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Early infancy from at-birth to 3 years is critical for cognitive, emotional and social development of infants. During this period, infant's developmental tempo and outcomes are potentially impacted by in utero exposure to endocrine disrupting compounds (EDCs), such as bisphenol A (BPA) and phthalates. We investigate effects of ten ubiquitous EDCs on the infant growth dynamics of body mass index (BMI) in a birth cohort study.Modeling growth acceleration is proposed to understand the "force of growth" through a class of semiparametric stochastic velocity models. The great flexibility of such a dynamic model enables us to capture subject-specific dynamics of growth trajectories and to assess effects of the EDCs on potential delay of growth. We adopted a Bayesian method with the Ornstein-Uhlenbeck process as the prior for the growth rate function, in which the World Health Organization global infant's growth curves were integrated into our analysis. We found that BPA and most of phthalates exposed during the first trimester of pregnancy were inversely associated with BMI growth acceleration, resulting in a delayed achievement of infant BMI peak. Such early growth deficiency has been reported as a profound impact on health outcomes in puberty (e.g., timing of sexual maturation) and adulthood.

Kidney paired donation is a partial solution to overcoming biological incompatibility preventing kidney transplants. A kidney paired donation (KPD) program consists of altruistic or non-directed donors (NDDs) and pairs, each of which comprises a candidate in need of a kidney transplant and her/his willing but incompatible donor. Potential transplants from NDDs or donors in pairs to compatible candidates in other pairs are determined by computer assessment, though various situations involving either the donor, candidate, or proposed transplant may lead to a potential transplant failing to proceed. A KPD program can be viewed as a directed graph with NDDs and pairs as vertices and potential transplants as edges, where failure probabilities are associated with each vertex and edge. Transplants are carried out in the form of directed cycles among pairs and directed paths initiated by NDDs, which we refer to respectively as cycles and chains. Previous research shows that selecting disjoint subgraphs with a view to creating fallback options when failures occur generates more realized transplants than optimal selection of disjoint chains and cycles. In this paper, we define such subgraphs, which are called locally relevant (LR) subgraphs, and present an efficient algorithm to enumerate all LR subgraphs. Its computational efficiency is significantly better than the previous, more restrictive, algorithms.

Objectives: (1) Examine associations of a branched-chain amino acid (BCAA) metabolite pattern with metabolic risk across adolescence; (2) use Least Absolute Shrinkage and Selection Operator (LASSO) to identify novel metabolites of metabolic risk., Methods: We used linear regression to examine associations of a BCAA score with change (∆) in metabolic biomarkers over 5-year follow-up in 179 adolescents 8-14 years at baseline. Next, we applied LASSO, a regularized regression technique well suited for reduction of high-dimensional data, to identify metabolite predictors of ∆biomarkers., Results: In boys, the BCAA score corresponded with decreasing C-peptide, C-peptide-based insulin resistance (CP-IR), total cholesterol (TC), and low-density-lipoprotein cholesterol (LDL). In pubertal girls, the BCAA pattern corresponded with increasing C-peptide and leptin. LASSO identified asparagine as a predictor of decreasing C-peptide (β = -0.33) and CP-IR (β = -0.012), and acetyl-carnitine (β = 2.098), 4-hydroxyproline (β = -0.050), ornithine (β = -0.353), and α-aminoisobutyric acid (β = -0.793) as determinants of TC in boys. In girls, histidine was a negative determinant of TC (β = -0.033)., Conclusions: The BCAA pattern was associated with ∆glycemia and ∆lipids in a sex-specific manner. LASSO identified asparagine, which influences growth hormone secretion, as a determinant of decreasing C-peptide and CP-IR in boys, and metabolites on lipid metabolism pathways as determinants of decreasing cholesterol in both sexes.

