Robust tests for multivariate repeated measures with small samples.

Multivariate repeated measures data naturally arise in clinical trials and other fields such as biomedical science, public health, agriculture, social science and so on. For data of this type, the classical approach is to conduct multivariate analysis of variance (MANOVA) based on Wilks' Lambda and other multivariate statistics, which require the assumptions of multivariate normality and homogeneity of within-cell covariance matrices. However, data being analyzed nowadays show marked departure from multivariate normality and homogeneity. This paper proposes a finite-sample test by modifying the sums of squares matrices to make them insensitive to the heterogeneity in MANOVA. The proposed test is invariant to affine transformation and robust against nonnormality. The proposed method can be used in various experimental designs, for example, factorial design and crossover design. Under various simulation settings, the proposed method outperforms the classical Doubly Multivariate Model and Multivariate Mixed Model proposed elsewhere, especially for unbalanced sample sizes with heteroscedasticity. The applications of the proposed method are illustrated with ophthalmology data in factorial and crossover designs. The proposed method successfully identified and validated a significant main effect and demonstrated that univariate analysis could be oversensitive to small but clinically unimportant interactions.

Multivariate nonparametric methods in two-way balanced designs: performances and limitations in small samples.

Investigations of multivariate population are pretty common in applied researches, and the two-way crossed factorial design is a common design used at the exploratory phase in industrial applications. When assumptions such as multivariate normality and covariance homogeneity are violated, the conventional wisdom is to resort to nonparametric tests for hypotheses testing. In this paper we compare the performances, and in particular the power, of some nonparametric and semi-parametric methods that have been developed in recent years. Specifically, we examined resampling methods and robust versions of classical multivariate analysis of variance (MANOVA) tests. In a simulation study, we generate data sets with different configurations of factor's effect, number of replicates, number of response variables under null hypothesis, and number of response variables under alternative hypothesis. The objective is to elicit practical advice and guides to practitioners regarding the sensitivity of the tests in the various configurations, the tradeoff between power and type I error, the strategic impact of increasing number of response variables, and the favourable performance of one test when the alternative is sparse. A real case study from an industrial engineering experiment in thermoformed packaging production is used to compare and illustrate the application of the various methods.

Estimation of multivariate treatment effects in contaminated clinical trials.

The paper addresses estimating and testing treatment effects with multivariate outcomes in clinical trials where imperfect diagnostic devices are used to assign subjects to treatment groups. The paper focuses on the pre-post design and proposes two novel methods for estimating and testing treatment effects. In addition, methods for sample size and power calculations are developed. The methods are compared with each other and with a traditional method in a simulation study. The new methods show significant advantages in terms of power, coverage probability, and required sample size. The application of the methods is illustrated with data from electroencephalogram (EEG) recordings of alcoholic and control subjects.

A Roadmap for Building Data Science Capacity for Health Discovery and Innovation in Africa.

Technological advances now make it possible to generate diverse, complex and varying sizes of data in a wide range of applications from business to engineering to medicine. In the health sciences, in particular, data are being produced at an unprecedented rate across the full spectrum of scientific inquiry spanning basic biology, clinical medicine, public health and health care systems. Leveraging these data can accelerate scientific advances, health discovery and innovations. However, data are just the raw material required to generate new knowledge, not knowledge on its own, as a pile of bricks would not be mistaken for a building. In order to solve complex scientific problems, appropriate methods, tools and technologies must be integrated with domain knowledge expertise to generate and analyze big data. This integrated interdisciplinary approach is what has become to be widely known as data science. Although the discipline of data science has been rapidly evolving over the past couple of decades in resource-rich countries, the situation is bleak in resource-limited settings such as most countries in Africa primarily due to lack of well-trained data scientists. In this paper, we highlight a roadmap for building capacity in health data science in Africa to help spur health discovery and innovation, and propose a sustainable potential solution consisting of three key activities: a graduate-level training, faculty development, and stakeholder engagement. We also outline potential challenges and mitigating strategies.

The nonparametric Behrens-Fisher problem in partially complete clustered data.

In randomized trials or observational studies involving clustered units, the assumption of independence within clusters is not practical. Existing parametric or semiparametric methods assume specific dependence structures within a cluster. Furthermore, parametric model assumptions may not even be realistic when data are measured in a nonmetric scale as commonly happens, for example, in quality-of-life outcomes. In this paper, nonparametric effect-size measures for clustered data that allow meaningful and interpretable probabilistic comparisons of treatments or intervention programs will be introduced. The dependence among observations within a cluster can be arbitrary. Point estimators along with their asymptotic properties for computing confidence intervals and performing hypothesis test will be discussed. Small sample approximations that retain some of the optimal asymptotic behaviors will be presented. In our setup, some clusters may involve observations coming from both intervention groups (referred to as complete clusters), while others may contain observations from one group only (referred to as incomplete clusters). In deriving the asymptotic theories, we do not impose any relation in the rate of divergence of the numbers of complete and incomplete clusters. Simulations show favorable performance of the methods for arbitrary combinations of complete and incomplete clusters. The developed nonparametric methods are illustrated using data from a randomized trial of indoor wood smoke reduction to improve asthma symptoms and a cluster-randomized trial for smoking cessation.

