Outcome-dependent sampling: an efficient sampling and inference procedure for studies with a continuous outcome

Statistical analysis of high-dimensional biomedical data: a gentle introduction to analytical goals, common approaches and challenges

BACKGROUND

In high-dimensional data (HDD) settings, the number of variables associated with each observation is very large. Prominent examples of HDD in biomedical research include omics data with a large number of variables such as many measurements across the genome, proteome, or metabolome, as well as electronic health records data that have large numbers of variables recorded for each patient. The statistical analysis of such data requires knowledge and experience, sometimes of complex methods adapted to the respective research questions.

METHODS

Advances in statistical methodology and machine learning methods offer new opportunities for innovative analyses of HDD, but at the same time require a deeper understanding of some fundamental statistical concepts. Topic group TG9 "High-dimensional data" of the STRATOS (STRengthening Analytical Thinking for Observational Studies) initiative provides guidance for the analysis of observational studies, addressing particular statistical challenges and opportunities for the analysis of studies involving HDD. In this overview, we discuss key aspects of HDD analysis to provide a gentle introduction for non-statisticians and for classically trained statisticians with little experience specific to HDD.

RESULTS

The paper is organized with respect to subtopics that are most relevant for the analysis of HDD, in particular initial data analysis, exploratory data analysis, multiple testing, and prediction. For each subtopic, main analytical goals in HDD settings are outlined. For each of these goals, basic explanations for some commonly used analysis methods are provided. Situations are identified where traditional statistical methods cannot, or should not, be used in the HDD setting, or where adequate analytic tools are still lacking. Many key references are provided.

CONCLUSIONS

This review aims to provide a solid statistical foundation for researchers, including statisticians and non-statisticians, who are new to research with HDD or simply want to better evaluate and understand the results of HDD analyses.

Design and analysis of two-phase studies with multivariate longitudinal data

Two-phase studies are crucial when outcome and covariate data are available in a first phase sample (e.g., a cohort study), but costs associated with retrospective ascertainment of a novel exposure limit the size of the second phase sample, in whom the exposure is collected. For longitudinal outcomes, one class of two-phase studies stratifies subjects based on an outcome vector summary (e.g., an average or a slope over time) and oversamples subjects in the extreme value strata while undersampling subjects in the medium value stratum. Based on the choice of the summary, two-phase studies for longitudinal data can increase efficiency of time-varying and/or time-fixed exposure parameter estimates. In this manuscript, we extend efficient, two-phase study designs to multivariate longitudinal continuous outcomes, and we detail two analysis approaches. The first approach is a multiple imputation analysis that combines complete data from subjects selected for phase two with the incomplete data from those not selected. The second approach is a conditional maximum likelihood analysis that is intended for applications where only data from subjects selected for phase two are available. Importantly, we show that both approaches can be applied to secondary analyses of previously conducted two-phase studies. We examine finite sample operating characteristics of the two approaches and use the Lung Health Study (Connett et al., 1993) to examine genetic associations with lung function decline over time. This article is protected by copyright. All rights reserved.

Two-Phase Sampling Designs for Data Validation in Settings with Covariate Measurement Error and Continuous Outcome

Measurement errors are present in many data collection procedures and can harm analyses by biasing estimates. To correct for measurement error, researchers often validate a subsample of records and then incorporate the information learned from this validation sample into estimation. In practice, the validation sample is often selected using simple random sampling (SRS). However, SRS leads to inefficient estimates because it ignores information on the error-prone variables, which can be highly correlated to the unknown truth. Applying and extending ideas from the two-phase sampling literature, we propose optimal and nearly-optimal designs for selecting the validation sample in the classical measurement-error framework. We target designs to improve the efficiency of model-based and design-based estimators, and show how the resulting designs compare to each other. Our results suggest that sampling schemes that extract more information from the error-prone data are substantially more efficient than SRS, for both design- and model-based estimators. The optimal procedure, however, depends on the analysis method, and can differ substantially. This is supported by theory and simulations. We illustrate the various designs using data from an HIV cohort study.

