Power of association and linkage tests when the disease alleles are unobserved.

Genomewide association studies have been advocated as a promising alternative to genomewide linkage scans for detection of small-effect genes in complex diseases. Comparisons of power and sample size between the two strategies have shown considerable advantages for the association studies. These comparisons assume that the set of markers includes the exact disease-related polymorphism. A concern, however, is that the power of an association study decreases when this is not the case, because of discrepant allele frequencies and less-than-maximum disequilibrium between the disease-related polymorphism and its nearest marker. Here, we quantify this concern by comparing the sample sizes needed by the two strategies when the markers exclude the disease-related polymorphism. For affected sib pairs and their parents, we found that incomplete disequilibrium and differing allele frequencies can have substantial negative impact on the power of association studies, resulting, in some circumstances, in little gain and even in loss of power, compared with linkage analysis. We provide some guidelines for choosing between strategies, for the detection of genes for complex diseases.     

Power calculations for matched case-control studies

Power calculations are derived for matched case-control studies in terms of the probability po of exposure among the control patients, the correlation coefficient phi for exposure between matched case and control patients, and the odds ratio psi for exposure in case and control patients. For given Type I and Type II error probabilities alpha and beta, the odds ratio that can be detected with a given sample size is derived as well as the sample size needed to detect a specified value of the odds ratio. Graphs are presented for paired designs that show the relationship between sample size and power for alpha = .05, beta = .2, and different values of po, phi, and psi. The sample size needed for designs involving M matched control patients can be derived from these graphs by means of a simple equation. These results quantify the loss of power associated with increasing correlation between the exposure status of matched case and control patients. Sample size requirements are also greatly increased for values of po near 0 or 1. The relationship between sample size, psi, phi, and po is discussed and illustrated by examples.     

Understanding Power in Indigenous Protected Areas: the Case of the Tla-o-qui-aht Tribal Parks

This article draws on concepts of power from political ecology and political sociology to describe the ways that the Tla-o-qui-aht First Nation (a Canadian indigenous people) have attempted to realize their goals under the broad rubric of their Tribal Parks initiative. Like some other Indigenous peoples’ and Community Conserved territories and Areas (ICCAs), the Tribal Parks example features de facto legal pluralism, lack of clear tenure and/or legal recognition, oppositional and/or cooperative relationships with other actors, and situations where local actors are influenced by intersecting global discourses on conservation and indigenous rights and culture. Globally, ICCAs are a form of protected area and are potentially critical in terms of meeting ambitious global protected area targets as well in addressing issues related to the rights and well-being of indigenous peoples. As such, understanding the ‘customary law or other effective means’, or the dynamics of power through which indigenous groups are able (or not) to realize their protected area goals is of global significance. This article illuminates the contours of power through two specific Tribal Parks case studies: the first involves contestations over industrial logging, while the second focuses on the establishment and implementation of what came to be called an ‘ecosystem services fee’ paid by ecotourism outfitters operating within a Tribal Park. Results highlight that the Tla-o-qui-aht have drawn power from different sources and exercised it by different means including turning to the Courts in a context of legal uncertainty, protest and direct action coupled with appeals to public opinion, developing and drawing on relationships with both local and non-local interests, and by strategically ‘tapping into’ prominent discourses.     

Informed Conditioning on Clinical Covariates Increases Power in Case-Control Association Studies

Genetic case-control association studies often include data on clinical covariates, such as body mass index (BMI), smoking status, or age, that may modify the underlying genetic risk of case or control samples. For example, in type 2 diabetes, odds ratios for established variants estimated from low–BMI cases are larger than those estimated from high–BMI cases. An unanswered question is how to use this information to maximize statistical power in case-control studies that ascertain individuals on the basis of phenotype (case-control ascertainment) or phenotype and clinical covariates (case-control-covariate ascertainment). While current approaches improve power in studies with random ascertainment, they often lose power under case-control ascertainment and fail to capture available power increases under case-control-covariate ascertainment. We show that an informed conditioning approach, based on the liability threshold model with parameters informed by external epidemiological information, fully accounts for disease prevalence and non-random ascertainment of phenotype as well as covariates and provides a substantial increase in power while maintaining a properly controlled false-positive rate. Our method outperforms standard case-control association tests with or without covariates, tests of gene x covariate interaction, and previously proposed tests for dealing with covariates in ascertained data, with especially large improvements in the case of case-control-covariate ascertainment. We investigate empirical case-control studies of type 2 diabetes, prostate cancer, lung cancer, breast cancer, rheumatoid arthritis, age-related macular degeneration, and end-stage kidney disease over a total of 89,726 samples. In these datasets, informed conditioning outperforms logistic regression for 115 of the 157 known associated variants investigated (P-value = 1×10⁻⁹). The improvement varied across diseases with a 16% median increase in χ² test statistics and a commensurate increase in power. This suggests that applying our method to existing and future association studies of these diseases may identify novel disease loci.     

