GLUMIP 2.0: SAS/IML Software for Planning Internal Pilots

Internal pilot designs involve conducting interim power analysis (without interim data analysis) to modify the final sample size. Recently developed techniques have been described to avoid the type~I error rate inflation inherent to unadjusted hypothesis tests, while still providing the advantages of an internal pilot design. We present GLUMIP 2.0, the latest version of our free SAS/IML software for planning internal pilot studies in the general linear univariate model (GLUM) framework. The new analytic forms incorporated into the updated software solve many problems inherent to current internal pilot techniques for linear models with Gaussian errors. Hence, the GLUMIP 2.0 software makes it easy to perform exact power analysis for internal pilots under the GLUM framework with independent Gaussian errors and fixed predictors.

GLUMIP 2.0: SAS/IML Software for Planning Internal Pilots

Internal pilot designs involve conducting interim power analysis (without interim data analysis) to modify the final sample size. Recently developed techniques have been described to avoid the type~I error rate inflation inherent to unadjusted hypothesis tests, while still providing the advantages of an internal pilot design. We present GLUMIP 2.0, the latest version of our free SAS/IML software for planning internal pilot studies in the general linear univariate model (GLUM) framework. The new analytic forms incorporated into the updated software solve many problems inherent to current internal pilot techniques for linear models with Gaussian errors. Hence, the GLUMIP 2.0 software makes it easy to perform exact power analysis for internal pilots under the GLUM framework with independent Gaussian errors and fixed predictors

Some Distributions and Their Implications for an Internal Pilot Study With a Univariate Linear Model

In planning a study, the choice of sample size may depend on a variance value based on speculation or obtained from an earlier study. Scientists may wish to use an internal pilot design to protect themselves against an incorrect choice of variance. Such a design involves collecting a portion of the originally planned sample and using it to produce a new variance estimate. This leads to a new power analysis and increasing or decreasing sample size. For any general linear univariate model, with fixed predictors and Gaussian errors, we prove that the uncorrected fixed sample F-statistic is the likelihood ratio test statistic. However, the statistic does not follow an F distribution. Ignoring the discrepancy may inflate test size. We derive and evaluate properties of the components of the likelihood ratio test statistic in order to characterize and quantify the bias. Most notably, the fixed sample size variance estimate becomes biased downward. The bias may inflate test size for any hypothesis test, even if the parameter being tested was not involved in the sample size re-estimation. Furthermore, using fixed sample size methods may create biased confidence intervals for secondary parameters and the variance estimate

Properties of doubly-truncated gamma variables

The truncated gamma distribution has been widely studied, primarily in life-testing and reliability settings. Most work has assumed an upper bound on the support of the random variable, i.e. the space of the distribution is (0, u). We consider a doubly-truncated gamma random variable restricted by both a lower (l) and upper (u) truncation point, both of which are considered known. We provide simple forms for the density, cumulative distribution function (CDF), moment generating function, cumulant generating function, characteristic function, and moments. We extend the results to describe the density, CDF, and moments of a doubly-truncated noncentral chi-square variable

Practical Methods for Bounding Type I Error Rate with an Internal Pilot Design

New analytic forms for distributions at the heart of internal pilot theory solve many problems inherent to current techniques for linear models with Gaussian errors. Internal pilot designs use a fraction of the data to re-estimate the error variance and modify the final sample size. Too small or too large a sample size caused by an incorrect planning variance can be avoided. However, the usual hypothesis test may need adjustment to control the Type I error rate. A bounding test achieves control of Type I error rate while providing most of the advantages of the unadjusted test. Unfortunately, the presence of both a doubly truncated and an untruncated chi-square random variable complicates the theory and computations. An expression for the density of the sum of the two chi-squares gives a simple form for the test statistic density. Examples illustrate that the new results make the bounding test practical by providing very stable, convergent, and much more accurate computations. Furthermore, the new computational methods are effectively never slower and usually much faster. All results apply to any univariate linear model with fixed predictors and Gaussian errors, with the t-test a special case

Predicting Progression in Parkinson's Disease Using Baseline and 1-Year Change Measures.

