Joint Modeling of Gene-Environment Correlations and Interactions Using Polygenic Risk Scores in Case-Control Studies.

Polygenic risk scores (PRS) are rapidly emerging as a way to measure disease risk by aggregating multiple genetic variants. Understanding the interplay of PRS with environmental factors is critical for interpreting and applying PRS in a wide variety of settings. We develop an efficient method for simultaneously modeling gene-environment correlations and interactions using PRS in case control studies. We use a logistic-normal regression modeling framework to specify the disease risk and PRS distribution in the underlying population and propose joint inference across the two models using the retrospective likelihood of the case-control data. Extensive simulation studies demonstrate the flexibility of the method in trading-off bias and efficiency for the estimation of various model parameters compared to the standard logistic regression or a case-only analysis for gene-environment interactions, or a control-only analysis for gene-environment correlations. Finally using simulated case-control data sets within the UK Biobank study, we demonstrate the power of our method for its ability to recover results from the full prospective cohort for the detection of an interaction between long-term oral contraceptive use and PRS on the risk of breast cancer. This method is computationally efficient and implemented in a user-friendly R package.

Measurement error models with zero inflation and multiple sources of zeros, with applications to hard zeros.

We consider measurement error models for two variables observed repeatedly and subject to measurement error. One variable is continuous, while the other variable is a mixture of continuous and zero measurements. This second variable has two sources of zeros. The first source is episodic zeros, wherein some of the measurements for an individual may be zero and others positive. The second source is hard zeros, i.e., some individuals will always report zero. An example is the consumption of alcohol from alcoholic beverages: some individuals consume alcoholic beverages episodically, while others never consume alcoholic beverages. However, with a small number of repeat measurements from individuals, it is not possible to determine those who are episodic zeros and those who are hard zeros. We develop a new measurement error model for this problem, and use Bayesian methods to fit it. Simulations and data analyses are used to illustrate our methods. Extensions to parametric models and survival analysis are discussed briefly.

Methodological examination of the 2018 World Cancer Research Fund/American Institute for Cancer Research (WCRF/AICR) Score.

The objective of this study was to examine the impact of methodological changes to the 2018 World Cancer Research Fund/American Institute for Cancer Research (WCRF/AICR) Score on associations with risk for all-cause mortality, cancer mortality, and cancer risk jointly among older adults in the NIH-AARP Diet and Health Study. Weights were incorporated for each Score component; a continuous point scale was developed in place of the Score's fully discrete cut-points; and cut-point values were changed for physical activity and red meat based on evidence-based recommendations. Exploratory aims also examined the impact of separating components with more than one sub-component and whether all components were necessary to retain within this population utilizing a penalized scoring approach. Findings suggested weighting the original 2018 WCRF/AICR Score improved the score's predictive performance in association with all-cause mortality and provided more precise estimates in relation to cancer risk and mortality outcomes. The importance of healthy weight, physically activity, and plant-based foods in relation to cancer and overall mortality risk were highlighted in this population of older adults. Further studies are needed to better understand the consistency and generalizability of these findings across other populations.

Learning competing risks across multiple hospitals: one-shot distributed algorithms.

OBJECTIVES: To characterize the complex interplay between multiple clinical conditions in a time-to-event analysis framework using data from multiple hospitals, we developed two novel one-shot distributed algorithms for competing risk models (ODACoR). By applying our algorithms to the EHR data from eight national children's hospitals, we quantified the impacts of a wide range of risk factors on the risk of post-acute sequelae of SARS-COV-2 (PASC) among children and adolescents. MATERIALS AND METHODS: Our ODACoR algorithms are effectively executed due to their devised simplicity and communication efficiency. We evaluated our algorithms via extensive simulation studies as applications to quantification of the impacts of risk factors for PASC among children and adolescents using data from eight children's hospitals including the Children's Hospital of Philadelphia, Cincinnati Children's Hospital Medical Center, Children's Hospital of Colorado covering over 6.5 million pediatric patients. The accuracy of the estimation was assessed by comparing the results from our ODACoR algorithms with the estimators derived from the meta-analysis and the pooled data. RESULTS: The meta-analysis estimator showed a high relative bias (∼40%) when the clinical condition is relatively rare (∼0.5%), whereas ODACoR algorithms exhibited a substantially lower relative bias (∼0.2%). The estimated effects from our ODACoR algorithms were identical on par with the estimates from the pooled data, suggesting the high reliability of our federated learning algorithms. In contrast, the meta-analysis estimate failed to identify risk factors such as age, gender, chronic conditions history, and obesity, compared to the pooled data. DISCUSSION: Our proposed ODACoR algorithms are communication-efficient, highly accurate, and suitable to characterize the complex interplay between multiple clinical conditions. CONCLUSION: Our study demonstrates that our ODACoR algorithms are communication-efficient and can be widely applicable for analyzing multiple clinical conditions in a time-to-event analysis framework.

