Better Power Methods for the Univariate Approach to Repeated Measures

New methods that improve upon current techniques related to power for UNIREP tests are introduced. The research is motivated by imaging applications, which often generate the type of data that can be handled with UNIREP techniques. The UNIREP Huynh-Feldt test is based on the Huynh-Feldt sphericity estimator. Claiming their estimator was a ratio of unbiased estimators, Huynh and Feldt developed it as an alternative to the sometimes biased Geisser-Greenhouse estimator. The Huynh-Feldt estimator is examined and shown to be a ratio of unbiased estimators only for the special case of rank of the design matrix, X, equal to 1. This realization results in a biased Huynh-Feldt test and power calculation when rank of X is greater than 1. A proper, adjusted Huynh-Feldt estimator for any rank of X is presented and shown to better estimate the population sphericity when rank of X is greater than 1. A power approximation for the rank-adjusted Huynh-Feldt test is also presented. For practical research situations, the rank-adjusted Huynh-Feldt power approximation is shown to perform as well as and, in most cases, better than the most accurate Huynh-Feldt power approximation in use. Furthermore, the Huynh-Feldt power approximation is shown to yield artificially inflated power values at a cost of inflated test size when rank of X is greater than 1. The rank-adjusted test is shown to control test size adequately. Approximate confidence intervals for UNIREP power in the case of an estimated covariance and fixed means are introduced and shown to provide reasonably accurate coverage probabilities for all four UNIREP tests. The approximate confidence intervals perform well in most cases considered, even for small sample sizes. The approximate confidence intervals are shown to perform better for higher power values than for lower power values, making them more useful in practical research conditions. Factors affecting UNIREP power confidence interval coverage probabilities are examined. These factors include sample size, rank of X and the degrees of freedom for both the estimating and target studies, as well as estimated sphericity multipliers. To provide tighter, more informative confidence bounds, one-sided confidence intervals are recommended

POWERLIB: SAS/IML Software for Computing Power in Multivariate Linear Models

The POWERLIB SAS/IML software provides convenient power calculations for a wide range of multivariate linear models with Gaussian errors. The software includes the Box, Geisser-Greenhouse, Huynh-Feldt, and uncorrected tests in the "univariate" approach to repeated measures (UNIREP), the Hotelling Lawley Trace, Pillai-Bartlett Trace, and Wilks Lambda tests in "multivariate" approach (MULTIREP), as well as a limited but useful range of mixed models. The familiar univariate linear model with Gaussian errors is an important special case. For estimated covariance, the software provides confidence limits for the resulting estimated power. All power and confidence limits values can be output to a SAS dataset, which can be used to easily produce plots and tables for manuscripts.

POWERLIB: SAS/IML Software for Computing Power in Multivariate Linear Models

The POWERLIB SAS/IML software provides convenient power calculations for a wide range of multivariate linear models with Gaussian errors. The software includes the Box, Geisser-Greenhouse, Huynh-Feldt, and uncorrected tests in the "univariate" approach to repeated measures (UNIREP), the Hotelling Lawley Trace, Pillai-Bartlett Trace, and Wilks Lambda tests in "multivariate" approach (MULTIREP), as well as a limited but useful range of mixed models. The familiar univariate linear model with Gaussian errors is an important special case. For estimated covariance, the software provides confidence limits for the resulting estimated power. All power and confidence limits values can be output to a SAS dataset, which can be used to easily produce plots and tables for manuscripts

Confidence regions for repeated measures ANOVA power curves based on estimated covariance

