently lower repeat revascularization rates in the CABG patients, overall major adverse cardiac and cerebrovascular event rates were significantly lower in the CABG group at 5 years.

Wavelet correlation between subjects: A time-scale data driven analysis for brain mapping using fMRI

Functional magnetic resonance imaging (fMRI) based on BOLD signal has been used to indirectly measure the local neural activity induced by cognitive tasks or stimulation. Most fMRI data analysis is carried out using the general linear model (GLM), a statistical approach which predicts the changes in the observed BOLD response based on an expected hemodynamic response function (HRF). In cases when the task is cognitively complex or in cases of diseases, variations in shape and/or delay may reduce the reliability of results. A novel exploratory method using fMRI data, which attempts to discriminate between neurophysiological signals induced by the stimulation protocol from artifacts or other confounding factors, is introduced in this paper. This new method is based on the fusion between correlation analysis and the discrete wavelet transform, to identify similarities in the time course of the BOLD signal in a group of volunteers. We illustrate the usefulness of this approach by analyzing fMRI data from normal subjects presented with standardized human face pictures expressing different degrees of sadness. The results show that the proposed wavelet correlation analysis has greater statistical power than conventional GLM or time domain intersubject correlation analysis. (C) 2010 Elsevier B.V. All rights reserved.

Involuntary smoking and head and neck cancer risk: Pooled analysis in the International Head and Neck Cancer Epidemiology Consortium

Although active tobacco smoking has been identified as a major risk factor for head and neck cancer, involuntary smoking has not been adequately evaluated because of the relatively low statistical power in previous studies. We took advantage of data pooled in the International Head and Neck Cancer Epidemiology Consortium to evaluate the role of involuntary smoking in head and neck carcinogenesis. Involuntary smoking exposure data were pooled across six case-control studies in Central Europe, Latin America, and the United States. Adjusted odds ratios (OR) and 95% confidence interval (95% CI) were estimated for 542 cases and 2,197 controls who reported never using tobacco, and the heterogeneity among the study-specific ORs was assessed. In addition, stratified analyses were done by subsite. No effect of ever involuntary smoking exposure either at home or at work was observed for head and neck cancer overall. However, long duration of involuntary smoking exposure at home and at work was associated with an increased risk (OR for >15 years at home, 1.60; 95% CI, 1.12-2.28; P(trend) <0-01; OR for >15 years at work, 1.55; 95% CI, 1.04-2.30; P(trend) = 0.13). The effect of duration of involuntary smoking exposure at home was stronger for pharyngeal and laryngeal cancers than for other subsites. An association between involuntary smoking exposure and the risk of head and neck cancer, particularly pharyngeal and laryngeal cancers, was observed for long duration of exposure. These results are consistent with those for active smoking and suggest that elimination of involuntary smoking exposure might reduce head and neck cancer risk among never smokers.