Can sodium and potassium measured in timed voids be used as reference instruments for validating self-report instruments? Results from a urine calibration study.

BACKGROUND: Sodium and potassium measured in 24-h urine collections are often used as reference measurements to validate self-reported dietary intake instruments. OBJECTIVES: To evaluate whether collection and analysis of a limited number of urine voids at specified times during the day ("timed voids") can provide alternative reference measurements, and to identify their optimal number and timing. METHODS: We used data from a urine calibration study among 441 adults aged 18-39 y. Participants collected each urine void in a separate container for 24 h and recorded the collection time. For the same day, they reported dietary intake using a 24-h recall. Urinary sodium and potassium were analyzed in a 24-h composite sample and in 4 timed voids (morning, afternoon, evening, and overnight). Linear regression models were used to develop equations predicting log-transformed 24-h urinary sodium or potassium levels using each of the 4 single timed voids, 6 pairs, and 4 triples. The equations also included age, sex, race, BMI (kg/m2), and log creatinine. Optimal combinations minimizing the mean squared prediction error were selected, and the observed and predicted 24-h levels were then used as reference measures to estimate the group bias and attenuation factors of the 24-h dietary recall. These estimates were compared. RESULTS: Optimal combinations found were as follows: single voids-evening; paired voids-afternoon + overnight (sodium) and morning + evening (potassium); and triple voids-morning + evening + overnight (sodium) and morning + afternoon + evening (potassium). Predicted 24-h urinary levels estimated 24-h recall group biases and attenuation factors without apparent bias, but with less precision than observed 24-h urinary levels. To recover lost precision, it was estimated that sample sizes need to be increased by ∼2.6-2.7 times for a single void, 1.7-2.1 times for paired voids, and 1.5-1.6 times for triple voids. CONCLUSIONS: Our results provide the basis for further development of new reference biomarkers based on timed voids. CLINICAL TRIAL REGISTRY: clinicaltrials.gov as NCT01631240.

One-shot distributed algorithms for addressing heterogeneity in competing risks data across clinical sites.

OBJECTIVE: To characterize the interplay between multiple medical conditions across sites and account for the heterogeneity in patient population characteristics across sites within a distributed research network, we develop a one-shot algorithm that can efficiently utilize summary-level data from various institutions. By applying our proposed algorithm to a large pediatric cohort across four national Children's hospitals, we replicated a recently published prospective cohort, the RISK study, and quantified the impact of the risk factors associated with the penetrating or stricturing behaviors of pediatric Crohn's disease (PCD). METHODS: In this study, we introduce the ODACoRH algorithm, a one-shot distributed algorithm designed for the competing risks model with heterogeneity. Our approach considers the variability in baseline hazard functions of multiple endpoints of interest across different sites. To accomplish this, we build a surrogate likelihood function by combining patient-level data from the local site with aggregated data from other external sites. We validated our method through extensive simulation studies and replication of the RISK study to investigate the impact of risk factors on the PCD for adolescents and children from four children's hospitals within the PEDSnet, A National Pediatric Learning Health System. To evaluate our ODACoRH algorithm, we compared results from the ODACoRH algorithms with those from meta-analysis as well as those derived from the pooled data. RESULTS: The ODACoRH algorithm had the smallest relative bias to the gold standard method (-0.2%), outperforming the meta-analysis method (-11.4%). In the PCD association study, the estimated subdistribution hazard ratios obtained through the ODACoRH algorithms are identical on par with the results derived from pooled data, which demonstrates the high reliability of our federated learning algorithms. From a clinical standpoint, the identified risk factors for PCD align well with the RISK study published in the Lancet in 2017 and other published studies, supporting the validity of our findings. CONCLUSION: With the ODACoRH algorithm, we demonstrate the capability of effectively integrating data from multiple sites in a decentralized data setting while accounting for between-site heterogeneity. Importantly, our study reveals several crucial clinical risk factors for PCD that merit further investigations.