The nonparametric Behrens-Fisher problem with dependent replicates.

Purely nonparametric methods are developed for general two-sample problems in which each experimental unit may have an individual number of possibly correlated replicates. In particular, equality of the variances, or higher moments, of the distributions of the data is not assumed, even under the null hypothesis of no treatment effect. Thus, a solution for the so-called nonparametric Behrens-Fisher problem is proposed for such models. The methods are valid for metric, count, ordered categorical, and even dichotomous data in a unified way. Point estimators of the treatment effects as well as their asymptotic distributions will be studied in detail. For small sample sizes, the distributions of the proposed test statistics are approximated using Satterthwaite-Welch-type t-approximations. Extensive simulation studies show favorable performance of the new methods, in particular, in small sample size situations. A real data set illustrates the application of the proposed methods.

Randomized Trial of Interventions to Improve Childhood Asthma in Homes with Wood-burning Stoves.

BACKGROUND: Household air pollution due to biomass combustion for residential heating adversely affects vulnerable populations. Randomized controlled trials to improve indoor air quality in homes of children with asthma are limited, and no such studies have been conducted in homes using wood for heating. OBJECTIVES: Our aims were to test the hypothesis that household-level interventions, specifically improved-technology wood-burning appliances or air-filtration devices, would improve health measures, in particular Pediatric Asthma Quality of Life Questionnaire (PAQLQ) scores, relative to placebo, among children living with asthma in homes with wood-burning stoves. METHODS: A three-arm placebo-controlled randomized trial was conducted in homes with wood-burning stoves among children with asthma. Multiple preintervention and postintervention data included PAQLQ (primary outcome), peak expiratory flow (PEF) monitoring, diurnal peak flow variability (dPFV, an indicator of airway hyperreactivity) and indoor particulate matter (PM) PM2.5. RESULTS: Relative to placebo, neither the air filter nor the woodstove intervention showed improvement in quality-of-life measures. Among the secondary outcomes, dPFV showed a 4.1 percentage point decrease in variability [95% confidence interval (CI)=-7.8 to -0.4] for air-filtration use in comparison with placebo. The air-filter intervention showed a 67% (95% CI: 50% to 77%) reduction in indoor PM2.5, but no change was observed with the improved-technology woodstove intervention. CONCLUSIONS: Among children with asthma and chronic exposure to woodsmoke, an air-filter intervention that improved indoor air quality did not affect quality-of-life measures. Intent-to-treat analysis did show an improvement in the secondary measure of dPFV. TRIAL REGISTRATION: ClincialTrials.gov NCT00807183. https://doi.org/10.1289/EHP849.

High-dimensional repeated measures.

Recently, new tests for main and simple treatment effects, time effects, and treatment by time interactions in possibly high-dimensional multigroup repeated-measures designs with unequal covariance matrices have been proposed. Technical details for using more than one between-subject and more than one within-subject factor are presented in this article. Furthermore, application to electroencephalography (EEG) data of a neurological study with two whole-plot factors (diagnosis and sex) and two subplot factors (variable and region) is shown with the R package HRM (high-dimensional repeated measures).

Task-induced Changes in Idiopathic Infantile Nystagmus Vary with Gaze.

PURPOSE: Investigations of infantile nystagmus syndrome (INS) at center or at the null position have reported that INS worsens when visual demand is combined with internal states, e.g. stress. Visual function and INS parameters such as foveation time, frequency, amplitude, and intensity can also be influenced by gaze position. We hypothesized that increases from baseline in visual demand and mental load would affect INS parameters at the null position differently than at other gaze positions. METHODS: Eleven participants with idiopathic INS were asked to determine the direction of Tumbling-E targets, whose visual demand was varied through changes in size and contrast, using a staircase procedure. Targets appeared between ±25° in 5° steps. The task was repeated with both mental arithmetic and time restriction to impose higher mental load, confirmed through subjective ratings and concurrent physiological measurements. RESULTS: Within-subject comparisons were limited to the null and 15° away from it. No significant main effects of task on any INS parameters were found. At both locations, high mental load worsened task performance metrics, i.e. lowest contrast (P = .001) and smallest optotype size reached (P = .012). There was a significant interaction between mental load and gaze position for foveation time (P = .02) and for the smallest optotype reached (P = .028). The increase in threshold optotype size from the low to high mental load was greater at the null than away from it. During high visual demand, foveation time significantly decreased from baseline at the null as compared to away from it (mean difference ± SE: 14.19 ± 0.7 msec; P = .010). CONCLUSIONS: Under high visual demand, the effects of increased mental load on foveation time and visual task performance differed at the null as compared to 15° away from it. Assessment of these effects could be valuable when evaluating INS clinically and when considering its impact on patients' daily activities.

