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

Using Power Analysis to Choose the Unit of Randomization, Outcome, and Approach for Subgroup Analysis for a Multilevel Randomized Controlled Clinical Trial to Reduce Disparities in Cardiovascular Health

We give examples of three features in the design of randomized controlled clinical trials which can increase power and thus decrease sample size and costs. We consider an example multilevel trial with several levels of clustering. For a fixed number of independent sampling units, we show that power can vary widely with the choice of the level of randomization. We demonstrate that power and interpretability can improve by testing a multivariate outcome rather than an unweighted composite outcome. Finally, we show that using a pooled analytic approach, which analyzes data for all subgroups in a single model, improves power for testing the intervention effect compared to a stratified analysis, which analyzes data for each subgroup in a separate model. The power results are computed for a proposed prevention research study. The trial plans to randomize adults to either telehealth (intervention) or in-person treatment (control) to reduce cardiovascular risk factors. The trial outcomes will be measures of the Essential Eight, a set of scores for cardiovascular health developed by the American Heart Association which can be combined into a single composite score. The proposed trial is a multilevel study, with outcomes measured on participants, participants treated by the same provider, providers nested within clinics, and clinics nested within hospitals. Investigators suspect that the intervention effect will be greater in rural participants, who live farther from clinics than urban participants. The results use published, exact analytic methods for power calculations with continuous outcomes. We provide example code for power analyses using validated software.

Holo-omics analysis reveals the influence of gut microbiota on obesity indicators in Jinhua pigs

BACKGROUND

The mechanisms behind obesity are complex and multi-faceted, involving the interplay of both host genomics and gut microbiome. In recent years, research has largely focused on these factors separately, but rarely from the viewpoint of holo-omics, which considers the host and microbiome as an integrated entity. To address this gap in knowledge, the present study aimed to investigate the holo-omics basis of obesity in Jinhua pigs, a Chinese indigenous breed known for its high degree of fat deposition and superior meat quality.

METHODS

Six pigs with extreme obesity phenotype were selected from a larger cohort of eighteen Jinhua pigs, and the contents of the jejunum, cecum, and colon regions were collected after slaughter at 240 days of age. The data obtained was processed, denoised, and annotated using QIIME2, with expression differences being analyzed using edgeR software.

RESULTS

The results showed significant differences in jejunal microbial diversity and composition between the two groups, with gut transcriptomics also indicating that differentially expressed genes in the jejunum were enriched in lipid metabolism pathways. These findings provide further evidence of the influence of the gut microbiome and host gene expression on fat deposition in Jinhua pigs.

CONCLUSIONS

This study provides valuable insights into the mechanisms of fat deposition in Jinhua pigs from the viewpoint of holo-omics. The integration of host transcriptomics and microbiome data helps shed light on the complex interactions between the host and gut microbiome, and highlights the importance of considering both factors in our understanding of obesity.

Power and sample size analysis for longitudinal mixed models of health in populations exposed to environmental contaminants: a tutorial

BACKGROUND

When evaluating the impact of environmental exposures on human health, study designs often include a series of repeated measurements. The goal is to determine whether populations have different trajectories of the environmental exposure over time. Power analyses for longitudinal mixed models require multiple inputs, including clinically significant differences, standard deviations, and correlations of measurements. Further, methods for power analyses of longitudinal mixed models are complex and often challenging for the non-statistician. We discuss methods for extracting clinically relevant inputs from literature, and explain how to conduct a power analysis that appropriately accounts for longitudinal repeated measures. Finally, we provide careful recommendations for describing complex power analyses in a concise and clear manner.

METHODS

For longitudinal studies of health outcomes from environmental exposures, we show how to [1] conduct a power analysis that aligns with the planned mixed model data analysis, [2] gather the inputs required for the power analysis, and [3] conduct repeated measures power analysis with a highly-cited, validated, free, point-and-click, web-based, open source software platform which was developed specifically for scientists.