Abstract Background Using covariance or mean estimates from previous data introduces randomness into each power value in a power curve. Creating confidence intervals about the power estimates improves study planning by allowing scientists to account for the uncertainty in the power estimates. Driving examples arise in many imaging applications. Methods We use both analytical and Monte Carlo simulation methods. Our analytical derivations apply to power for tests with the univariate approach to repeated measures (UNIREP). Approximate confidence intervals and regions for power based on an estimated covariance matrix and fixed means are described. Extensive simulations are used to examine the properties of the approximations. Results Closed-form expressions are given for approximate power and confidence intervals and regions. Monte Carlo simulations support the accuracy of the approximations for practical ranges of sample size, rank of the design matrix, error degrees of freedom, and the amount of deviation from sphericity. The new methods provide accurate coverage probabilities for all four UNIREP tests, even for small sample sizes. Accuracy is higher for higher power values than for lower power values, making the methods especially useful in practical research conditions. The new techniques allow the plotting of power confidence regions around an estimated power curve, an approach that has been well received by researchers. Free software makes the new methods readily available. Conclusions The new techniques allow a convenient way to account for the uncertainty of using an estimated covariance matrix in choosing a sample size for a repeated measures ANOVA design. Medical imaging and many other types of healthcare research often use repeated measures ANOVA

Analytic, Computational, and Approximate Forms for Ratios of Noncentral and Central Gaussian Quadratic Forms

Many useful statistics equal the ratio of a possibly noncentral chi-square to a quadratic form in Gaussian variables with all positive weights. Expressing the density and distribution function as positively weighted sums of corresponding F functions has many advantages. The mixture forms have analytic value when embedded within a more complex problem. The mixture forms also have computational value. The expansions work well with quadratic forms having few components and small degrees of freedom. A more general algorithm from earlier literature can take longer or fail to converge in the same setting. Many approximations have been suggested for the problem. a positively weighted noncentral quadratic form can always have two moments matched to a noncentral chi-square. For a single quadratic form, the noncentral form performs neither uniformly more or less accurately than older approximations. The approach also gives a noncentral F approximation for any ratio of a positively weighted noncentral form to a positively weighted central quadratic form. The method provides better accuracy for noncentral ratios than approximations based on a single chi-square. The accuracy suffices for many practical applications, such as power analysis, even with few degrees of freedom. Naturally the approximation proves much faster and simpler to compute than any exact method. Embedding the approximation in analytic expressions provides simple forms which correctly guarantee only positive values have nonzero probabilities, and also automatically reduce to partially or fully exact results when either quadratic form has only one term

Power calculation for overall hypothesis testing with high-dimensional commensurate outcomes: Overall power for HDLSS

The complexity of system biology means that any metabolic, genetic, or proteomic pathway typically includes so many components (e.g., molecules) that statistical methods specialized for overall testing of high-dimensional and commensurate outcomes are required. While many overall tests have been proposed, very few have power and sample size methods. We develop accurate power and sample size methods and software to facilitate study planning for high-dimensional pathway analysis. With an account of any complex correlation structure between high-dimensional outcomes, the new methods allow power calculation even when the sample size is less than the number of variables. We derive the exact (finite-sample) and approximate non-null distributions of the ‘univariate’ approach to repeated measures test statistic, as well as power-equivalent scenarios useful to generalize our numerical evaluations. Extensive simulations of group comparisons support the accuracy of the approximations even when the ratio of number of variables to sample size is large. We derive a minimum set of constants and parameters sufficient and practical for power calculation. Using the new methods and specifying the minimum set to determine power for a study of metabolic consequences of vitamin B6 deficiency helps illustrate the practical value of the new results. Free software implementing the power and sample size methods applies to a wide range of designs, including one group pre-intervention and post-intervention comparisons, multiple parallel group comparisons with one-way or factorial designs, and the adjustment and evaluation of covariate effects

POWERLIB : SAS/IML Software for Computing Power in Multivariate Linear Models

The POWERLIB SAS/IML software provides convenient power calculations for a wide range of multivariate linear models with Gaussian errors. The software includes the Box, Geisser-Greenhouse, Huynh-Feldt, and uncorrected tests in the “univariate” approach to repeated measures (UNIREP), the Hotelling Lawley Trace, Pillai-Bartlett Trace, and Wilks Lambda tests in “multivariate” approach (MULTIREP), as well as a limited but useful range of mixed models. The familiar univariate linear model with Gaussian errors is an important special case. For estimated covariance, the software provides confidence limits for the resulting estimated power. All power and confidence limits values can be output to a SAS dataset, which can be used to easily produce plots and tables for manuscripts

Project overview and update on WEAVE: the next generation wide-field spectroscopy facility for the William Herschel Telescope