Inference for low- and high-dimensional multigroup repeated measures designs with unequal covariance matrices.

We propose tests for main and simple treatment effects, time effects, as well as treatment by time interactions in possibly high-dimensional multigroup repeated measures designs. The proposed inference procedures extend the work by Brunner et al. (2012) from two to several treatment groups and remain valid for unbalanced data and under unequal covariance matrices. In addition to showing consistency when sample size and dimension tend to infinity at the same rate, we provide finite sample approximations and evaluate their performance in a simulation study, demonstrating better maintenance of the nominal α-level than the popular Box-Greenhouse-Geisser and Huynh-Feldt methods, and a gain in power for informatively increasing dimension. Application is illustrated using electroencephalography (EEG) data from a neurological study involving patients with Alzheimer's disease and other cognitive impairments.

High-Dimensional Multivariate Repeated Measures Analysis with Unequal Covariance Matrices.

In this paper, test statistics for repeated measures design are introduced when the dimension is large. By large dimension is meant the number of repeated measures and the total sample size grow together but either one could be larger than the other. Asymptotic distribution of the statistics are derived for the equal as well as unequal covariance cases in the balanced as well as unbalanced cases. The asymptotic framework considered requires proportional growth of the sample sizes and the dimension of the repeated measures in the unequal covariance case. In the equal covariance case, one can grow at much faster rate than the other. The derivations of the asymptotic distributions mimic that of Central Limit Theorem with some important peculiarities addressed with sufficient rigor. Consistent and unbiased estimators of the asymptotic variances, which make efficient use of all the observations, are also derived. Simulation study provides favorable evidence for the accuracy of the asymptotic approximation under the null hypothesis. Power simulations have shown that the new methods have comparable power with a popular method known to work well in low-dimensional situation but the new methods have shown enormous advantage when the dimension is large. Data from Electroencephalograph (EEG) experiment is analyzed to illustrate the application of the results.

Health risk perceptions predict smoking-related outcomes in Greek college students.

Health risk perception in smoking behavior was prospectively evaluated in a cluster-randomized trial for smoking cessation in Greek college students. Perceived Vulnerability (PV), Precaution Effectiveness, Optimistic Bias, and smoking behavior measures (quit attempts and cessation) were assessed in college-aged Greek student smokers at baseline, end of treatment (3 months), and follow-up (6 months). Using generalized estimating equations, baseline risk perception variables and change in risk perception variables between baseline and end of treatment were examined as predictors of the dichotomous smoking outcome variables. Results revealed that higher baseline PV [OR = 1.42 (1.21, 1.68)] predicted a greater likelihood of a quit attempt (n = 267). An increased likelihood of cessation [OR = 1.41 (1.15, 1.72)] was also predicted by an increase in PV from baseline to end of treatment (n = 243). Overall results suggested that PV was the strongest predictor of smoking behavior change, supporting further examination of health risk perceptions in promoting smoking cessation among Greek college smokers.

Accurate mean comparisons for paired samples with missing data: an application to a smoking-cessation trial.

In this paper, we consider mean comparisons for paired samples in which a certain portion of the observations are missing. This type of data commonly arises in medical researches where the outcomes are assessed at two time points after the application of treatments. New methods for statistical inference are proposed by making finiteness correction based on asymptotic expansions of some intuitive statistics. The comparison methods naturally extend to the two-group case after some suitable manipulations. Simulation study is carried out to demonstrate the numerical accuracy of the proposed methods. Data from a smoking-cessation trial are used to illustrate the application of the methods.

Mood management intervention for college smokers with elevated depressive symptoms: a pilot study.

OBJECTIVE: This pilot study examined smoking reduction and cessation among college smokers with elevated depressive symptomatology participating in a group-based behavioral counseling, mood management, and motivational enhancement combined intervention (CBT). PARTICIPANTS AND METHODS: Fifty-eight smokers (smoked 6 days in the past 30) were randomized to 6 sessions of CBT (n = 29) or a nutrition-focused attention-matched control group (CG; n = 29). RESULTS: Relative to CG participants, significantly more CBT participants reduced smoking intensity by 50% (χ(2)[1, N = 58] = 4.86, p = .028) at end of treatment. Although CBT participants maintained smoking reductions at 3- and 6-month follow-up, group differences were no longer significant. No group differences in cessation emerged. Finally, participants in both groups evidenced increased motivation to reduce smoking at end of treatment (F[1, 44] = 11.717, p = .001, η(p)(2) = .207). CONCLUSIONS: Findings demonstrate the utility of this intervention for smoking reduction and maintenance of reductions over time among a population of college students with elevated depressive symptomatology.