RESULTS

As an example, we describe the power analysis for a proposed study of repeated measures of per- and polyfluoroalkyl substances (PFAS) in human blood. We show how to align data analysis and power analysis plan to account for within-participant correlation across repeated measures. We illustrate how to perform a literature review to find inputs for the power analysis. We emphasize the need to examine the sensitivity of the power values by considering standard deviations and differences in means that are smaller and larger than the speculated, literature-based values. Finally, we provide an example power calculation and a summary checklist for describing power and sample size analysis.

CONCLUSIONS

This paper provides a detailed roadmap for conducting and describing power analyses for longitudinal studies of environmental exposures. It provides a template and checklist for those seeking to write power analyses for grant applications.

Power for balanced linear mixed models with complex missing data processes

When designing repeated measures studies, both the amount and the pattern of missing outcome data can affect power. The chance that an observation is missing may vary across measurements, and missingness may be correlated across measurements. For example, in a physiotherapy study of patients with Parkinson's disease, increasing intermittent dropout over time yielded missing measurements of physical function. In this example, we assume data are missing completely at random, since the chance that a data point was missing appears to be unrelated to either outcomes or covariates. For data missing completely at random, we propose noncentral F power approximations for the Wald test for balanced linear mixed models with Gaussian responses. The power approximations are based on moments of missing data summary statistics. The moments were derived assuming a conditional linear missingness process. The approach provides approximate power for both complete-case analyses, which include independent sampling units where all measurements are present, and observed-case analyses, which include all independent sampling units with at least one measurement. Monte Carlo simulations demonstrate the accuracy of the method in small samples. We illustrate the utility of the method by computing power for proposed replications of the Parkinson's study.

Experimentally Manipulated Low Social Status and Food Insecurity Alter Eating Behavior Among Adolescents: A Randomized Controlled Trial

OBJECTIVE

This randomized trial experimentally manipulated social status to assess effects on acute eating behavior and 24-hour energy balance.

METHODS

Participants (n = 133 Hispanics; age 15-21 years; 60.2% females) were randomized to low social status ("LOW") or high social status ("HIGH") conditions in a rigged game of Monopoly (Hasbro, Inc.). Acute energy intake in a lunchtime meal was measured by food scales. Twenty-four-hour energy balance was assessed via summation of resting metabolic rate (metabolic cart), physical activity energy expenditure (accelerometer), thermic effect of food, and subtraction of twenty-four-hour energy intake (food diary).

RESULTS

In the total sample, no significant differences were observed by study condition at lunchtime. LOW females consumed a greater percent of lunchtime daily energy needs (37.5%) relative to HIGH females (34.3%); however, this difference was not statistically significant (P = 0.291). In males, however, LOW consumed significantly less (36.5%) of their daily energy needs relative to HIGH males (45.8%; P = 0.001). For 24-hour energy balance, sex differences were nearly significant (P = 0.057; LOW females: surplus +200 kcal; HIGH males: surplus +445 kcal). Food-insecure individuals consumed a nearly significant greater lunchtime percent daily energy than those with food security (40.7% vs. 36.3%; P = 0.0797).

CONCLUSIONS

The data demonstrate differential acute and 24-hour eating behavior responses between Hispanic male and female adolescents in experimentally manipulated conditions of low social status.

Targeted exome sequencing identifies five novel loci at genome-wide significance for modulating antidepressant response in patients with major depressive disorder

In order to determine the role of single nucleotide variants (SNVs) in modulating antidepressant response, we conducted a study, consisting of 929 major depressive disorder (MDD) patients, who were treated with antidepressant drugs (drug-only) or in combination with a repetitive transcranial magnetic stimulation (plus-rTMS), followed by targeted exome sequencing analysis. We found that the "plus-rTMS" patients presented a more effective response to the treatment when compared to the 'drug-only' group. Our data firstly demonstrated that the SNV burden had a significant impact on the antidepressant response presented in the "drug-only" group, but was limited in the "plus-rTMS" group. Further, after controlling for overall SNV burden, seven single nucleotide polymorphisms (SNPs) at five loci, IL1A, GNA15, PPP2CB, PLA2G4C, and GBA, were identified as affecting the antidepressant response at genome-wide significance (P < 5 × 10^-08). Additional multiple variants achieved a level of correction for multiple testing, including GNA11, also shown as a strong signal for MDD risk. Our study showed some promising evidence on genetic variants that could be used as individualized therapeutic guides for MDD patients.