Envisioning Power: Ideologies of Dominance and Crisis

Envisioning Power: Ideologies of Dominance and Crisis. Eric R. Wolf. Berkeley: University of California Press, 1999. 339 pp.     

Power analysis for case–control association studies of samples with known family histories

Genome-wide case–control studies have been widely used to identify genetic variants that predispose to human diseases. Such studies are powerful in detecting common genetic variants with moderate effects, but quickly lose power as allele frequency and genotype relative risk decrease. Because patients with one or more affected relatives are more likely to inherit disease-predisposing alleles of a genetic disease than patients without family histories of the disease, sampling patients with affected relatives almost always increases the frequency of disease predisposing alleles in cases and improves the power of case–control association studies. This paper evaluates the power of case–control studies that select cases and/or controls according to their family histories of disease. Our results showed that this study design can dramatically increase the power of a case–control association study for a wide range of disease types. Because each additional affected relative of a patient reduces the required sample size roughly by a pair of case and control, inclusion of cases with affected relatives can dramatically decrease the required sample size and thus the cost of such studies.     

Knowledge and Power in the Clinical Setting

In this paper we consider the three categories offered by Howard Brody for understanding power in medicine. In his book, The Healer's Power Brody separates out power in medicine into the categories of Aesculapian, Social, and Charismatic power. We examine these three categories and then apply them to a case. In this case set in an Obstetric ward, a junior member of the medical staff makes a clinical decision about a patient. This clinical decision is overruled by a senior medical staff member who then carries out his plan with disastrous consequences for the woman and her baby. This case challenges the three categories of power offered by Brody and highlights the need for a further category of Hierarchical power to be added to Brody's framework. We conclude by suggesting that there is a need to recognise the discrepancy in power not only between physician and patient but also between senior and junior staff in a clinical setting.     

Large scale in vitro experiment system for 2 GHz exposure

A beam formed radiofrequency (RF) exposure-incubator employing a horn antenna, a dielectric lens, and a culture case in an anechoic chamber is developed for large scale in vitro studies. The combination of an open type RF exposure source and a culture case through which RF is transmitted realizes a uniform electric field (+/-1.5 dB) in a 300 x 300 mm area that accommodates 49 35 mm diameter culture dishes. This large culture dish area enables simultaneous RF exposure of a large number of cells or various cell lines. The RF exposure source operates at 2142.5 MHz corresponding to the middle frequency of the downlink band of the International Mobile Telecommunication 2000 (IMT-2000) cellular system. The dielectric lens, which has a gain of 7 dB, focuses RF energy in the direction of the culture case and provides a uniform electric field. The culture case is sealed and connected to the main unit for environmental control, located outside the anechoic chamber, via ducts. The temperature at the center of the tray, which contains the culture dishes in the culture room, is maintained at 37.0 +/- 0.2 degrees C by air circulation. In addition, the appropriate CO2 density and humidity supplied to the culture case realizes stable long-term culture conditions. Specific absorption rate (SAR) dosimetry is performed using an electric field measurement technique and the Finite Difference Time Domain (FDTD) calculation method. The results indicate that the mean SAR of the culture fluid at the bottom of the 49 (7 x 7 array) culture dishes used in the in vitro experiments is 0.175 W/kg for an antenna input power of 1 W and the standard deviation of the SAR distribution is 59%. When only 25 culture dishes (5 x 5 array) are evaluated, the mean SAR is 0.139 W/kg for the same antenna input power and the standard deviation of the SAR distribution is 47%. The proliferation of the H4 cell line in 72 h in a pair of RF exposure-incubators reveals that the culture conditions are equivalent to those of a common CO2 incubator.     

Case studies in reproducibility

Reproducible research is a concept of providing access to data and software along with published scientific findings. By means of some case studies from different disciplines, we will illustrate reasons why readers should be given the possibility to look at the data and software independently from the authors of the original publication. We report results of a survey comprising 100 papers recently published in Bioinformatics. The main finding is that authors of this journal share a culture of making data available. However, the number of papers where source code for simulation studies or analyzes is available is still rather limited.     

Enhancing the Power of Genetic Association Studies through the Use of Silver Standard Cases Derived from Electronic Medical Records

The feasibility of using imperfectly phenotyped “silver standard” samples identified from electronic medical record diagnoses is considered in genetic association studies when these samples might be combined with an existing set of samples phenotyped with a gold standard technique. An analytic expression is derived for the power of a chi-square test of independence using either research-quality case/control samples alone, or augmented with silver standard data. The subset of the parameter space where inclusion of silver standard samples increases statistical power is identified. A case study of dementia subjects identified from electronic medical records from the Electronic Medical Records and Genomics (eMERGE) network, combined with subjects from two studies specifically targeting dementia, verifies these results.     

