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1.  POWERLIB: SAS/IML Software for Computing Power in Multivariate Linear Models 
Journal of statistical software  2008;30(5):http://www.jstatsoft.org/v30/i05.
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.
PMCID: PMC4228969  PMID: 25400516
power; multivariate linear models; mixed models; Gaussian errors
2.  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.
doi:10.1198/106186006X112954
PMCID: PMC3704188  PMID: 23843686
Cumulative distribution function; Mixture distribution; Noncentral F
3.  Confidence regions for repeated measures ANOVA power curves based on estimated covariance 
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.
doi:10.1186/1471-2288-13-57
PMCID: PMC3738257  PMID: 23586676
Sample size; Replication study; Study planning; Univariate approach; UNIREP
4.  Global hypothesis testing for high-dimensional repeated measures outcomes 
Statistics in medicine  2011;31(8):724-742.
High-throughput technology in metabolomics, genomics, and proteomics gives rise to high dimension, low sample size data when the number of metabolites, genes, or proteins exceeds the sample size. For a limited class of designs, the classic ‘univariate approach’ for Gaussian repeated measures can provide a reasonable global hypothesis test. We derive new tests that not only accurately allow more variables than subjects, but also give valid analyses for data with complex between-subject and within-subject designs. Our derivations capitalize on the dual of the error covariance matrix, which is nonsingular when the number of variables exceeds the sample size, to ensure correct statistical inference and enhance computational efficiency. Simulation studies demonstrate that the new tests accurately control Type I error rate and have reasonable power even with a handful of subjects and a thousand outcome variables. We apply the new methods to the study of metabolic consequences of vitamin B6 deficiency. Free software implementing the new 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.
doi:10.1002/sim.4435
PMCID: PMC3396026  PMID: 22161561
UNIREP; dual matrix; commensurate multivariate data; general linear multivariate model; MULTIREP; MANOVA
5.  BRIEF REPORT: How Well Do Clinic-Based Blood Pressure Measurements Agree with the Mercury Standard? 
BACKGROUND
Obtaining accurate blood pressure (BP) readings is a challenge faced by health professionals. Clinical trials implement strict protocols, whereas clinical practices and studies that assess quality of care utilize a less rigorous protocol for BP measurement.
OBJECTIVE
To examine agreement between real-time clinic-based assessment of BP and the standard mercury assessment of BP.
DESIGN
Prospective reliability study.
PATIENTS
One hundred patients with an International Classification of Diseases—9th edition code for hypertension were enrolled.
MEASURES
Two BP measurements were obtained with the Hawksley random-zero mercury sphygmomanometer and averaged. The clinic-based BP was extracted from the computerized medical records.
RESULTS
Agreement between the mercury and clinic-based systolic blood pressure (SBP) was good, intraclass correlation coefficient (ICC)=0.91 (95% confidence interval (CI): 0.83 to 0.94); the agreement for the mercury and clinic-based diastolic blood pressure (DBP) was satisfactory, ICC=0.77 (95% CI: 0.62 to 0.86). Overall, clinic-based readings overestimated the mercury readings, with a mean overestimation of 8.3 mmHg for SBP and 7.1 mmHg for DBP. Based on the clinic-based measure, 21% of patients were misdiagnosed with uncontrolled hypertension.
CONCLUSIONS
Health professionals should be aware of this potential difference when utilizing clinic-based BP values for making treatment decisions and/or assessing quality of care.
doi:10.1111/j.1525-1497.2005.0105.x
PMCID: PMC1490157  PMID: 16050862
blood pressure measurement assessment; clinic method; mercury device

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