Bayesian sample size determination for longitudinal studies with continuous response based on different scientific questions of interest

Longitudinal study designs are commonly applied in much scientific research, especially in the medical, social, and economic sciences. Longitudinal studies allow researchers to measure changes in each individual's responses over time and often have higher statistical power than cross-sectional studies. Choosing an appropriate sample size is a crucial step in a successful study. In longitudinal studies, because of the complexity of their design, including the selection of the number of individuals and the number of repeated measurements, sample size determination is less studied. This paper uses a simulation-based method to determine the sample size from a Bayesian perspective. For this purpose, several Bayesian criteria for sample size determination are used, of which the most important one is the Bayesian power criterion. We determine the sample size of a longitudinal study based on the scientific question of interest, by the choice of an appropriate model. Most of the methods of determining sample size are based on the definition of a single hypothesis. In this paper, in addition to using this method, we determine the sample size using multiple hypotheses. Using several examples, the proposed Bayesian methods are illustrated and discussed.

Power and Sample Size for Fixed-Effects Inference in Reversible Linear Mixed Models

Despite the popularity of the general linear mixed model for data analysis, power and sample size methods and software are not generally available for commonly used test statistics and reference distributions. Statisticians resort to simulations with homegrown and uncertified programs or rough approximations which are misaligned with the data analysis. For a wide range of designs with longitudinal and clustering features, we provide accurate power and sample size approximations for inference about fixed effects in linear models we call reversible. We show that under widely applicable conditions, the general linear mixed-model Wald test has non-central distributions equivalent to well-studied multivariate tests. In turn, exact and approximate power and sample size results for the multivariate Hotelling-Lawley test provide exact and approximate power and sample size results for the mixed-model Wald test. The calculations are easily computed with a free, open-source product that requires only a web browser to use. Commercial software can be used for a smaller range of reversible models. Simple approximations allow accounting for modest amounts of missing data. A real-world example illustrates the methods. Sample size results are presented for a multicenter study on pregnancy. The proposed study, an extension of a funded project, has clustering within clinic. Exchangeability among participants allows averaging across them to remove the clustering structure. The resulting simplified design is a single level longitudinal study. Multivariate methods for power provide an approximate sample size. All proofs and inputs for the example are in the Supplementary Materials (available online).

Assessing the reliability of the short form 12 (SF-12) health survey in adults with mental health conditions: a report from the wellness incentive and navigation (WIN) study

Background

Although Short Form (SF)-12 × 2® has been extensively studied and used as a valid measure of health-related quality of life in a variety of population groups, no systematic studies have described the reliability of the measure in patients with behavioral conditions or serious mental illness (SMI).

Methods and results

We assessed the internal consistency, split-half reliability and annual test-retest correlations in a sample of 1587 participants with either a combination of physical and behavioral conditions or SMI. The Mosier’s alpha was 0.70 for the Physical Composite Scale (PCS) and 0.69 for the Mental Health Composite Scale (MCS), indicating good internal consistency. We observed strong correlations between physical functioning, physical role and body pain scales (r = 0.55–0.56), and between social functioning, emotional role, and mental health (r = 0.53–0.58). We calculated split-half reliabilities to be 0.74 for physical functioning, 0.75 for physical role, 0.73 for emotional role and 0.65 for mental health respectively. We assessed the annual test-retest correlation using intraclass correlation (ICC) and found an ICC of 0.61 for PCS and 0.57 for MCS composite scores, adjusting for age, sex, race/ethnicity, and CRG. We found no decline in the correlations between baseline and the following study years until year 3.