Two-wave two-phase outcome-dependent sampling designs, with applications to longitudinal binary data

Two-phase outcome-dependent sampling (ODS) designs are useful when resource constraints prohibit expensive exposure ascertainment on all study subjects. One class of ODS designs for longitudinal binary data stratifies subjects into three strata according to those who experience the event at none, some, or all follow-up times. For time-varying covariate effects, exclusively selecting subjects with response variation can yield highly efficient estimates. However, if interest lies in the association of a time-invariant covariate, or the joint associations of time-varying and time-invariant covariates with the outcome, then the optimal design is unknown. Therefore, we propose a class of two-wave two-phase ODS designs for longitudinal binary data. We split the second-phase sample selection into two waves, between which an interim design evaluation analysis is conducted. The interim design evaluation analysis uses first-wave data to conduct a simulation-based search for the optimal second-wave design that will improve the likelihood of study success. Although we focus on longitudinal binary response data, the proposed design is general and can be applied to other response distributions. We believe that the proposed designs can be useful in settings where (1) the expected second-phase sample size is fixed and one must tailor stratum-specific sampling probabilities to maximize estimation efficiency, or (2) relative sampling probabilities are fixed across sampling strata and one must tailor sample size to achieve a desired precision. We describe the class of designs, examine finite sampling operating characteristics, and apply the designs to an exemplar longitudinal cohort study, the Lung Health Study.

Accelerated failure time model for data from outcome-dependent sampling

Outcome-dependent sampling designs such as the case-control or case-cohort design are widely used in epidemiological studies for their outstanding cost-effectiveness. In this article, we propose and develop a smoothed weighted Gehan estimating equation approach for inference in an accelerated failure time model under a general failure time outcome-dependent sampling scheme. The proposed estimating equation is continuously differentiable and can be solved by the standard numerical methods. In addition to developing asymptotic properties of the proposed estimator, we also propose and investigate a new optimal power-based subsamples allocation criteria in the proposed design by maximizing the power function of a significant test. Simulation results show that the proposed estimator is more efficient than other existing competing estimators and the optimal power-based subsamples allocation will provide an ODS design that yield improved power for the test of exposure effect. We illustrate the proposed method with a data set from the Norwegian Mother and Child Cohort Study to evaluate the relationship between exposure to perfluoroalkyl substances and women's subfecundity.

Utilizing centralized biorepository samples for biomarkers of cystic fibrosis lung disease severity

BACKGROUND

Circulating biomarkers reflective of lung disease activity and severity have the potential to improve patient care and accelerate drug development in CF. The objective of this study was to leverage banked specimens to test the hypothesis that blood-based biomarkers discriminate CF children segregated by lung disease severity.

METHODS

Banked serum samples were selected from children who were categorized into two extremes of phenotype associated with lung function ('mild' or 'severe') based on CF-specific data and were matched on age, gender, CFTR genotype, and P. aeruginosa infection status. Targeted inflammatory proteins, lipids, and discovery metabolite profiles were measured in these serum samples.

RESULTS

The severe cohort, characterized by a lower CF-specific FEV1 percentile, had significantly higher circulating concentrations of high sensitivity C-reactive protein, serum amyloid A, granulocyte colony stimulating factor, and calprotectin compared to the mild cohort. The mild cohort tended to have higher serum linoleic acid concentrations. The metabolite arabitol was lower in the severe cohort while other CF relevant metabolic pathways showed non-significant differences after adjusting for multiple comparisons. A sensitivity analysis to correct for biased estimates that may result from selecting subjects using an extremes of phenotype approach confirmed the protein biomarker findings.

CONCLUSIONS

Circulating inflammatory proteins differ in CF children segregated by lung function. These findings serve to demonstrate the value of maintaining centralized, high quality patient derived samples for future research, with linkage to clinical information to answer testable hypotheses in biomarker development.

Two-Phase, Generalized Case-Control Designs for the Study of Quantitative Longitudinal Outcomes

We propose a general class of 2-phase epidemiologic study designs for quantitative, longitudinal data that are useful when phase 1 longitudinal outcome and covariate data are available but data on the exposure (e.g., a biomarker) can only be collected on a subset of subjects during phase 2. To conduct a study using a design in the class, one first summarizes the longitudinal outcomes by fitting a simple linear regression of the response on a time-varying covariate for each subject. Sampling strata are defined by splitting the estimated regression intercept or slope distributions into distinct (low, medium, and high) regions. Stratified sampling is then conducted from strata defined by the intercepts, by the slopes, or from a mixture. In general, samples selected with extreme intercept values will yield low variances for associations of time-fixed exposures with the outcome and samples enriched with extreme slope values will yield low variances for associations of time-varying exposures with the outcome (including interactions with time-varying exposures). We describe ascertainment-corrected maximum likelihood and multiple-imputation estimation procedures that permit valid and efficient inferences. We embed all methodological developments within the framework of conducting a substudy that seeks to examine genetic associations with lung function among continuous smokers in the Lung Health Study (United States and Canada, 1986-1994).