We present an overview of and status report on the WEAVE next-generation spectroscopy facility for the William Herschel Telescope (WHT). WEAVE principally targets optical ground-based follow up of upcoming ground-based (LOFAR) and space-based (Gaia) surveys. WEAVE is a multi-object and multi-IFU facility utilizing a new 2-degree prime focus field of view at the WHT, with a buffered pick-and-place positioner system hosting 1000 multi-object (MOS) fibres, 20 integral field units, or a single large IFU for each observation. The fibres are fed to a single spectrograph, with a pair of 8k(spectral) x 6k (spatial) pixel cameras, located within the WHT GHRIL enclosure on the telescope Nasmyth platform, supporting observations at R~5000 over the full 370-1000nm wavelength range in a single exposure, or a high resolution mode with limited coverage in each arm at R~20000. The project is now in the final design and early procurement phase, with commissioning at the telescope expected in 2017.Comment: 11 pages, 11 Figures, Summary of a presentation to Astronomical Telescopes and Instrumentation 201

Cost-effectiveness of Population Screening for BRCA Mutations in Ashkenazi Jewish Women Compared With Family History-Based Testing

BACKGROUND: Population-based testing for BRCA1/2 mutations detects the high proportion of carriers not identified by cancer family history (FH)-based testing. We compared the cost-effectiveness of population-based BRCA testing with the standard FH-based approach in Ashkenazi Jewish (AJ) women. METHODS: A decision-analytic model was developed to compare lifetime costs and effects amongst AJ women in the UK of BRCA founder-mutation testing amongst: 1) all women in the population age 30 years or older and 2) just those with a strong FH (≥10% mutation risk). The model assumes that BRCA carriers are offered risk-reducing salpingo-oophorectomy and annual MRI/mammography screening or risk-reducing mastectomy. Model probabilities utilize the Genetic Cancer Prediction through Population Screening trial/published literature to estimate total costs, effects in terms of quality-adjusted life-years (QALYs), cancer incidence, incremental cost-effectiveness ratio (ICER), and population impact. Costs are reported at 2010 prices. Costs/outcomes were discounted at 3.5%. We used deterministic/probabilistic sensitivity analysis (PSA) to evaluate model uncertainty. RESULTS: Compared with FH-based testing, population-screening saved 0.090 more life-years and 0.101 more QALYs resulting in 33 days' gain in life expectancy. Population screening was found to be cost saving with a baseline-discounted ICER of -£2079/QALY. Population-based screening lowered ovarian and breast cancer incidence by 0.34% and 0.62%. Assuming 71% testing uptake, this leads to 276 fewer ovarian and 508 fewer breast cancer cases. Overall, reduction in treatment costs led to a discounted cost savings of £3.7 million. Deterministic sensitivity analysis and 94% of simulations on PSA (threshold £20000) indicated that population screening is cost-effective, compared with current NHS policy. CONCLUSION: Population-based screening for BRCA mutations is highly cost-effective compared with an FH-based approach in AJ women age 30 years and older

Construction progress of WEAVE: the next generation wide-field spectroscopy facility for the William Herschel Telescope

We present an update on the overall construction progress of the WEAVE next-generation spectroscopy facility for the William Herschel Telescope (WHT), now that all the major fabrication contracts are in place. We also present a summary of the current planning behind the 5-year initial phase of survey operations, and some detailed end-to-end science simulations that have been effected to evaluate the final on-sky performance after data processing. WEAVE will provide optical ground-based follow up of ground-based (LOFAR) and space-based (Gaia) surveys. WEAVE is a multi-object and multi-IFU facility utilizing a new 2-degree prime focus field of view at the WHT, with a buffered pick-and-place positioner system hosting 1000 multi-object (MOS) fibres, 20 integral field units, or a single large IFU for each observation. The fibres are fed to a single (dual-beam) spectrograph, with total of 16k spectral pixels, located within the WHT GHRIL enclosure on the telescope Nasmyth platform, supporting observations at R 5000 over the full 370-1000nm wavelength range in a single exposure, or a high resolution mode with limited coverage in each arm at R 20000. The project has experienced some delays in procurement and now has first light expected for the middle of 2019