Major Gaps in Understanding Dietary Supplement Use in Health and Disease.

Precise dietary assessment is critical for accurate exposure classification in nutritional research, typically aimed at understanding how diet relates to health. Dietary supplement (DS) use is widespread and represents a considerable source of nutrients. However, few studies have compared the best methods to measure DSs. Our literature review on the relative validity and reproducibility of DS instruments in the United States [e.g., product inventories, questionnaires, and 24-h dietary recalls (24HR)] identified five studies that examined validity (n = 5) and/or reproducibility (n = 4). No gold standard reference method exists for validating DS use; thus, each study's investigators chose the reference instrument used to measure validity. Self-administered questionnaires agreed well with 24HR and inventory methods when comparing the prevalence of commonly used DSs. The inventory method captured nutrient amounts more accurately than the other methods. Reproducibility (over 3 months to 2.4 years) of prevalence of use estimates on the questionnaires was acceptable for common DSs. Given the limited body of research on measurement error in DS assessment, only tentative conclusions on these DS instruments can be drawn at present. Further research is critical to advancing knowledge in DS assessment for research and monitoring purposes.

Baseline Gait and Motor Function Predict Long-Term Severity of Neurological Outcomes of Viral Infection.

Neurological dysfunction following viral infection varies among individuals, largely due to differences in their genetic backgrounds. Gait patterns, which can be evaluated using measures of coordination, balance, posture, muscle function, step-to-step variability, and other factors, are also influenced by genetic background. Accordingly, to some extent gait can be characteristic of an individual, even prior to changes in neurological function. Because neuromuscular aspects of gait are under a certain degree of genetic control, the hypothesis tested was that gait parameters could be predictive of neuromuscular dysfunction following viral infection. The Collaborative Cross (CC) mouse resource was utilized to model genetically diverse populations and the DigiGait treadmill system used to provide quantitative and objective measurements of 131 gait parameters in 142 mice from 23 CC and SJL/J strains. DigiGait measurements were taken prior to infection with the neurotropic virus Theiler's Murine Encephalomyelitis Virus (TMEV). Neurological phenotypes were recorded over 90 days post-infection (d.p.i.), and the cumulative frequency of the observation of these phenotypes was statistically associated with discrete baseline DigiGait measurements. These associations represented spatial and postural aspects of gait influenced by the 90 d.p.i. phenotype score. Furthermore, associations were found between these gait parameters with sex and outcomes considered to show resistance, resilience, or susceptibility to severe neurological symptoms after long-term infection. For example, higher pre-infection measurement values for the Paw Drag parameter corresponded with greater disease severity at 90 d.p.i. Quantitative trait loci significantly associated with these DigiGait parameters revealed potential relationships between 28 differentially expressed genes (DEGs) and different aspects of gait influenced by viral infection. Thus, these potential candidate genes and genetic variations may be predictive of long-term neurological dysfunction. Overall, these findings demonstrate the predictive/prognostic value of quantitative and objective pre-infection DigiGait measurements for viral-induced neuromuscular dysfunction.

Joint Modeling of Gene-Environment Correlations and Interactions using Polygenic Risk Scores in Case-Control Studies.

Polygenic risk scores (PRS) are rapidly emerging as aggregated measures of disease-risk associated with many genetic variants. Understanding the interplay of PRS with environmental factors is critical for interpreting and applying PRS in a wide variety of settings. We develop an efficient method for simultaneously modeling gene-environment correlations and interactions using PRS in case-control studies. We use a logistic-normal regression modeling framework to specify the disease risk and PRS distribution in the underlying population and propose joint inference across the two models using the retrospective likelihood of the case-control data. Extensive simulation studies demonstrate the flexibility of the method in trading-off bias and efficiency for the estimation of various model parameters compared to the standard logistic regression or a case-only analysis for gene-environment interactions, or a control-only analysis for gene-environment correlations. Finally, using simulated case-control datasets within the UK Biobank study, we demonstrate the power of the proposed method for its ability to recover results from the full prospective cohort for the detection of an interaction between long-term oral contraceptive use and PRS on the risk of breast cancer. This method is computationally efficient and implemented in a user-friendly R package.

A robust approach for electronic health record-based case-control studies with contaminated case pools.