Likelihood-based analysis of outcome-dependent sampling designs with longitudinal data

The use of outcome-dependent sampling with longitudinal data analysis has previously been shown to improve efficiency in the estimation of regression parameters. The motivating scenario is when outcome data exist for all cohort members but key exposure variables will be gathered only on a subset. Inference with outcome-dependent sampling designs that also incorporates incomplete information from those individuals who did not have their exposure ascertained has been investigated for univariate but not longitudinal outcomes. Therefore, with a continuous longitudinal outcome, we explore the relative contributions of various sources of information toward the estimation of key regression parameters using a likelihood framework. We evaluate the efficiency gains that alternative estimators might offer over random sampling, and we offer insight into their relative merits in select practical scenarios. Finally, we illustrate the potential impact of design and analysis choices using data from the Cystic Fibrosis Foundation Patient Registry.

On the Analysis of Case-Control Studies in Cluster-correlated Data Settings

In resource-limited settings, long-term evaluation of national antiretroviral treatment (ART) programs often relies on aggregated data, the analysis of which may be subject to ecological bias. As researchers and policy makers consider evaluating individual-level outcomes such as treatment adherence or mortality, the well-known case-control design is appealing in that it provides efficiency gains over random sampling. In the context that motivates this article, valid estimation and inference requires acknowledging any clustering, although, to our knowledge, no statistical methods have been published for the analysis of case-control data for which the underlying population exhibits clustering. Furthermore, in the specific context of an ongoing collaboration in Malawi, rather than performing case-control sampling across all clinics, case-control sampling within clinics has been suggested as a more practical strategy. To our knowledge, although similar outcome-dependent sampling schemes have been described in the literature, a case-control design specific to correlated data settings is new. In this article, we describe this design, discuss balanced versus unbalanced sampling techniques, and provide a general approach to analyzing case-control studies in cluster-correlated settings based on inverse probability-weighted generalized estimating equations. Inference is based on a robust sandwich estimator with correlation parameters estimated to ensure appropriate accounting of the outcome-dependent sampling scheme. We conduct comprehensive simulations, based in part on real data on a sample of N = 78,155 program registrants in Malawi between 2005 and 2007, to evaluate small-sample operating characteristics and potential trade-offs associated with standard case-control sampling or when case-control sampling is performed within clusters.

Outcome-dependent sampling with interval-censored failure time data

Epidemiologic studies and disease prevention trials often seek to relate an exposure variable to a failure time that suffers from interval-censoring. When the failure rate is low and the time intervals are wide, a large cohort is often required so as to yield reliable precision on the exposure-failure-time relationship. However, large cohort studies with simple random sampling could be prohibitive for investigators with a limited budget, especially when the exposure variables are expensive to obtain. Alternative cost-effective sampling designs and inference procedures are therefore desirable. We propose an outcome-dependent sampling (ODS) design with interval-censored failure time data, where we enrich the observed sample by selectively including certain more informative failure subjects. We develop a novel sieve semiparametric maximum empirical likelihood approach for fitting the proportional hazards model to data from the proposed interval-censoring ODS design. This approach employs the empirical likelihood and sieve methods to deal with the infinite-dimensional nuisance parameters, which greatly reduces the dimensionality of the estimation problem and eases the computation difficulty. The consistency and asymptotic normality of the resulting regression parameter estimator are established. The results from our extensive simulation study show that the proposed design and method works well for practical situations and is more efficient than the alternative designs and competing approaches. An example from the Atherosclerosis Risk in Communities (ARIC) study is provided for illustration.

Outcome-Dependent Sampling Design and Inference for Cox's Proportional Hazards Model

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed. A criteria that can be used to optimally implement the ODS design in practice is proposed and studied. The small sample performance of the proposed method is evaluated by simulation studies. The proposed design and inference procedure is shown to be statistically more powerful than existing alternative designs with the same sample sizes. We illustrate the proposed method with an existing real data from the Cancer Incidence and Mortality of Uranium Miners Study.