Power lines and the geomagnetic field

The metric of prime interest in power line epidemiological studies has been AC magnetic intensity. To consider also possible geomagnetic involvement, the orientation of a long straight power line is examined relative to a uniform geomagnetic field (GMF) with dip angle α. An expression is derived for the component of the total GMF that is parallel, at an elevation β, to the circuital magnetic field that surrounds the line. This component is a function of the angles α and β, the total geomagnetic intensity B_T, and the angle θ between the axis of the power line and magnetic north. Plotting these geomagnetic parameters for known leukemia residences allows one to test for possible ion cyclotron resonance or other GMF interactions. This approach, in principle, is an easy addition to existing or planned studies, because residential access is not required to obtain local values for α, β, θ, and B_T. We recommend including these parameters in the design of epidemiological studies examining power line fields and childhood leukemia. © 1995 Wiley-Liss, Inc.     

Power calculations for a general class of family-based association tests: dichotomous traits

Using large-sample theory, we present a unified approach to power calculations for family-based association tests. Currently available methods for power calculations are restricted to special designs or require approximations or simulations. Our analytical approach to power calculations is broadly applicable in many settings. We discuss power calculations for two scenarios that have high practical relevance and in which power previously could only be assessed by simulation studies or by approximations: (1) studies using both affected and unaffected offspring and (2) studies with missing parental information. When the population prevalence is high, it can be worthwhile to genotype unaffected offspring. For many scenarios, high power can be achieved with reasonable sample sizes, even when no parental information is available.     

Designing Genome-Wide Association Studies: Sample Size, Power, Imputation, and the Choice of Genotyping Chip

Genome-wide association studies are revolutionizing the search for the genes underlying human complex diseases. The main decisions to be made at the design stage of these studies are the choice of the commercial genotyping chip to be used and the numbers of case and control samples to be genotyped. The most common method of comparing different chips is using a measure of coverage, but this fails to properly account for the effects of sample size, the genetic model of the disease, and linkage disequilibrium between SNPs. In this paper, we argue that the statistical power to detect a causative variant should be the major criterion in study design. Because of the complicated pattern of linkage disequilibrium (LD) in the human genome, power cannot be calculated analytically and must instead be assessed by simulation. We describe in detail a method of simulating case-control samples at a set of linked SNPs that replicates the patterns of LD in human populations, and we used it to assess power for a comprehensive set of available genotyping chips. Our results allow us to compare the performance of the chips to detect variants with different effect sizes and allele frequencies, look at how power changes with sample size in different populations or when using multi-marker tags and genotype imputation approaches, and how performance compares to a hypothetical chip that contains every SNP in HapMap. A main conclusion of this study is that marked differences in genome coverage may not translate into appreciable differences in power and that, when taking budgetary considerations into account, the most powerful design may not always correspond to the chip with the highest coverage. We also show that genotype imputation can be used to boost the power of many chips up to the level obtained from a hypothetical “complete” chip containing all the SNPs in HapMap. Our results have been encapsulated into an R software package that allows users to design future association studies and our methods provide a framework with which new chip sets can be evaluated.     

Estimating the Power of the Gehan Test

A bootstrap method suggested by COLLINGS and HAMILTON (1988) to estimate the power of the two-sample Wilcoxon test is adapted to use for estimating the power of the Gehan test. A Monte Carlo simulation study is done to determine how well the method works in this case.     

Power and potential bias in field studies of natural selection

The advent of multiple regression analyses of natural selection has facilitated estimates of both the direct and indirect effects of selection on many traits in numerous organisms. However, low power in selection studies has possibly led to a bias in our assessment of the levels of selection shaping natural populations. Using calculations and simulations based on the statistical properties of selection coefficients, we find that power to detect total selection (the selection differential) depends on sample size and the strength of selection relative to the opportunity of selection. The power of detecting direct selection (selection gradients) is more complicated and depends on the relationship between the correlation of each trait and fitness and the pattern of correlation among traits. In a review of 298 previously published selection differentials, we find that most studies have had insufficient power to detect reported levels of selection acting on traits and that, in general, the power of detecting weak levels of selection is low given current study designs. We also find that potential publication bias could explain the trend that reported levels of direct selection tend to decrease as study sizes increase, suggesting that current views of the strength of selection may be inaccurate and biased upward. We suggest that studies should be designed so that selection is analyzed on at least several hundred individuals, the total opportunity of selection be considered along with the pattern of selection on individual traits, and nonsignificant results be actively reported combined with an estimate of power.     