Objective: To assess whether adiposity measures differed according to joint categories of sleep duration and sleep variability in a sample of Mexican adolescents., Study Design: A sample of 528 Mexico City adolescents aged 9-17 years wore wrist actigraphs for 6-7 days. Average sleep duration was categorized as age-specific sufficient or insufficient. Sleep variability, the standard deviation of sleep duration, was split at the median into stable versus variable. Adiposity measures-body mass index (BMI)-for-age Z score (BMIz), triceps skinfolds, waist circumference, and percent body fat-were collected by trained assistants. We regressed adiposity measures on combined sleep duration and variability categories. Log binomial models were used to estimate prevalence ratios and 95% CI for obesity (>2 BMIz) by joint categories of sleep duration and variability, adjusting for sex, age, and maternal education., Results: Approximately 40% of the adolescents had insufficient sleep and 13% were obese. Relative to sufficient-stable sleepers, adolescents with insufficient-stable sleep had higher adiposity across all 4 measures (eg, adjusted difference in BMIz was 0.68; 95% CI, 0.35-1.00) and higher obesity prevalence (prevalence ratio, 2.54; 95% CI, 1.36-4.75). Insufficient-variable sleepers had slightly higher BMIz than sufficient-stable sleepers (adjusted difference, 0.30; 95% CI, 0.00-0.59)., Conclusions: Adolescents with consistently insufficient sleep could be at greater risk for obesity. The finding that insufficient-variable sleepers had only slightly higher adiposity suggests that opportunities for "catch-up" sleep may be protective., (Copyright © 2018 Elsevier Inc. All rights reserved.)

In kidney paired donation (KPD), incompatible donor-candidate pairs and non-directed (also known as altruistic) donors are pooled together with the aim of maximizing the total utility of transplants realized via donor exchanges. We consider a setting in which disjoint sets of potential transplants are selected at regular intervals, with fallback options available within each proposed set in the case of individual donor, candidate or match failure. We develop methods for calculating the expected utility for such sets under a realistic probability model for the KPD. Exact expected utility calculations for these sets are compared to estimates based on Monte Carlo samples of the underlying network. Models and methods are extended to include transplant candidates who join KPD with more than one incompatible donor. Microsimulations demonstrate the superiority of accounting for failure probability and fallback options, as well as candidates joining with additional donors, in terms of realized transplants and waiting time for candidates.

Background: Older adults have high rates of asthma morbidity and mortality. Asthma is now recognized as a heterogeneous disease, yet the distinct phenotypes among older adults are unknown., Objective: The objective of this study was to identify asthma phenotypes in a diverse population of elderly patients with asthma., Methods: Using cluster analysis, 180 older adults with persistent asthma were analyzed. Subjects completed detailed questionnaires, skin prick testing, and spirometry with reversibility. Twenty-four core variables were analyzed., Results: Four groups were identified. Subjects in cluster 1 (n = 69) typically had asthma diagnosed after the age of 40 and the shortest duration of asthma. Cluster 2 (n = 40) had the mildest asthma defined by spirometry, Asthma Control test (ACT), and Asthma Quality of Life Questionnaire (AQLQ). They also had the lowest body mass index (BMI), lowest depression score, and least number of comorbidities. Cluster 3 (n = 46) had the longest duration of asthma (56 years) and the highest atopic skin test sensitization (74%). Cluster 4 (n = 25) had the most severe asthma, with extremely low FEV 1 % predicted (37.8%), lowest ACT, and lowest AQLQ scores. They were more likely to be black and had the highest comorbidities. Using BMI, posttreatment FEV 1 % predicted, and duration of asthma, 95.6% of subjects were able to be correctly classified., Conclusions: In older adults with asthma, distinct phenotypes vary on key features that are more pronounced among the elderly, including comorbidities, fixed airway obstruction, and duration of asthma ≥40 years. Further work is required to determine the clinical and therapeutic implications for different asthma phenotypes in older adults., (Copyright © 2017 American Academy of Allergy, Asthma & Immunology. Published by Elsevier Inc. All rights reserved.)

While there is a growing need for kidney transplants to treat end stage kidney disease, the supply of transplantable kidneys is in serious shortage. Kidney paired donation (KPD) programs serve as platforms for candidates with willing but incompatible donors to assess the possibility of exchanging donors, thus opening up new transplant opportunities for these candidates. In recent years, non-directed (or altruistic) donors (NDDs) have been incorporated into KPD programs beginning chains of transplants that benefit many candidates. In such programs, making optimal decisions in transplant exchange selection is of critical importance. With the aim of improving the selection of chains beginning with an NDD, this paper introduces a look-ahead multiple decision strategy to select chains, that are easy to extend in the future. Simulation studies are adopted to assess performance of this strategy. Taking into account the extensibility of chains increases the number of realized transplants.