Estimating relative risk of a log-transformed exposure measured in pools

Pooling biospecimens prior to performing laboratory assays is a useful tool to reduce costs, achieve minimum volume requirements and mitigate assay measurement error. When estimating the risk of a continuous, pooled exposure on a binary outcome, specialized statistical techniques are required. Current methods include a regression calibration approach, where the expectation of the individual-level exposure is calculated by adjusting the observed pooled measurement with additional covariate data. While this method employs a linear regression calibration model, we propose an alternative model that can accommodate log-linear relationships between the exposure and predictive covariates. The proposed model permits direct estimation of the relative risk associated with a log-transformation of an exposure measured in pools. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

Statistical inferences for data from studies conducted with an aggregated multivariate outcome-dependent sample design

Outcome-dependent sampling (ODS) scheme is a cost-effective sampling scheme where one observes the exposure with a probability that depends on the outcome. The well-known such design is the case-control design for binary response, the case-cohort design for the failure time data, and the general ODS design for a continuous response. While substantial work has been carried out for the univariate response case, statistical inference and design for the ODS with multivariate cases remain under-developed. Motivated by the need in biological studies for taking the advantage of the available responses for subjects in a cluster, we propose a multivariate outcome-dependent sampling (multivariate-ODS) design that is based on a general selection of the continuous responses within a cluster. The proposed inference procedure for the multivariate-ODS design is semiparametric where all the underlying distributions of covariates are modeled nonparametrically using the empirical likelihood methods. We show that the proposed estimator is consistent and developed the asymptotically normality properties. Simulation studies show that the proposed estimator is more efficient than the estimator obtained using only the simple-random-sample portion of the multivariate-ODS or the estimator from a simple random sample with the same sample size. The multivariate-ODS design together with the proposed estimator provides an approach to further improve study efficiency for a given fixed study budget. We illustrate the proposed design and estimator with an analysis of association of polychlorinated biphenyl exposure to hearing loss in children born to the Collaborative Perinatal Study. Copyright © 2016 John Wiley & Sons, Ltd.

Estimation of a partially linear additive model for data from an outcome-dependent sampling design with a continuous outcome

Outcome-dependent sampling (ODS) designs have been well recognized as a cost-effective way to enhance study efficiency in both statistical literature and biomedical and epidemiologic studies. A partially linear additive model (PLAM) is widely applied in real problems because it allows for a flexible specification of the dependence of the response on some covariates in a linear fashion and other covariates in a nonlinear non-parametric fashion. Motivated by an epidemiological study investigating the effect of prenatal polychlorinated biphenyls exposure on children's intelligence quotient (IQ) at age 7 years, we propose a PLAM in this article to investigate a more flexible non-parametric inference on the relationships among the response and covariates under the ODS scheme. We propose the estimation method and establish the asymptotic properties of the proposed estimator. Simulation studies are conducted to show the improved efficiency of the proposed ODS estimator for PLAM compared with that from a traditional simple random sampling design with the same sample size. The data of the above-mentioned study is analyzed to illustrate the proposed method.

Statistical inference for the additive hazards model under outcome-dependent sampling

Cost-effective study design and proper inference procedures for data from such designs are always of particular interests to study investigators. In this article, we propose a biased sampling scheme, an outcome-dependent sampling (ODS) design for survival data with right censoring under the additive hazards model. We develop a weighted pseudo-score estimator for the regression parameters for the proposed design and derive the asymptotic properties of the proposed estimator. We also provide some suggestions for using the proposed method by evaluating the relative efficiency of the proposed method against simple random sampling design and derive the optimal allocation of the subsamples for the proposed design. Simulation studies show that the proposed ODS design is more powerful than other existing designs and the proposed estimator is more efficient than other estimators. We apply our method to analyze a cancer study conducted at NIEHS, the Cancer Incidence and Mortality of Uranium Miners Study, to study the risk of radon exposure to cancer.

