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PubMed2006

Statistical power calculations.

This article focuses on how to do meaningful power calculations and sample-size determination for common study designs. There are 3 important guiding principles. First, certain types of retrospective power calculations should be avoided, because they add no new information to an analysis. Second, effect size should be specified on the actual scale of measurement, not on a standardized scale. Third, rarely can a definitive study be done without first doing a pilot study. Some simple examples as well as a complex example are given. Power calculations are illustrated using Java applets developed by the author.

Data Interpretation, Statistical↗
PubMed2002

Sex specificity, life-span QTLs, and statistical power.

Most of the quantitative trait loci (QTLs) that have been found to influence life span in Drosophila and Mus organisms are reported to have genetic effects limited to one sex. Here I study the statistical properties of sex-limited QTLs by randomly sampling data from an exceptionally large Drosophila experiment, and then asking how sample size influences outcomes. The sampling study suggests that, for the particular data analyzed here, even moderately large experiments, of the order of 10(4) individuals, can have a high probability of detecting sex-limited effects when they are not actually present. If a particular QTL is present in both sexes, and if the probability of detecting it in each sex is moderately high, say 80%, then there is a 32% chance of erroneously concluding that there is sex specificity. A comparison of interval mapping and composite interval mapping methods of data analysis suggests that the latter can inflate the appearance of sex specificity and sexual antagonism, depending on the choice of number of background covariates in the analysis. Conclusive evidence for sex-limited QTLs will require demonstration that results are robust to methods of statistical analysis, and experimental replication.

Animals↗
PubMed2002

On statistical power for average bioequivalence testing under replicated crossover designs.

In its recent guidance on bioequivalence, the U.S. Food and Drug Administration (FDA) recommends a two-sequence, four-period (2 x 4) replicated crossover design be used for assessment of population and individual bioequivalence [FDA. Guidance for Industry on Statistical Approaches to Establishing Bioequivalence; Center for Drug Evaluation and Research, Food and Drug Administration: Rockville, MD, 2001]. The recommended replicated crossover design not only allows estimates of both the inter-subject and the intra-subject variabilities and the variability due to subject-by-formulation interaction, but also provides an assessment of average bioequivalence (ABE). In this article, power function for assessment of ABE under a general replicated crossover design (i.e., a 2 x 2m replicated crossover design) based on the traditional analysis of variance model and the mixed effects model as suggested by the FDA are studied. It is found that the power of a 2 x 2m replicated crossover design depends upon the variability due to subject-by-formulation interaction and the number of replicates. Based on the derived power function, formula for sample size calculation for assessment of ABE under a 2 x 2m replicated crossover design is also provided.

Algorithms↗
PubMed2006

Statistical power and analytical quantification.

It is suggested that power analysis should be formally incorporated into quantification experiment reports in order to substantiate the conclusions derived from experimental data more effectively. The article addressed the issues of power analysis calculation, sample size estimation and appropriate data reporting in quantitative analytical comparisons. Illustrative examples from the literature are used to show how the described power analysis theory could be applied in practice.

Chemistry Techniques, Analytical↗
PubMed2001

Statistical power of QTL mapping methods applied to bacteria counts.

Most QTL mapping methods assume that phenotypes follow a normal distribution, but many phenotypes of interest are not normally distributed, e.g. bacteria counts (or colony-forming units, CFU). Such data are extremely skewed to the right and can present a high amount of zero values, which are ties from a statistical point of view. Our objective is therefore to assess the efficiency of four QTL mapping methods applied to bacteria counts: (1) least-squares (LS) analysis, (2) maximum-likelihood (ML) analysis, (3) non-parametric (NP) mapping and (4) nested ANOVA (AN). A transformation based on quantiles is used to mimic observed distributions of bacteria counts. Single positions (1 marker, 1 QTL) as well as chromosome scans (11 markers, 1 QTL) are simulated. When compared with the analysis of a normally distributed phenotype, the analysis of raw bacteria counts leads to a strong decrease in power for parametric methods, but no decrease is observed for NP. However, when a mathematical transformation (MT) is applied to bacteria counts prior to analysis, parametric methods have the same power as NP. Furthermore, parametric methods, when coupled with MT, outperform NP when bacteria counts have a very high proportion of zeros (70.8%). Our results show that the loss of power is mainly explained by the asymmetry of the phenotypic distribution, for parametric methods, and by the existence of ties, for the non-parametric method. Therefore, mapping of QTL for bacterial diseases, as well as for other diseases assessed by a counting process, should focus on the occurrence of ties in phenotypes before choosing the appropriate QTL mapping method.