Conclusions

Our results encourage using SF-12v2® to assess health-related quality of life in the Medicaid population with combined physical and behavioral conditions or similar cohorts.

Trial registration

The WIN study was registered with clinicaltrials.gov on April 22, 2015. Trial registration number: NCT02440906. Retrospectively registered.

The wellness incentives and navigation project: design and methods

Background

About 35 % of non-elderly U.S. adult Medicaid enrollees have a behavioral health condition, such as anxiety, mood disorders, substance use disorders, and/or serious mental illness. Individuals with serious mental illness, in particular, have mortality rates that are 2 to 3 times higher as the general population, which are due to multiple factors including inactivity, poor nutrition, and tobacco use. 61 % of Medicaid beneficiaries with behavioral health conditions also have multiple other co-occurring chronic physical health conditions, which further contributes to morbidity and mortality. The Wellness Incentives and Navigation (WIN) project is one of 10 projects under the Centers for Medicare and Medicaid Services “Medicaid Incentives for the Prevention of Chronic Diseases” Initiative, to “test the effectiveness of providing incentives directly to Medicaid beneficiaries of all ages who participate in prevention programs, and change their health risks and outcomes by adopting healthy behaviors.”

Methods/Design

WIN is a three-year randomized pragmatic clinical trial designed to examine the comparative effectiveness of the combined use of personal navigators, motivational interviewing, and a flexible wellness account on cardiovascular risk reduction among individuals in Medicaid with co-occurring physical and mental health conditions or serious mental illness alone relative to the usual care provided within Medicaid Managed Care. 1250 individuals, identified through Medicaid claims data, were recruited and randomly assigned to an intervention group or control group with outcomes tracked annually. A comparison group was also recruited to help assess the study’s internal validity.

Discussion

The primary outcomes are physical and mental health related quality-of-life as measured by the SF-12, and BMI, blood pressure, LDL-C, and Hba1c results for those who are diabetic measured clinically. The purpose of this paper is to present the unique design of the WIN trial prior to results becoming available in hopes of assisting other researchers in conducting community-based randomized pragmatic trials. Outcomes will be assessed through the linkage of patient reported outcomes, health care claims, and electronic health record data.

Trial Registration

NCT02440906

Multivariate test power approximations for balanced linear mixed models in studies with missing data

Multilevel and longitudinal studies are frequently subject to missing data. For example, biomarker studies for oral cancer may involve multiple assays for each participant. Assays may fail, resulting in missing data values that can be assumed to be missing completely at random. Catellier and Muller proposed a data analytic technique to account for data missing at random in multilevel and longitudinal studies. They suggested modifying the degrees of freedom for both the Hotelling-Lawley trace F statistic and its null case reference distribution. We propose parallel adjustments to approximate power for this multivariate test in studies with missing data. The power approximations use a modified non-central F statistic, which is a function of (i) the expected number of complete cases, (ii) the expected number of non-missing pairs of responses, or (iii) the trimmed sample size, which is the planned sample size reduced by the anticipated proportion of missing data. The accuracy of the method is assessed by comparing the theoretical results to the Monte Carlo simulated power for the Catellier and Muller multivariate test. Over all experimental conditions, the closest approximation to the empirical power of the Catellier and Muller multivariate test is obtained by adjusting power calculations with the expected number of complete cases. The utility of the method is demonstrated with a multivariate power analysis for a hypothetical oral cancer biomarkers study. We describe how to implement the method using standard, commercially available software products and give example code. Copyright © 2015 John Wiley & Sons, Ltd.

GLIMMPSE Lite: calculating power and sample size on smartphone devices

Researchers seeking to develop complex statistical applications for mobile devices face a common set of difficult implementation issues. In this work, we discuss general solutions to the design challenges. We demonstrate the utility of the solutions for a free mobile application designed to provide power and sample size calculations for univariate, one-way analysis of variance (ANOVA), GLIMMPSE Lite. Our design decisions provide a guide for other scientists seeking to produce statistical software for mobile platforms.