We consider analyses of case-control studies assembled from electronic health records (EHRs) where the pool of cases is contaminated by patients who are ineligible for the study. These ineligible patients, referred to as "false cases," should be excluded from the analyses if known. However, the true outcome status of a patient in the case pool is unknown except in a subset whose size may be arbitrarily small compared to the entire pool. To effectively remove the influence of the false cases on estimating odds ratio parameters defined by a working association model of the logistic form, we propose a general strategy to adaptively impute the unknown case status without requiring a correct phenotyping model to help discern the true and false case statuses. Our method estimates the target parameters as the solution to a set of unbiased estimating equations constructed using all available data. It outperforms existing methods by achieving robustness to mismodeling the relationship between the outcome status and covariates of interest, as well as improved estimation efficiency. We further show that our estimator is root-n-consistent and asymptotically normal. Through extensive simulation studies and analysis of real EHR data, we demonstrate that our method has desirable robustness to possible misspecification of both the association and phenotyping models, along with statistical efficiency superior to the competitors.

Trends in Overall and Micronutrient-Containing Dietary Supplement Use in US Adults and Children, NHANES 2007-2018.

BACKGROUND: Dietary supplement (DS) use is widespread in the United States and contributes large amounts of micronutrients to users. Most studies have relied on data from 1 assessment method to characterize the prevalence of DS use. Combining multiple methods enhances the ability to capture nutrient exposures from DSs and examine trends over time. OBJECTIVES: The objective of this study was to characterize DS use and examine trends in any DS as well as micronutrient-containing (MN) DS use in a nationally representative sample of the US population (≥1 y) from the 2007-2018 NHANES using a combined approach. METHODS: NHANES obtains an in-home inventory with a frequency-based dietary supplement and prescription medicine questionnaire (DSMQ), and two 24-h dietary recalls (24HRs). Trends in the prevalence of use and selected types of products used were estimated for the population and by sex, age, race/Hispanic origin, family income [poverty-to-income ratio (PIR)], and household food security (food-secure vs. food-insecure) using the DSMQ or ≥ 1 24HR. Linear trends were tested using orthogonal polynomials (significance set at P < 0.05). RESULTS: DS use increased from 50% in 2007 to 56% in 2018 (P = 0.001); use of MN products increased from 46% to 49% (P = 0.03), and single-nutrient DS (e.g., magnesium, vitamins B-12 and D) use also increased (all P < 0.001). In contrast, multivitamin-mineral use decreased (70% to 56%; P < 0.001). In adults (≥19 y), any (54% to 61%) and MN (49% to 54%) DS use increased, especially in men, non-Hispanic blacks and Hispanics, and low-income adults (PIR ≤130%). In children (1-18 y), any DS use remained stable (∼38%), as did MN use, except for food-insecure children, whose use increased from 24% to 31% over the decade (P = 0.03). CONCLUSIONS: The prevalence of any and MN DS use increased over time in the United States. This may be partially attributed to increased use of single-nutrient products. Population subgroups differed in their DS use.

A narrative review of nutrient based indexes to assess diet quality and the proposed total nutrient index that reflects total dietary exposures.

A priori dietary indices provide a standardized, reproducible way to evaluate adherence to dietary recommendations across different populations. Existing nutrient-based indices were developed to reflect food/beverage intake; however, given the high prevalence of dietary supplement (DS) use and its potentially large contribution to nutrient intakes for those that use them, exposure classification without accounting for DS is incomplete. The purpose of this article is to review existing nutrient-based indices and describe the development of the Total Nutrient Index (TNI), an index developed to capture usual intakes from all sources of under-consumed micronutrients among the U.S. population. The TNI assesses U.S. adults' total nutrient intakes relative to recommended nutrient standards for eight under-consumed micronutrients identified by the Dietary Guidelines for Americans: calcium, magnesium, potassium, choline, and vitamins A, C, D, E. The TNI is scored from 0 to 100 (truncated at 100). The mean TNI score of U.S. adults (≥19 y; n = 9,954) based on dietary data from NHANES 2011-2014, was 75.4; the mean score for the index ignoring DS contributions was only 69.0 (t-test; p < 0.001). The TNI extends existing measures of diet quality by including nutrient intakes from all sources and was developed for research, monitoring, and policy purposes.Supplemental data for this article is available online at https://doi.org/10.1080/10408398.2021.1967872.

Semiparametric Estimation of the Distribution of Episodically Consumed Foods Measured With Error.