Identifying novel biomarkers to predict renal graft survival is important in post-transplant clinical practice. Serum creatinine, currently the most popular surrogate biomarker, offers limited information of the underlying allograft profiles. It is known to perform unsatisfactorily to predict renal function. In this paper, we apply a LASSO machine-learning algorithm in the Cox proportional hazards model to identify promising proteins that are associated with the hazard of allograft loss after renal transplantation, motivated by a clinical pilot study that collected 47 patients receiving renal transplants at the University of Michigan Hospital. We assess the association of 17 proteins previously identified by Cibrik et al. [5] with allograft rejection in our regularized Cox regression analysis, where the LASSO variable selection method is applied to select important proteins that predict the hazard of allograft loss. We also develop a post-selection inference to further investigate the statistical significance of the proteins on the hazard of allograft loss, and conclude that two proteins KIM-1 and VEGF-R2 are important protein markers for risk prediction.

Objective: The goal of this study was to identify metabolites associated with metabolic risk, separately by sex, in Mexican adolescents., Methods: Untargeted metabolomic profiling was carried out on fasting serum of 238 youth aged 8 to 14 years, and metabolites associated with a metabolic syndrome risk z-score (MetRisk z-score) were identified separately for boys and girls, using the simulation and extrapolation algorithm. Associations of each metabolite with MetRisk z-score were examined using linear regression models that accounted for maternal education, child's age, and pubertal status., Results: Of the 938 features identified in metabolomics analysis, 7 named compounds (of 27 identified metabolites) were associated with MetRisk z-score in girls, and 3 named compounds (of 14 identified) were associated with MetRisk z-score in boys. In girls, diacylglycerol (DG) 16:0/16:0, 1,3-dielaidin, myo-inositol, and urate corresponded with higher MetRisk z-score, whereas N-acetylglycine, thymine, and dodecenedioic acid were associated with lower MetRisk z-score. For example, each z-score increment in DG 16:0/16:0 corresponded with 0.60 (95% CI: 0.47-0.74) units higher MetRisk z-score. In boys, positive associations of DG 16:0/16:0, tyrosine, and 5'-methylthioadenosine with MetRisk z-score were found., Conclusions: Metabolites on lipid, amino acid, and carbohydrate metabolism pathways are associated with metabolic risk in girls. Compounds on lipid and DNA pathways correspond with metabolic risk in boys., (© 2017 The Obesity Society.)

Background: Few interventions have focused on the difficulties that African American women face when managing asthma., Objective: To evaluate a telephone-based self-regulation intervention that emphasized African American women's management of asthma in a series of 6 sessions., Methods: A total of 422 African American women with persistent asthma were randomly assigned to either an intervention or control group receiving usual care. Behavioral factors, symptoms and asthma control, asthma-related quality of life, and health care use at baseline and 2 years after baseline were assessed. Generalized estimating equations were used to assess the long-term effect of the intervention on outcomes., Results: Compared with the control group, those who completed the full intervention (6 sessions) had significant gains in self-regulation of their asthma (B estimate, 0.73; 95% CI, 0.17-1.30; P < .01), noticing changes to their asthma during their menstrual cycle (B estimate, 1.42; 95% CI, 0.69-2.15; P < .001), and when having premenstrual syndrome (B estimate, 1.70; 95% CI, 0.67-2.72; P < .001). They also had significant reductions in daytime symptoms (B estimate, -0.15; 95% CI, -0.27 to -0.03; P < .01), asthma-related hospitalization (B estimate, 0.51; 95% CI, 0.00-1.02; P < .05), and improved asthma control (B estimate, 1.34; 95% CI, 0.57-2.12; P < .001). However, neither grouped changed over time in outcomes., Conclusion: Despite high comorbidity, African American women who completed a culturally responsive self-management program had improvements in asthma outcomes compared with the control group. Future work should address significant comorbidities and psychosocial issues alongside asthma management to improve asthma outcomes in the long term., Trial Registration: clinicaltrials.gov Identifier NCT01117805., (Copyright © 2016 American College of Allergy, Asthma & Immunology. Published by Elsevier Inc. All rights reserved.)