Algorithms↗
PubMed2006

Guidelines for the conduct of clinical trials for spinal cord injury as developed by the ICCP panel: spontaneous recovery after spinal cord injury and statistical power needed for therapeutic clinical trials.

The International Campaign for Cures of Spinal Cord Injury Paralysis (ICCP) supported an international panel tasked with reviewing the methodology for clinical trials in spinal cord injury (SCI), and making recommendations on the conduct of future trials. This is the first of four papers. Here, we examine the spontaneous rate of recovery after SCI and resulting consequences for achieving statistically significant results in clinical trials. We have reanalysed data from the Sygen trial to provide some of this information. Almost all people living with SCI show some recovery of motor function below the initial spinal injury level. While the spontaneous recovery of motor function in patients with motor-complete SCI is fairly limited and predictable, recovery in incomplete SCI patients (American spinal injury Association impairment scale (AIS) C and AIS D) is both more substantial and highly variable. With motor complete lesions (AIS A/AIS B) the majority of functional return is within the zone of partial preservation, and may be sufficient to reclassify the injury level to a lower spinal level. The vast majority of recovery occurs in the first 3 months, but a small amount can persist for up to 18 months or longer. Some sensory recovery occurs after SCI, on roughly the same time course as motor recovery. Based on previous data of the magnitude of spontaneous recovery after SCI, as measured by changes in ASIA motor scores, power calculations suggest that the number of subjects required to achieve a significant result from a trial declines considerably as the start of the study is delayed after SCI. Trials of treatments that are most efficacious when given soon after injury will therefore, require larger patient numbers than trials of treatments that are effective at later time points. As AIS B patients show greater spontaneous recovery than AIS A patients, the number of AIS A patients requiring to be enrolled into a trial is lower. This factor will have to be balanced against the possibility that some treatments will be more effective in incomplete patients. Trials involving motor incomplete SCI patients, or trials where an accurate assessment of AIS grade cannot be made before the start of the trial, will require large subject numbers and/or better objective assessment methods.

Clinical Trials as Topic↗
PubMed2006

Inadequate statistical power of negative clinical trials in urological literature.

PURPOSE: Negative studies provide valuable information. However, conducting studies with inadequate power is unethical and an inefficient use of resources. The purpose of this study was to determine the prevalence of negative studies with inadequate power in urological literature. MATERIALS AND METHODS: The Journal of Urology, Urology and BJU International (formerly British Journal of Urology) from 1982 to 2002 were searched using the Ovid MEDLINE database. All clinical trials that contained the phrase "no difference" were identified. Data necessary for power calculation were extracted from applicable studies. RESULTS: Of the 417 articles identified in the MEDLINE search, 127 were negative studies that contained enough information to be analyzed. There were 70 (55%) articles from The Journal of Urology, 35 (28%) from BJU International and 22 (17%) from Urology. Of the studies that used continuous variables 65% had adequate power (greater than 80%) to detect a 50% difference between groups and 32% had adequate power to detect a 25% difference. Of the studies that used dichotomous variables only 33% had adequate power to detect a 50% difference between groups and 23% had adequate power to detect a 25% difference. Levels of adequate power in negative studies did not improve over time (p = 0.258). CONCLUSIONS: Many negative studies in urological literature are inconclusive because they lack adequate power to detect even large differences between groups. Inadequately powered studies often result in false conclusions that alter clinical behavior and deter further research. Therefore, it is imperative to consider power when interpreting literature. When designing future investigations power calculations should be performed to ensure sufficient patient recruitment to attain clinically meaningful results.

Bibliometrics↗
PubMed2004

Covariate adjustment in randomized controlled trials with dichotomous outcomes increases statistical power and reduces sample size requirements.