Power and phase properties of oscillatory neural responses in the presence of background activity

Natural sensory inputs, such as speech and music, are often rhythmic. Recent studies have consistently demonstrated that these rhythmic stimuli cause the phase of oscillatory, i.e. rhythmic, neural activity, recorded as local field potential (LFP), electroencephalography (EEG) or magnetoencephalography (MEG), to synchronize with the stimulus. This phase synchronization, when not accompanied by any increase of response power, has been hypothesized to be the result of phase resetting of ongoing, spontaneous, neural oscillations measurable by LFP, EEG, or MEG. In this article, however, we argue that this same phenomenon can be easily explained without any phase resetting, and where the stimulus-synchronized activity is generated independently of background neural oscillations. It is demonstrated with a simple (but general) stochastic model that, purely due to statistical properties, phase synchronization, as measured by ‘inter-trial phase coherence’, is much more sensitive to stimulus-synchronized neural activity than is power. These results question the usefulness of analyzing the power and phase of stimulus-synchronized activity as separate and complementary measures; particularly in the case of attempting to demonstrate whether stimulus-synchronized neural activity is generated by phase resetting of ongoing neural oscillations.     

Clinical and cytogenetic studies in a large (4;8) translocation family with pre- and postnatal Wolf syndrome

Partial deletion of 4p (Wolf syndrome) is reported in two cases resulting from paternal balanced t(4;8)(p163;p231). One of them was diagnosed prenatally and aborted. Autopsy revealed dysmorphic face, and malformed heart and kidneys. The other case, the mentally retarded sister, had no clinical signs of internal malformations, only slightly dysmorphic appearance. We concluded that loss of the terminal segment of 4p(4p163) seems sufficient to produce the clinical entity of Wolf syndrome, and partial trisomy of the short arm of chromosome 8 did not mask the 4p- phenotype. Segregation analysis showed risk figures of about 15% for a malformed child comparable to previously given figures concerning the outcome of autosomal reciprocal translocations.     

Multiethnic Genetic Association Studies Improve Power for Locus Discovery

To date, genome-wide association studies have focused almost exclusively on populations of European ancestry. These studies continue with the advent of next-generation sequencing, designed to systematically catalog and test low-frequency variation for a role in disease. A complementary approach would be to focus further efforts on cohorts of multiple ethnicities. This leverages the idea that population genetic drift may have elevated some variants to higher allele frequency in different populations, boosting statistical power to detect an association. Based on empirical allele frequency distributions from eleven populations represented in HapMap Phase 3 and the 1000 Genomes Project, we simulate a range of genetic models to quantify the power of association studies in multiple ethnicities relative to studies that exclusively focus on samples of European ancestry. In each of these simulations, a first phase of GWAS in exclusively European samples is followed by a second GWAS phase in any of the other populations (including a multiethnic design). We find that nontrivial power gains can be achieved by conducting future whole-genome studies in worldwide populations, where, in particular, African populations contribute the largest relative power gains for low-frequency alleles (<5%) of moderate effect that suffer from low power in samples of European descent. Our results emphasize the importance of broadening genetic studies to worldwide populations to ensure efficient discovery of genetic loci contributing to phenotypic trait variability, especially for those traits for which large numbers of samples of European ancestry have already been collected and tested.     

Power production in MFCs inoculated with Shewanella oneidensis MR‐1 or mixed cultures

Power densities and oxidation–reduction potentials (ORPs) of MFCs containing a pure culture of Shewanella oneidensis MR‐1 were compared to mixed cultures (wastewater inoculum) in cube shaped, 1‐, 2‐, and 3‐bottle batch‐fed MFC reactor configurations. The reactor architecture influenced the relative power produced by the different inocula, with the mixed culture generating 68–480% more power than MR‐1 in each MFC configuration. The mixed culture produced the maximum power density of 858 ± 9 mW m^?2 in the cubic MFC, while MR‐1 produced 148 ± 20 mW m^?2. The higher power by the mixed culture was primarily a result of lower internal resistances than those produced by the pure culture. Power was a direct function of ohmic resistance for the mixed culture, but not for strain MR‐1. ORP of the anode compartment varied with reactor configuration and inoculum, and it was always negative during maximum power production but it did not vary in proportion to power output. The ORP varied primarily at the end of the cycle when substrate was depleted, with a change from a reductive environment during maximum power production (approximately ?175 mV for mixed and approximately ?210 mV for MR‐1 in cubic MFCs), to an oxidative environment at the end of the batch cycle (～250 mV for mixed and ～300 mV for MR‐1). Mixed cultures produced more power than MR‐1 MFCs even though their redox potential was less negative. These results demonstrate that differences between power densities produced by pure and mixed cultures depend on the MFC architecture. Biotechnol. Bioeng. 2010; 105: 489–498. © 2009 Wiley Periodicals, Inc.