BIASED SAMPLING DESIGNS TO IMPROVE RESEARCH EFFICIENCY: FACTORS INFLUENCING PULMONARY FUNCTION OVER TIME IN CHILDREN WITH ASTHMA

Substudies of the Childhood Asthma Management Program (CAMP Research Group, 1999, 2000) seek to identify patient characteristics associated with asthma symptoms and lung function. To determine if genetic measures are associated with trajectories of lung function as measured by forced vital capacity (FVC), children in the primary cohort study retrospectively had candidate loci evaluated. Given participant burden and constraints on financial resources, it is often desirable to target a sub-sample for ascertainment of costly measures. Methods that can leverage the longitudinal outcome on the full cohort to selectively measure informative individuals have been promising, but have been restricted in their use to analysis of the targeted sub-sample. In this paper we detail two multiple imputation analysis strategies that exploit outcome and partially observed covariate data on the non-sampled subjects, and we characterize alternative design and analysis combinations that could be used for future studies of pulmonary function and other outcomes. Candidate predictor (e.g. IL10 cytokine polymorphisms) associations obtained from targeted sampling designs can be estimated with very high efficiency compared to standard designs. Further, even though multiple imputation can dramatically improve estimation efficiency for covariates available on all subjects (e.g., gender and baseline age), only modest efficiency gains were observed in parameters associated with predictors that are exclusive to the targeted sample. Our results suggest that future studies of longitudinal trajectories can be efficiently conducted by use of outcome-dependent designs and associated full cohort analysis.

Effect of oral and vaginal hormonal contraceptives on inflammatory blood biomarkers

The use of combined hormonal contraceptives has been reported to increase the level of C-reactive protein (CRP). We assessed the effect of hormonal contraceptive use on inflammatory cytokines including CRP, monocyte chemotactic protein-1, soluble tumor necrosis factor (sTNF), interleukin-6 (IL-6), and soluble CD40 ligand. We used 79 female subjects (19 to 30 years old) who were combined oral contraceptives users (n = 29), combined vaginal contraceptive users (n = 20), and nonusers (n = 30) with CRP values of ≤1 (n = 46) or ≥3 (n = 33). Information on medical history, physical activities, and dietary and sleeping habits were collected. Both oral and vaginal contraceptive users had higher levels of CRP (P < 0.0001), compared to nonusers. Only oral contraceptive users exhibited elevated sCD40L (P < 0.01). When comparing the groups with CRP ≤ 1 and CRP ≥ 3, levels of IL-6 and sTNF-RI were positively correlated with CRP among oral contraceptive users. We did not observe the same elevation for other inflammatory biomarkers for the CRP ≥ 3 group among vaginal contraceptive users. The clear cause of elevation in CRP level due to the use of different hormonal contraceptive formulations and methods is not well understood. Longitudinal studies with larger sample size are required to better assess the true cause of CRP elevation among hormonal contraceptive users.

A likelihood ratio test for nested proportions

For policy and medical issues, it is important to know if the proportion of an event changes after an intervention is administered. When the later proportion can only be calculated in a portion of the sample used to compute the previous proportion, the two proportions are nested. The motivating example for this work comes from the need to test whether admission rates in emergency departments are different between the first and a return visit. Here, subjects who contribute to the admission rate at the return visit must be included in the first rate and also return, but not vice versa. This conditionality means that existing methods, including the basic test of equality of two proportions, longitudinal data analysis methods, and recurrent event approaches are not directly applicable. Currently, researchers can only explore this question by the use of descriptive statistics. We propose a likelihood ratio test to compare two nested proportions by using the product of conditional probabilities. This test accommodates the conditionality, subject dependencies, and cluster effects and can be implemented in SAS PROC NLMIXED allowing for the proposed method to be readily used in an applied setting. Simulation studies showed that our approach provides unbiased estimates and reasonable power. Moreover, it generally outperforms the two-sample proportion z-test, in the presence of heterogeneity, and the Cochran-Mantel-Haenszel test. An example based on readmission rates through an emergency department is used to illustrate the proposed method.

Maternal glomerular filtration rate in pregnancy and fetal size

Background

The relationship of maternal glomerular filtration rate (GFR) in pregnancy to fetal size needs to be better characterized as it impacts an ongoing debate about confounding effect of maternal GFR in investigations of important environmental contaminants. We aimed to characterize the size of the association between maternal GFR and infant birth weight.

Materials and Methods

A sub-cohort of 953 selected women (470 women with and 483 women without preeclampsia) in the Norwegian Mother and Child Cohort (MoBa), recruited during 2003–2007 were analyzed. GFR in the second trimester was estimated based on plasma creatinine. Birth weight was ascertained from the Medical Birth Registry of Norway. Multivariate linear regression was used to evaluate the association between maternal GFR in second trimester (estimated by the Cockroft-Gault [GFR-CG] and the modification of diet in renal disease [GFR-MDRD] formulas) and infant birth weight. Partial correlation coefficients were also calculated.