BackgroundImproved prediction of Parkinson's disease (PD) progression is needed to support clinical decision-making and to accelerate research trials.ObjectivesTo examine whether baseline measures and their 1-year change predict longer-term progression in early PD.MethodsParkinson's Progression Markers Initiative study data were used. Participants had disease duration ≤2 years, abnormal dopamine transporter (DAT) imaging, and were untreated with PD medications. Baseline and 1-year change in clinical, cerebrospinal fluid (CSF), and imaging measures were evaluated as candidate predictors of longer-term (up to 5 years) change in Movement Disorders Society-Unified Parkinson's Disease Rating Scale (MDS-UPDRS) score and DAT specific binding ratios (SBR) using linear mixed-effects models.ResultsAmong 413 PD participants, median follow-up was 5 years. Change in MDS-UPDRS from year-2 to last follow-up was associated with disease duration (β= 0.351; 95% CI = 0.146, 0.555), male gender (β= 3.090; 95% CI = 0.310, 5.869), and baseline (β= -0.199; 95% CI = -0.315, -0.082) and 1-year change (β= 0.540; 95% CI = 0.423, 0.658) in MDS-UPDRS; predictors in the model accounted for 17.6% of the variance in outcome. Predictors of percent change in mean SBR from year-2 to last follow-up included baseline rapid eye movement sleep behavior disorder score (β= -0.6229; 95% CI = -1.2910, 0.0452), baseline (β= 7.232; 95% CI = 2.268, 12.195) and 1-year change (β= 45.918; 95% CI = 35.994,55.843) in mean striatum SBR, and 1-year change in autonomic symptom score (β= -0.325;95% CI = -0.695, 0.045); predictors in the model accounted for 44.1% of the variance.ConclusionsBaseline clinical, CSF, and imaging measures in early PD predicted change in MDS-UPDRS and dopamine-transporter binding, but the predictive value of the models was low. Adding the short-term change of possible predictors improved the predictive value, especially for modeling change in dopamine-transporter binding

The Association of the Metabolic Syndrome with PAI-1 and t-PA Levels

Background. We used a random sample (n = 2, 495) from the population-based Prevention of Renal and Vascular End-stage Disease (PREVEND) study population to examine the association of the metabolic syndrome (Met S) with plasminogen activator inhibitor type 1 (PAI-1) and tissue plasminogen activator (t-PA) antigen levels. Results. The overall prevalence of the Met S was 18%, was dependent on age and gender, and was positively associated with higher antigen levels of both PAI-1 and t-PA. These significant effects were maintained after adjustment for age, gender, BMI, elevated C-reactive protein, smoking status, urinary albumin excretion, and insulin levels. We found no significant interactions between the Met S and other covariates on PAI-1 and t-PA levels. Conclusions. Our study demonstrates that those with the Met S have significantly higher levels of PAI-1 and t-PA antigen, factors known to increase the risk of cardiovascular disease

An application of conditional logistic regression and multifactor dimensionality reduction for detecting gene-gene Interactions on risk of myocardial infarction: The importance of model validation

BACKGROUND: To examine interactions among the angiotensin converting enzyme (ACE) insertion/deletion, plasminogen activator inhibitor-1 (PAI-1) 4G/5G, and tissue plasminogen activator (t-PA) insertion/deletion gene polymorphisms on risk of myocardial infarction using data from 343 matched case-control pairs from the Physicians Health Study. We examined the data using both conditional logistic regression and the multifactor dimensionality reduction (MDR) method. One advantage of the MDR method is that it provides an internal prediction error for validation. We summarize our use of this internal prediction error for model validation. RESULTS: The overall results for the two methods were consistent, with both suggesting an interaction between the ACE I/D and PAI-1 4G/5G polymorphisms. However, using ten-fold cross validation, the 46% prediction error for the final MDR model was not significantly lower than that expected by chance. CONCLUSIONS: The significant interaction initially observed does not validate and may represent a type I error. As data-driven analytic methods continue to be developed and used to examine complex genetic interactions, it will become increasingly important to stress model validation in order to ensure that significant effects represent true relationships rather than chance findings