Dietary data collected from 24-hour dietary recalls are observed with significant measurement errors. In the nonparametric curve estimation literature, much of the effort has been devoted to designing methods that are consistent under contamination by noise, and which have been traditionally applied for analyzing those data. However, some foods such as alcohol or fruits are consumed only episodically, and may not be consumed during the day when the 24-hour recall is administered. These so-called excess zeros make existing nonparametric estimators break down, and new techniques need to be developed for such data. We develop two new consistent semiparametric estimators of the distribution of such episodically consumed food data, making parametric assumptions only on some less important parts of the model. We establish its theoretical properties and illustrate the good performance of our fully data-driven method in simulated and real data. Supplementary materials for this article are available online.

Chlorogenic Acid and Quercetin in a Diet with Fermentable Fiber Influence Multiple Processes Involved in DSS-Induced Ulcerative Colitis but Do Not Reduce Injury.

Ulcerative colitis (UC) patients often avoid foods containing fermentable fibers as some can promote symptoms during active disease. Pectin has been identified as a more protective fermentable fiber, but little has been done to determine the interaction between pectin and bioactive compounds present in foods containing that fiber type. Quercetin and chlorogenic acid, two bioactives in stone fruits, may have anti-cancer, anti-oxidant, and anti-inflammatory properties. We hypothesized that quercetin and chlorogenic acid, in the presence of the fermentable fiber pectin, may suppress the expression of pro-inflammatory molecules, alter the luminal environment, and alter colonocyte proliferation, thereby protecting against recurring bouts of UC. Rats (n = 63) received one of three purified diets (control, 0.45% quercetin, 0.05% chlorogenic acid) containing 6% pectin for 3 weeks before exposure to dextran sodium sulfate (DSS, 3% for 48 h, 3x, 2 wk separation, n = 11/diet) in drinking water to initiate UC, or control (no DSS, n = 10/diet) treatments prior to termination at 9 weeks. DSS increased the fecal moisture content (p < 0.05) and SCFA concentrations (acetate, p < 0.05; butyrate, p < 0.05). Quercetin and chlorogenic acid diets maintained SLC5A8 (SCFA transporter) mRNA levels in DSS-treated rats at levels similar to those not exposed to DSS. DSS increased injury (p < 0.0001) and inflammation (p < 0.01) scores, with no differences noted due to diet. Compared to the control diet, chlorogenic acid decreased NF-κB activity in DSS-treated rats (p < 0.05). Quercetin and chlorogenic acid may contribute to the healthy regulation of NF-κB activation (via mRNA expression of IκΒα, Tollip, and IL-1). Quercetin enhanced injury-repair molecule FGF-2 expression (p < 0.01), but neither diet nor DSS treatment altered proliferation. Although quercetin and chlorogenic acid did not protect against overt indicators of injury and inflammation, or fecal SCFA concentrations, compared to the control diet, their influence on the expression of injury repair molecules, pro-inflammatory cytokines, SCFA transport proteins, and NF-κB inhibitory molecules suggests beneficial influences on major pathways involved in DSS-induced UC. Therefore, in healthy individuals or during periods of remission, quercetin and chlorogenic acid may promote a healthier colon, and may suppress some of the signaling involved in inflammation promotion during active disease.

Predictive Functional Linear Models with Diverging Number of Semiparametric Single-Index Interactions.

When predicting crop yield using both functional and multivariate predictors, the prediction performances benefit from the inclusion of the interactions between the two sets of predictors. We assume the interaction depends on a nonparametric, single-index structure of the multivariate predictor and reduce each functional predictor's dimension using functional principal component analysis (FPCA). Allowing the number of FPCA scores to diverge to infinity, we consider a sequence of semiparametric working models with a diverging number of predictors, which are FPCA scores with estimation errors. We show that the parametric component of the model is root-n consistent and asymptotically normal, the overall prediction error is dominated by the estimation of the nonparametric interaction function, and justify a CV-based procedure to select the tuning parameters.

Serum Cytokines Predict Neurological Damage in Genetically Diverse Mouse Models.