Results

Maternal GFR-CG (β: 0.73 g/ml/min, p = 0.04) and GFR-MDRD (β: 0.83 g/ml/min, p = 0.04) were associated with infant birth weight in models adjusted for maternal weight in kilograms, preeclampsia, and gestational age at delivery (days). Partial correlation coefficients for the association between infant birth weight and GFR were 0.07 for both formulas. Although the birth weight-GFR association was stronger among the women with preeclampsia, the difference from women without preeclampsia was not statistically significant.

Conclusion

These data support an association between GFR during pregnancy and infant birth weight, and indicate that GFR may confound selected epidemiologic associations.

Persistent organochlorines and hypertensive disorders of pregnancy

Although there is indirect evidence to suggest that persistent organochlorines might increase risk of hypertensive disorders of pregnancy, there are no epidemiologic studies directly addressing this question. In this cohort study, sampled from the Collaborative Perinatal Project, 1933 women had complete data on organochlorine measurements, covariates, and pregnancy outcomes. Exposures to organochlorines were divided into quintiles, and levels were much higher in these patients recruited from 1959 to 1965 compared to levels in the general population at present. Among included women, 364 developed gestational hypertension (hypertension without proteinuria) and 131 developed preeclampsia (hypertension with proteinuria). We found essentially no association between serum DDE and total PCBs and risk of either gestational hypertension or preeclampsia. Results for other organochlorines showed varying patterns of results: DDT was inversely associated with risk of gestational hypertension (p for trend <0.001), B-Hexachlorocyclohexane and heptachlor epoxide were inversely related to gestational hypertension (p trend <0.01 and 0.10, respectively), dieldrin had a modestly positive association with gestational hypertension (p for trend=0.12), and hexachlorobenzene, trans-nonachlor, and oxychlordane yielded results close to the null. Hexachlorobenzene showed an inverse association with preeclampsia (p for trend <0.001). The study suggests that persistent organochlorines present at historically high level are not likely to increase the risk of hypertensive disorders of pregnancy, suggesting that other toxicants that have similar biologic effects are also unlikely to do so.

Prenatal exposure to persistent organochlorines and childhood obesity in the US collaborative perinatal project

BACKGROUND

In some previous studies, prenatal exposure to persistent organochlorines such as 1,1,-dichloro-2,2-bis(p-chlorophenyl)ethylene (p,p´-DDE), polychlorinated biphenyls (PCBs), and hexachlorobenzene (HCB) has been associated with higher body mass index (BMI) in children.

OBJECTIVE

Our goal was to evaluate the association of maternal serum levels of β-hexachlorocyclohexane (β-HCH), p,p´-DDE, dichlorodiphenyltrichloroethane (p,p´-DDT), dieldrin, heptachlor epoxide, HCB, trans-nonachlor, oxychlordane, and PCBs with offspring obesity during childhood.

METHODS

The analysis was based on a subsample of 1,915 children followed until 7 years of age as part of the U.S. Collaborative Perinatal Project (CPP). The CPP enrolled pregnant women in 1959-1965; exposure levels were measured in third-trimester maternal serum that was collected before these organochlorines were banned in the United States. Childhood overweight and obesity were defined using age- and sex-specific cut points for BMI as recommended by the International Obesity Task Force.

RESULTS

Adjusted results did not show clear evidence for an association between organochlorine exposure and obesity; however, a suggestive finding emerged for dieldrin. Compared with those in the lowest quintile (dieldrin, < 0.57 μg/L), odds of obesity were 3.6 (95% CI: 1.3, 10.5) for the fourth and 2.3 (95% CI: 0.8, 7.1) for the highest quintile. Overweight and BMI were unrelated to organochlorine exposure.

CONCLUSIONS

In this population with relatively high levels of exposure to organochlorines, no clear associations with obesity or BMI emerged.