Contrasting signals of positive selection in genes involved in human skin color variation from tests based on SNP scans and resequencing

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.Abstract Background Numerous genome-wide scans conducted by genotyping previously ascertained single-nucleotide polymorphisms (SNPs) have provided candidate signatures for positive selection in various regions of the human genome, including in genes involved in pigmentation traits. However, it is unclear how well the signatures discovered by such haplotype-based test statistics can be reproduced in tests based on full resequencing data. Four genes (oculocutaneous albinism II (OCA2), tyrosinase-related protein 1 (TYRP1), dopachrome tautomerase (DCT), and KIT ligand (KITLG)) implicated in human skin-color variation, have shown evidence for positive selection in Europeans and East Asians in previous SNP-scan data. In the current study, we resequenced 4.7 to 6.7 kb of DNA from each of these genes in Africans, Europeans, East Asians, and South Asians. Results Applying all commonly used neutrality-test statistics for allele frequency distribution to the newly generated sequence data provided conflicting results regarding evidence for positive selection. Previous haplotype-based findings could not be clearly confirmed. Although some tests were marginally significant for some populations and genes, none of them were significant after multiple-testing correction. Combined P values for each gene-population pair did not improve these results. Application of Approximate Bayesian Computation Markov chain Monte Carlo based to these sequence data using a simple forward simulator revealed broad posterior distributions of the selective parameters for all four genes, providing no support for positive selection. However, when we applied this approach to published sequence data on SLC45A2, another human pigmentation candidate gene, we could readily confirm evidence for positive selection, as previously detected with sequence-based and some haplotype-based tests. Conclusions Overall, our data indicate that even genes that are strong biological candidates for positive selection and show reproducible signatures of positive selection in SNP scans do not always show the same replicability of selection signals in other tests, which should be considered in future studies on detecting positive selection in genetic data.Published versio

Response to ibudilast treatment according to progressive multiple sclerosis disease phenotype

OBJECTIVE: Determine whether a treatment effect of ibudilast on brain atrophy rate differs between participants with primary (PPMS) and secondary (SPMS) progressive multiple sclerosis. BACKGROUND: Progressive forms of MS are both associated with continuous disability progression. Whether PPMS and SPMS differ in treatment response remains unknown. DESIGN/METHODS: SPRINT-MS was a randomized, placebo-controlled 96-week phase 2 trial in both PPMS (n = 134) and SPMS (n = 121) patients. The effect of PPMS and SPMS phenotype on the rate of change of brain atrophy measured by brain parenchymal fraction (BPF) was examined by fitting a three-way interaction linear-mixed model. Adjustment for differences in baseline demographics, disease measures, and brain size was explored. RESULTS: Analysis showed that there was a three-way interaction between the time, treatment effect, and disease phenotype (P \u3c 0.06). After further inspection, the overall treatment effect was primarily driven by patients with PPMS (P \u3c 0.01), and not by patients with SPMS (P = 0.97). This difference may have been due to faster brain atrophy progression seen in the PPMS placebo group compared to SPMS placebo (P \u3c 0.02). Although backward selection (P \u3c 0.05) retained age, T2 lesion volume, RNFL, and longitudinal diffusivity as significant baseline covariates in the linear-mixed model, the adjusted overall treatment effect was still driven by PPMS (P \u3c 0.01). INTERPRETATION: The previously reported overall treatment effect of ibudilast on worsening of brain atrophy in progressive MS appears to be driven by patients with PPMS that may be, in part, because of the faster atrophy progression rates seen in the placebo-treated group