: Online Power Computation for Linear Models with and without a Baseline Covariate

GLIMMPSE is a free, web-based software tool that calculates power and sample size for the general linear multivariate model with Gaussian errors (http://glimmpse.SampleSizeShop.org/). GLIMMPSE provides a user-friendly interface for the computation of power and sample size. We consider models with fixed predictors, and models with fixed predictors and a single Gaussian covariate. Validation experiments demonstrate that GLIMMPSE matches the accuracy of previously published results, and performs well against simulations. We provide several online tutorials based on research in head and neck cancer. The tutorials demonstrate the use of GLIMMPSE to calculate power and sample size.

Selecting a sample size for studies with repeated measures

Many researchers favor repeated measures designs because they allow the detection of within-person change over time and typically have higher statistical power than cross-sectional designs. However, the plethora of inputs needed for repeated measures designs can make sample size selection, a critical step in designing a successful study, difficult. Using a dental pain study as a driving example, we provide guidance for selecting an appropriate sample size for testing a time by treatment interaction for studies with repeated measures. We describe how to (1) gather the required inputs for the sample size calculation, (2) choose appropriate software to perform the calculation, and (3) address practical considerations such as missing data, multiple aims, and continuous covariates.

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.

On summary measure analysis of linear trend repeated measures data: performance comparison with two competing methods

Background

The summary measure approach (SMA) is sometimes the only applicable tool for the analysis of repeated measurements in medical research, especially when the number of measurements is relatively large. This study aimed to describe techniques based on summary measures for the analysis of linear trend repeated measures data and then to compare performances of SMA, linear mixed model (LMM), and unstructured multivariate approach (UMA).

Methods

Practical guidelines based on the least squares regression slope and mean of response over time for each subject were provided to test time, group, and interaction effects. Through Monte Carlo simulation studies, the efficacy of SMA vs. LMM and traditional UMA, under different types of covariance structures, was illustrated. All the methods were also employed to analyze two real data examples.

Results

Based on the simulation and example results, it was found that the SMA completely dominated the traditional UMA and performed convincingly close to the best-fitting LMM in testing all the effects. However, the LMM was not often robust and led to non-sensible results when the covariance structure for errors was misspecified. The results emphasized discarding the UMA which often yielded extremely conservative inferences as to such data.

Conclusions

It was shown that summary measure is a simple, safe and powerful approach in which the loss of efficiency compared to the best-fitting LMM was generally negligible. The SMA is recommended as the first choice to reliably analyze the linear trend data with a moderate to large number of measurements and/or small to moderate sample sizes.

Avoiding bias in mixed model inference for fixed effects

Analysis of a large longitudinal study of children motivated our work. The results illustrate how accurate inference for fixed effects in a general linear mixed model depends on the covariance model selected for the data. Simulation studies have revealed biased inference for the fixed effects with an underspecified covariance structure, at least in small samples. One underspecification common for longitudinal data assumes a simple random intercept and conditional independence of the within-subject errors (i.e., compound symmetry). We prove that the underspecification creates bias in both small and large samples, indicating that recruiting more participants will not alleviate inflation of the Type I error rate associated with fixed effect inference. Enumerations and simulations help quantify the bias and evaluate strategies for avoiding it. When practical, backwards selection of the covariance model, starting with an unstructured pattern, provides the best protection. Tutorial papers can guide the reader in minimizing the chances of falling into the often spurious software trap of nonconvergence. In some cases, the logic of the study design and the scientific context may support a structured pattern, such as an autoregressive structure. The sandwich estimator provides a valid alternative in sufficiently large samples. Authors reporting mixed-model analyses should note possible biases in fixed effects inference because of the following: (i) the covariance model selection process; (ii) the specific covariance model chosen; or (iii) the test approximation.

GLUMIP 2.0: 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.