Outcome vector dependent sampling with longitudinal continuous response data: stratified sampling based on summary statistics

The analysis of longitudinal trajectories usually focuses on evaluation of explanatory factors that are either associated with rates of change, or with overall mean levels of a continuous outcome variable. In this article, we introduce valid design and analysis methods that permit outcome dependent sampling of longitudinal data for scenarios where all outcome data currently exist, but a targeted substudy is being planned in order to collect additional key exposure information on a limited number of subjects. We propose a stratified sampling based on specific summaries of individual longitudinal trajectories, and we detail an ascertainment corrected maximum likelihood approach for estimation using the resulting biased sample of subjects. In addition, we demonstrate that the efficiency of an outcome-based sampling design relative to use of a simple random sample depends highly on the choice of outcome summary statistic used to direct sampling, and we show a natural link between the goals of the longitudinal regression model and corresponding desirable designs. Using data from the Childhood Asthma Management Program, where genetic information required retrospective ascertainment, we study a range of designs that examine lung function profiles over 4 years of follow-up for children classified according to their genotype for the IL 13 cytokine.

In-utero exposure to dichlorodiphenyltrichloroethane and cognitive development among infants and school-aged children

BACKGROUND

Dichlorodiphenyltrichloroethane (DDT) continues to be used for control of infectious diseases in several countries. In-utero exposure to DDT and dichlorodiphenyldichloroethylene (DDE) has been associated with developmental and cognitive impairment among children. We examined this association in an historical cohort in which the level of exposure was greater than in previous studies.

METHODS

The association of in-utero DDT and DDE exposure with infant and child neurodevelopment was examined in 1100 subjects in the Collaborative Perinatal Project, a prospective birth cohort enrolling pregnant women from 12 study centers in the United States from 1959 to 1965. Maternal DDT and DDE concentrations were measured in archived serum specimens. Infant mental and motor development was assessed at age 8 months using the Bayley Scales of Infant Development, and child cognitive development was assessed at age 7 years, using the Wechsler Intelligence Scale for Children.

RESULTS

Although levels of DDT and DDE were relatively high in this population (median DDT concentration, 8.9 μg/L; DDE, 24.5 μg/L), neither were related to Mental or Psychomotor Development scores on the Bayley Scales nor to Full-Scale Intelligence Quotient at 7 years of age. Categorical analyses showed no evidence of dose- response for either maternal DDT or DDE, and estimates of the association between continuous measures of exposure and neurodevelopment were indistinguishable from 0.

CONCLUSIONS

Adverse associations were not observed between maternal serum DDT and DDE concentrations and offspring neurodevelopment at 8 months or 7 years in this cohort.

Estimation of AUC or Partial AUC under Test-Result-Dependent Sampling

The area under the ROC curve (AUC) and partial area under the ROC curve (pAUC) are summary measures used to assess the accuracy of a biomarker in discriminating true disease status. The standard sampling approach used in biomarker validation studies is often inefficient and costly, especially when ascertaining the true disease status is costly and invasive. To improve efficiency and reduce the cost of biomarker validation studies, we consider a test-result-dependent sampling (TDS) scheme, in which subject selection for determining the disease state is dependent on the result of a biomarker assay. We first estimate the test-result distribution using data arising from the TDS design. With the estimated empirical test-result distribution, we propose consistent nonparametric estimators for AUC and pAUC and establish the asymptotic properties of the proposed estimators. Simulation studies show that the proposed estimators have good finite sample properties and that the TDS design yields more efficient AUC and pAUC estimates than a simple random sampling (SRS) design. A data example based on an ongoing cancer clinical trial is provided to illustrate the TDS design and the proposed estimators. This work can find broad applications in design and analysis of biomarker validation studies.

A trigger-based design for evaluating the safety of in utero antiretroviral exposure in uninfected children of human immunodeficiency virus-infected mothers

The Pediatric HIV/AIDS Cohort Study's Surveillance Monitoring of ART Toxicities Study is a prospective cohort study conducted at 22 US sites between 2007 and 2011 that was designed to evaluate the safety of in utero antiretroviral drug exposure in children not infected with human immunodeficiency virus who were born to mothers who were infected. This ongoing study uses a "trigger-based" design; that is, initial assessments are conducted on all children, and only those meeting certain thresholds or "triggers" undergo more intensive evaluations to determine whether they have had an adverse event (AE). The authors present the estimated rates of AEs for each domain of interest in the Surveillance Monitoring of ART Toxicities Study. They also evaluated the efficiency of this trigger-based design for estimating AE rates and for testing associations between in utero exposures to antiretroviral drugs and AEs. The authors demonstrate that estimated AE rates from the trigger-based design are unbiased after correction for the sensitivity of the trigger for identifying AEs. Even without correcting for bias based on trigger sensitivity, the trigger approach is generally more efficient for estimating AE rates than is evaluating a random sample of the same size. Minor losses in efficiency when comparing AE rates between persons exposed and unexposed in utero to particular antiretroviral drugs or drug classes were observed under most scenarios.