Background: Cadmium is a toxic metal with modifiable exposure sources including diet. In pregnant women and children, unique dietary habits may contribute to DCd, and the relationship of diet to overall cadmium exposure can depend on specific factors during these transitional time periods., Objectives: This study aimed to identify and quantify food sources of DCd, describe the distribution of UCd, and determine the relationship of DCd and intake of specific foods with UCd, stratified by maternal smoking history, among pregnant women and children in a well-characterized Mexico City birth cohort., Methods: Our sample included 192 pregnant women (third trimester) and 223 children (7-15years). DCd was calculated using FFQ and the U.S. TDS. We also measured UCd, maternal history of smoking, and additional covariates., Results: Pregnant women and children had geometric mean UCd concentrations of 0.19±0.78μg/L and 0.14±0.60μg/L, respectively. On average, estimated daily DCd intake was 9.3±3.5μg for women and 12.2±5.4μg for children. Adjusted linear regression models showed a positive association between DCd and UCd among women (p=0.03) and children (p=0.03) without a maternal history of smoking. Intake of fruit and vegetables among women and potato consumption among children were positively associated with UCd., Conclusions: Pregnant women and their children are exposed to cadmium at dietary and urinary levels similar to those previously reported. Higher estimated DCd for children than for women could be attributed to the different FFQs or related to dietary pattern changes between age groups. DCd contributed to UCd in those without a maternal smoking history., (Copyright © 2016 Elsevier B.V. All rights reserved.)

This paper concerns regression methodology for assessing relationships between multi-dimensional response variables and covariates that are correlated within a network. To address analytical challenges associated with the integration of network topology into the regression analysis, we propose a hybrid quadratic inference method that uses both prior and data-driven correlations among network nodes. A Godambe information-based tuning strategy is developed to allocate weights between the prior and data-driven network structures, so the estimator is efficient. The proposed method is conceptually simple and computationally fast, and has appealing large-sample properties. It is evaluated by simulation, and its application is illustrated using neuroimaging data from an association study of the effects of iron deficiency on auditory recognition memory in infants.

As data sets of related studies become more easily accessible, combining data sets of similar studies is often undertaken in practice to achieve a larger sample size and higher power. A major challenge arising from data integration pertains to data heterogeneity in terms of study population, study design, or study coordination. Ignoring such heterogeneity in data analysis may result in biased estimation and misleading inference. Traditional techniques of remedy to data heterogeneity include the use of interactions and random effects, which are inferior to achieving desirable statistical power or providing a meaningful interpretation, especially when a large number of smaller data sets are combined. In this paper, we propose a regularized fusion method that allows us to identify and merge inter-study homogeneous parameter clusters in regression analysis, without the use of hypothesis testing approach. Using the fused lasso, we establish a computationally efficient procedure to deal with large-scale integrated data. Incorporating the estimated parameter ordering in the fused lasso facilitates computing speed with no loss of statistical power. We conduct extensive simulation studies and provide an application example to demonstrate the performance of the new method with a comparison to the conventional methods.

Merging multiple datasets collected from studies with identical or similar scientific objectives is often undertaken in practice to increase statistical power. This article concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics, such as different follow-up schedules and study-specific missing covariates (e.g., covariates observed in some studies but missing in other studies). The presence of study-specific missing covariates presents great statistical methodology challenge in data merging and analysis. We propose a joint estimating function approach to addressing this challenge, in which a novel nonparametric estimating function constructed via splines-based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates. Under mild regularity conditions, we show that the proposed estimator is consistent and asymptotically normal. We evaluate finite-sample performances of the proposed method through simulation studies. In comparison to the conventional multiple imputation approach, our method exhibits smaller estimation bias. We provide an illustrative data analysis using longitudinal cohorts collected in Mexico City to assess the effect of lead exposures on children's somatic growth., (© 2015, The International Biometric Society.)