Gene set analysis for longitudinal gene expression data.

BACKGROUND: Gene set analysis (GSA) has become a successful tool to interpret gene expression profiles in terms of biological functions, molecular pathways, or genomic locations. GSA performs statistical tests for independent microarray samples at the level of gene sets rather than individual genes. Nowadays, an increasing number of microarray studies are conducted to explore the dynamic changes of gene expression in a variety of species and biological scenarios. In these longitudinal studies, gene expression is repeatedly measured over time such that a GSA needs to take into account the within-gene correlations in addition to possible between-gene correlations. RESULTS: We provide a robust nonparametric approach to compare the expressions of longitudinally measured sets of genes under multiple treatments or experimental conditions. The limiting distributions of our statistics are derived when the number of genes goes to infinity while the number of replications can be small. When the number of genes in a gene set is small, we recommend permutation tests based on our nonparametric test statistics to achieve reliable type I error and better power while incorporating unknown correlations between and within-genes. Simulation results demonstrate that the proposed method has a greater power than other methods for various data distributions and heteroscedastic correlation structures. This method was used for an IL-2 stimulation study and significantly altered gene sets were identified. CONCLUSIONS: The simulation study and the real data application showed that the proposed gene set analysis provides a promising tool for longitudinal microarray analysis. R scripts for simulating longitudinal data and calculating the nonparametric statistics are posted on the North Dakota INBRE website http://ndinbre.org/programs/bioinformatics.php. Raw microarray data is available in Gene Expression Omnibus (National Center for Biotechnology Information) with accession number GSE6085.

Analysis of smoking patterns and contexts among college student smokers.

Many who smoke in college do so infrequently and smoking conditions are not well understood. We examined smoking patterns among college fraternity and sorority members (N = 207) from a Midwestern university in three successive fall semesters in 2006-2008. Participants completed calendar-assisted retrospective assessments of 30-day smoking at up to five assessment points over 96 days. Overall smoking rates declined over the course of each semester and higher smoking on weekends was observed, with more variability among daily smokers. The most frequent categories of events to cue recall of smoking were socializing, work, and school. Findings can be used to target prevention efforts.

Enforcing an outdoor smoking ban on a college campus: effects of a multicomponent approach.

OBJECTIVES: Data on effective strategies to enforce policies banning outdoor smoking are sparse. This study tested the effects of an enforcement package implemented on a college campus. PARTICIPANTS: Thirty-nine observers recorded compliance of 709 outside smokers. METHODS: Smoking within 25 feet of buildings was noncompliant. The intervention included moving receptacles, marking the ground, improving signage, and distributing reinforcements and reminder cards. RESULTS: The proportion of smokers complying with the ban was 33% during the baseline observation period, increased to 74% during the intervention week, and was at 54% during the follow-up. Differences across conditions was statistically significant (chi2(2, N = 709) = 6.299, p <.001). Compliance proportions varied by location in all conditions. CONCLUSIONS: Enforcing an outdoor smoking ban using a multiple component package increased compliance with the nonsmoking policy on a college campus.

Some contributions to the analysis of multivariate data.

In this paper, we provide an overview of recently developed methods for the analysis of multivariate data that do not necessarily emanate from a normal universe. Multivariate data occur naturally in the life sciences and in other research fields. When drawing inference, it is generally recommended to take the multivariate nature of the data into account, and not merely analyze each variable separately. Furthermore, it is often of major interest to select an appropriate set of important variables. We present contributions in three different, but closely related, research areas: first, a general approach to the comparison of mean vectors, which allows for profile analysis and tests of dimensionality; second, non-parametric and parametric methods for the comparison of independent samples of multivariate observations; and third, methods for the situation where the experimental units are observed repeatedly, for example, over time, and the main focus is on analyzing different time profiles when the number p of repeated observations per subject is larger than the number n of subjects.

Examination of a brief Smoking Consequences Questionnaire for college students.

This study examined the factor structure of a brief version of the Smoking Consequences Questionnaire-Adult (SCQ-A) among 315 college freshman and sophomore smokers. A comparison of results from two confirmatory factor analyses demonstrated that a nine-factor model provided superior fit to a four-factor model. Furthermore, results revealed a lack of factorial invariance of factor loadings for daily and nondaily smokers, and of latent mean structures for smoking category and gender. In addition, concurrent validity tests demonstrated that positive expectancies increased with smoking rate and nicotine dependence. These results and their implications are discussed.