Viral infections contribute to neurological and immunological dysfunction driven by complex genetic networks. Theiler's murine encephalomyelitis virus (TMEV) causes neurological dysfunction in mice and can model human outcomes to viral infections. Here, we used genetically distinct mice from five Collaborative Cross mouse strains and C57BL/6J to demonstrate how TMEV-induced immune responses in serum may predict neurological outcomes in acute infection. To test the hypothesis that serum cytokine levels can provide biomarkers for phenotypic outcomes of acute disease, we compared cytokine levels at pre-injection, 4 days post-injection (d.p.i.), and 14 d.p.i. Each strain produced unique baseline cytokine levels and had distinct immune responses to the injection procedure itself. Thus, we eliminated the baseline responses to the injection procedure itself and identified cytokines and chemokines induced specifically by TMEV infection. Then, we identified strain-specific longitudinal cytokine profiles in serum during acute disease. Using stepwise regression analysis, we identified serum immune markers predictive for TMEV-induced neurological phenotypes of the acute phase, e.g., IL-9 for limb paralysis; and TNF-α, IL-1ß, and MIP-1ß for limb weakness. These findings indicate how temporal differences in immune responses are influenced by host genetic background and demonstrate the potential of serum biomarkers to track the neurological effects of viral infection.

Estimation of sparse functional quantile regression with measurement error: a SIMEX approach.

Quantile regression is a semiparametric method for modeling associations between variables. It is most helpful when the covariates have complex relationships with the location, scale, and shape of the outcome distribution. Despite the method's robustness to distributional assumptions and outliers in the outcome, regression quantiles may be biased in the presence of measurement error in the covariates. The impact of function-valued covariates contaminated with heteroscedastic error has not yet been examined previously; although, studies have investigated the case of scalar-valued covariates. We present a two-stage strategy to consistently fit linear quantile regression models with a function-valued covariate that may be measured with error. In the first stage, an instrumental variable is used to estimate the covariance matrix associated with the measurement error. In the second stage, simulation extrapolation (SIMEX) is used to correct for measurement error in the function-valued covariate. Point-wise standard errors are estimated by means of nonparametric bootstrap. We present simulation studies to assess the robustness of the measurement error corrected for functional quantile regression. Our methods are applied to National Health and Examination Survey data to assess the relationship between physical activity and body mass index among adults in the United States.

Robust methods to correct for measurement error when evaluating a surrogate marker.

The identification of valid surrogate markers of disease or disease progression has the potential to decrease the length and costs of future studies. Most available methods that assess the value of a surrogate marker ignore the fact that surrogates are often measured with error. Failing to adjust for measurement error can erroneously identify a useful surrogate marker as not useful or vice versa. We investigate and propose robust methods to correct for the effect of measurement error when evaluating a surrogate marker using multiple estimators developed for parametric and nonparametric estimates of the proportion of treatment effect explained by the surrogate marker. In addition, we quantify the attenuation bias induced by measurement error and develop inference procedures to allow for variance and confidence interval estimation. Through a simulation study, we show that our proposed estimators correct for measurement error in the surrogate marker and that our inference procedures perform well in finite samples. We illustrate these methods by examining a potential surrogate marker that is measured with error, hemoglobin A1c, using data from the Diabetes Prevention Program clinical trial.

Feature screening with large-scale and high-dimensional survival data.

Data with a huge size present great challenges in modeling, inferences, and computation. In handling big data, much attention has been directed to settings with "large p small n", and relatively less work has been done to address problems with p and n being both large, though data with such a feature have now become more accessible than before, where p represents the number of variables and n stands for the sample size. The big volume of data does not automatically ensure good quality of inferences because a large number of unimportant variables may be collected in the process of gathering informative variables. To carry out valid statistical analysis, it is imperative to screen out noisy variables that have no predictive value for explaining the outcome variable. In this paper, we develop a screening method for handling large-sized survival data, where the sample size n is large and the dimension p of covariates is of non-polynomial order of the sample size n, or the so-called NP-dimension. We rigorously establish theoretical results for the proposed method and conduct numerical studies to assess its performance. Our research offers multiple extensions of existing work and enlarges the scope of high-dimensional data analysis. The proposed method capitalizes on the connections among useful regression settings and offers a computationally efficient screening procedure. Our method can be applied to different situations with large-scale data including genomic data.

A semiparametric risk score for physical activity.

We develop a generalized partially additive model to build a single semiparametric risk scoring system for physical activity across multiple populations. A score comprised of distinct and objective physical activity measures is a new concept that offers challenges due to the nonlinear relationship between physical behaviors and various health outcomes. We overcome these challenges by modeling each score component as a smooth term, an extension of generalized partially linear single-index models. We use penalized splines and propose two inferential methods, one using profile likelihood and a nonparametric bootstrap, the other using a full Bayesian model, to solve additional computational problems. Both methods exhibit similar and accurate performance in simulations. These models are applied to the National Health and Nutrition Examination Survey and quantify nonlinear and interpretable shapes of score components for all-cause mortality.