Injury resulting from motor vehicle crashes is the leading cause of death among teenagers in the US. Few programs or policies have been found to be effective in reducing the risk of fatal car crashes for young novice drivers. One effective policy that has been widely implemented is Graduated Driver Licensing (GDL). Published articles have mostly reported on the temporal effectiveness of GDL in the US. This article reports on the development of spatial statistical modeling approaches to evaluate and compare the effectiveness of GDL policy across eighty-three counties in the state of Michigan. Data were gathered from several publicly available databases, including the US Fatality Analysis Reporting System (FARS), US Census Bureau, US Bureau of Labor Statistics, and US Department of Agriculture. To account for spatial dependence among crash counts from adjacent counties we invoke spatial random effects, which we provide with a Conditionally AutoRegressive (CAR) prior. Our analysis confirms previous findings that GDL in Michigan is an effective policy that significantly reduces the risk of fatal car crashes among novice teenage drivers. In addition, it indicates that rurality is an important contextual variable associated with spatial differences in GDL effectiveness across the state of Michigan. Finally, our findings provide information that can be used to strengthen GDL policy and its implementation to further enhance teenage-driver safety., (Copyright © 2013 Elsevier Ltd. All rights reserved.)

In recent years, kidney paired donation (KPD) has been extended to include living non-directed or altruistic donors, in which an altruistic donor donates to the candidate of an incompatible donor-candidate pair with the understanding that the donor in that pair will further donate to the candidate of a second pair, and so on; such a process continues and thus forms an altruistic donor-initiated chain. In this paper, we propose a novel strategy to sequentially allocate the altruistic donor (or bridge donor) so as to maximize the expected utility; analogous to the way a computer plays chess, the idea is to evaluate different allocations for each altruistic donor (or bridge donor) by looking several moves ahead in a derived look-ahead search tree. Simulation studies are provided to illustrate and evaluate our proposed method.

Background: Older adults with asthma have worse quality of life, asthma control and increased health care utilization than do healthy peers. Factors that contribute to this are currently unknown., Objective: To identify demographic, psychological or physiologic characteristics associated with asthma quality of life, control and health care utilization in older adults., Methods: By using a cross-sectional design, subjects older than 65 years with a history of physician-diagnosed asthma were enrolled. Demographic, psychological and physiological characteristics (including spirometry, atopy testing and exhaled nitric oxide) were collected. Correlations between these factors and the mini Asthma Quality of Life Questionnaire, Asthma Control Questionnaire and health care utilization were assessed., Results: Seventy subjects were enrolled in the study, with a mean age of 73.3 years and mean duration of asthma diagnosis of 28.5 years. Higher depression screening scores and self-reported depression were strongly correlated with poorer quality of life and asthma control after controlling for confounding effects through a regression model. In addition, worse overall functional status was correlated with poorer asthma quality of life (P < .01), presence of atopy was associated with decreased health care utilization (P < .01) and subjects who lived alone were more likely to have unscheduled visits to a physician's office (P = .06)., Conclusions: Comorbid depression is strongly associated with poorer asthma quality of life and control in older adults. In addition, worse functional status and living alone may be associated with poorer outcomes. Screening for these conditions is important in the care of the elderly asthmatic population., (Copyright © 2013 American Academy of Allergy, Asthma & Immunology. Published by Elsevier Inc. All rights reserved.)

Objectives: To assess the relationship between season of birth and presence of asthma and allergy in preteen, low-income, African American children., Methods: The study consisted of a self-administered survey followed by telephone interviews of parents of children attending 19 middle schools in Detroit, Michigan. Out of 4194 children, 1292 were identified with asthma and 962 parents of these children provided informed consent and took part in telephone interviews., Results: No statistically significant relationships were observed between season of birth and diagnosis of asthma (p > .05) or with diagnosis adjusting for income, age, gender, parent's education, or parent being a smoker (p > .05). No statistically significant association was evident between season of birth and presence of allergy (p > .05) or with allergy adjusting for the above variables (p > .05)., Conclusions: Identifying children vulnerable to problems with asthma and allergy, especially in populations exhibiting high prevalence of the conditions and significant disparities in outcomes, requires use of all possible means. Season of birth does not appear to be a useful indicator in identification of such children. The findings from this study do not support the proposition that season of birth, associated with early exposure to viruses as evident in the winter and to seasonal allergens, contributes to more asthma and/or allergy.

In longitudinal biomedical studies, there is often interest in the rate functions, which describe the functional rates of change of biomarker profiles. This paper proposes a semiparametric approach to model these functions as the realizations of stochastic processes defined by stochastic differential equations. These processes are dependent on the covariates of interest and vary around a specified parametric function. An efficient Markov chain Monte Carlo algorithm is developed for inference. The proposed method is compared with several existing methods in terms of goodness-of-fit and more importantly the ability to forecast future functional data in a simulation study. The proposed methodology is applied to prostate-specific antigen profiles for illustration. Supplementary materials for this paper are available online.