OBJECTIVE: Randomized controlled trials (RCTs) with dichotomous outcomes may be analyzed with or without adjustment for baseline characteristics (covariates). We studied type I error, power, and potential reduction in sample size with several covariate adjustment strategies. STUDY DESIGN AND SETTING: Logistic regression analysis was applied to simulated data sets (n=360) with different treatment effects, covariate effects, outcome incidences, and covariate prevalences. Treatment effects were estimated with or without adjustment for a single dichotomous covariate. Strategies included always adjusting for the covariate ("prespecified"), or only when the covariate was predictive or imbalanced. RESULTS: We found that the type I error was generally at the nominal level. The power was highest with prespecified adjustment. The potential reduction in sample size was higher with stronger covariate effects (from 3 to 46%, at 50% outcome incidence and covariate prevalence) and independent of the treatment effect. At lower outcome incidences and/or covariate prevalences, the reduction was lower. CONCLUSION: We conclude that adjustment for a predictive baseline characteristic may lead to a potentially important increase in power of analyses of treatment effect. Adjusted analysis should, hence, be considered more often for RCTs with dichotomous outcomes.

Data Interpretation, Statistical↗
PubMed2003

Detecting disease associations due to linkage disequilibrium using haplotype tags: a class of tests and the determinants of statistical power.

In the 'indirect' method of detecting genetic associations between a trait and a DNA variant, we type several markers in a gene or chromosome region of linkage disequilibrium. If there is association between markers and the trait, we presume the existence of one or more causal polymorphisms in the region. In order to obtain a sufficiently dense set of markers it will almost always be necessary to use single nucleotide polymorphisms (SNPs). Although there is an emerging literature on methods for choosing an optimal set of 'haplotype tag SNPs' (htSNPs) to detect association between a genetic region and a trait, less attention has been given to the problem of how such studies should be analysed when completed, and how the initial data which was used to select the htSNPs should be incorporated into the analysis. This paper discusses this problem for both population- and family-based association studies. The role of the R2 measure of association between a causal locus and various methods of scoring of marker haplotypes is highlighted. In most cases, the simplest method of scoring (locus coding), which does not require phase resolution, is shown generally to be more powerful than scoring methods that include haplotype information. A new 'multi-locus TDT' is also proposed.

Data Interpretation, Statistical↗
PubMed1997

Image quality versus statistical power.

We investigated whether SPET studies of neuroactivation might benefit from a similar approach used in PET; that is, increase the number of scans per task and accept poorer individual scan quality. Different study paradigms were simulated by varying the scanning parameters: (1) administered radiation activity per scan, (2) number of scans per task and (3) scan acquisition time. The maximum total dose received by each simulated subject remained the same. Areas of activation of varying signal strength were added to the scans using a customized graphics package. To establish the statistical benefits of a replication paradigm versus a non-replication paradigm, the datasets were analysed using SPM95 statistics software. This simulation was able to show that, when an SPM investigation is used for data analysis, study replication is more important than the individual image quality typically available from a high-performance SPET system.

Brain↗
PubMed2005

A model of the statistical power of comparative genome sequence analysis.

Comparative genome sequence analysis is powerful, but sequencing genomes is expensive. It is desirable to be able to predict how many genomes are needed for comparative genomics, and at what evolutionary distances. Here I describe a simple mathematical model for the common problem of identifying conserved sequences. The model leads to some useful rules of thumb. For a given evolutionary distance, the number of comparative genomes needed for a constant level of statistical stringency in identifying conserved regions scales inversely with the size of the conserved feature to be detected. At short evolutionary distances, the number of comparative genomes required also scales inversely with distance. These scaling behaviors provide some intuition for future comparative genome sequencing needs, such as the proposed use of "phylogenetic shadowing" methods using closely related comparative genomes, and the feasibility of high-resolution detection of small conserved features.

Animals↗
PubMed2001

Statistical power for nonequivalent pretest-posttest designs. The impact of change-score versus ANCOVA models.

Nonequivalent controlled pretest-posttest designs are central to evaluation science, yet no practical and unified approach for estimating power in the two most widely used analytic approaches to these designs exists. This article fills the gap by presenting and comparing useful, unified power formulas for ANCOVA and change-score analyses, indicating the implications of each on sample-size requirements. The authors close with practical recommendations for evaluators. Mathematical details and a simple spreadsheet approach are included in appendices.

Analysis of Variance↗