In order to assist physicians and other health professionals for health care improvement, clinical decision support systems, through interactive computerized software, become very popular in clinical practice. The crisis associated with kidney organ shortage has triggered an innovative strategy, termed as Kidney Paired Donation (KPD) program, to address a rapidly expanding demand for donor kidneys. KPD program involves how to making optimal decision for allowing patients with incompatible living donors to receive compatible organs by best matching donors. Although some computerized optimization tools are being used in the current KPD program, there still lacks a general decision support system which enables us to evaluate and compare different kidney allocation strategies and effects of policy. In this paper, we discuss a general computer-based KPD decision model that appropriately reflects the real world clinical application. Also, the whole decision process is to be visualized by our Graphical User Interface (GUI) software, which offers a user friendly platform not only to provide a convenient interface for clinicians but also to assess different kidney exchange strategies of clinical importance.

Background: Living kidney donors (LKD) allow for increased access to lifesaving organs for transplantation. There is a relative paucity of African American (AA) live kidney donors. The prevalence of medical disease in LKD candidates has not been well studied. We examined the medical limitations to living kidney donation in a large Midwestern transplant center., Methods: A total of 2519 adults (age ≥ 18) evaluated as potential LKD (PD) between January 1, 1996 and June 30, 2006 were prospectively followed until evaluation outcome (completed live donation, medical exclusion from live donation, non-medical exclusion from live donation). Logistic regression was used to examine the effect of age on donor exclusion, and chi-square tests were used to compare the likelihood of donor exclusions between racial and gender groups., Results: Sixty percent of PD were female (n = 1300), and 86% were Caucasian (CA) (n = 1862). Overall, 48.7% of PD who underwent evaluation became LKD. The odds of donation were 52% lower in AA compared to CA (OR 0.48 p < 0.001). Among PD excluded from donation, the most common medical diagnoses were hypertension (HTN) (24.7%), inadequate creatinine clearance (10.6%) and a positive final crossmatch (10.5%). The rate of PD exclusion for obesity was twofold higher in AA compared to CA (12.8% vs. 5.8%, p < 0.001)., Conclusions: Hypertension in PD is equally significant barrier to living kidney donation in AA and CA whereas obesity is a greater barrier in AA., (© 2009 John Wiley & Sons A/S.)

This article presents a new class of nonnormal linear mixed models that provide an efficient estimation of subject-specific disease progression in the analysis of longitudinal data from the Modification of Diet in Renal Disease (MDRD) trial. This new analysis addresses the previously reported finding that the distribution of the random effect characterizing disease progression is negatively skewed. We assume a log-gamma distribution for the random effects and provide the maximum likelihood inference for the proposed nonnormal linear mixed model. We derive the predictive distribution of patient-specific disease progression rates, which demonstrates rather different individual progression profiles from those obtained from the normal linear mixed model analysis. To validate the adequacy of the log-gamma assumption versus the usual normality assumption for the random effects, we propose a lack-of-fit test that clearly indicates a better fit for the log-gamma modeling in the analysis of the MDRD data. The full maximum likelihood inference is also advantageous in dealing with the missing at random (MAR) type of dropouts encountered in the MDRD data.

Background: Numerous nonparametric approaches have been proposed in literature to detect differential gene expression in the setting of two user-defined groups. However, there is a lack of nonparametric procedures to analyze microarray data with multiple factors attributing to the gene expression. Furthermore, incorporating interaction effects in the analysis of microarray data has long been of great interest to biological scientists, little of which has been investigated in the nonparametric framework., Results: In this paper, we propose a set of nonparametric tests to detect treatment effects, clinical covariate effects, and interaction effects for multifactorial microarray data. When the distribution of expression data is skewed or heavy-tailed, the rank tests are substantially more powerful than the competing parametric F tests. On the other hand, in the case of light or medium-tailed distributions, the rank tests appear to be marginally less powerful than the parametric competitors., Conclusion: The proposed rank tests enable us to detect differential gene expression and establish interaction effects for microarray data with various non-normally distributed expression measurements across genome. In the presence of outliers, they are advantageous alternative approaches to the existing parametric F tests due to the robustness feature.