Outcome-dependent sampling from existing cohorts with longitudinal binary response data: study planning and analysis

When novel scientific questions arise after longitudinal binary data have been collected, the subsequent selection of subjects from the cohort for whom further detailed assessment will be undertaken is often necessary to efficiently collect new information. Key examples of additional data collection include retrospective questionnaire data, novel data linkage, or evaluation of stored biological specimens. In such cases, all data required for the new analyses are available except for the new target predictor or exposure. We propose a class of longitudinal outcome-dependent sampling schemes and detail a design corrected conditional maximum likelihood analysis for highly efficient estimation of time-varying and time-invariant covariate coefficients when resource limitations prohibit exposure ascertainment on all participants. Additionally, we detail an important study planning phase that exploits available cohort data to proactively examine the feasibility of any proposed substudy as well as to inform decisions regarding the most desirable study design. The proposed designs and associated analyses are discussed in the context of a study that seeks to examine the modifying effect of an interleukin-10 cytokine single nucleotide polymorphism on asthma symptom regression in adolescents participating Childhood Asthma Management Program Continuation Study. Using this example we assume that all data necessary to conduct the study are available except subject-specific genotype data. We also assume that these data would be ascertained by analyzing stored blood samples, the cost of which limits the sample size.

A Partially Linear Regression Model for Data from an Outcome-Dependent Sampling Design

The outcome dependent sampling scheme has been gaining attention in both the statistical literature and applied fields. Epidemiological and environmental researchers have been using it to select the observations for more powerful and cost-effective studies. Motivated by a study of the effect of in utero exposure to polychlorinated biphenyls on children's IQ at age 7, in which the effect of an important confounding variable is nonlinear, we consider a semi-parametric regression model for data from an outcome-dependent sampling scheme where the relationship between the response and covariates is only partially parameterized. We propose a penalized spline maximum likelihood estimation (PSMLE) for inference on both the parametric and the nonparametric components and develop their asymptotic properties. Through simulation studies and an analysis of the IQ study, we compare the proposed estimator with several competing estimators. Practical considerations of implementing those estimators are discussed.

Statistical inference for a two-stage outcome-dependent sampling design with a continuous outcome

The two-stage case-control design has been widely used in epidemiology studies for its cost-effectiveness and improvement of the study efficiency (White, 1982, American Journal of Epidemiology 115, 119-128; Breslow and Cain, 1988, Biometrika 75, 11-20). The evolution of modern biomedical studies has called for cost-effective designs with a continuous outcome and exposure variables. In this article, we propose a new two-stage outcome-dependent sampling (ODS) scheme with a continuous outcome variable, where both the first-stage data and the second-stage data are from ODS schemes. We develop a semiparametric empirical likelihood estimation for inference about the regression parameters in the proposed design. Simulation studies were conducted to investigate the small-sample behavior of the proposed estimator. We demonstrate that, for a given statistical power, the proposed design will require a substantially smaller sample size than the alternative designs. The proposed method is illustrated with an environmental health study conducted at National Institutes of Health.

A partial linear model in the outcome-dependent sampling setting to evaluate the effect of prenatal PCB exposure on cognitive function in children

Outcome-dependent sampling (ODS) has been widely used in biomedical studies because it is a cost-effective way to improve study efficiency. However, in the setting of a continuous outcome, the representation of the exposure variable has been limited to the framework of linear models, due to the challenge in terms of both theory and computation. Partial linear models (PLM) are a powerful inference tool to nonparametrically model the relation between an outcome and the exposure variable. In this article, we consider a case study of a PLM for data from an ODS design. We propose a semiparametric maximum likelihood method to make inferences with a PLM. We develop the asymptotic properties and conduct simulation studies to show that the proposed ODS estimator can produce a more efficient estimate than that from a traditional simple random sampling design with the same sample size. Using this newly developed method, we were able to explore an open question in epidemiology: whether in utero exposure to background levels of polychlorinated biphenyls (PCBs) is associated with children's intellectual impairment. Our model provides further insights into the relation between low-level PCB exposure and children's cognitive function. The results shed new light on a body of inconsistent epidemiologic findings.

Design and inference for cancer biomarker study with an outcome and auxiliary-dependent subsampling

In cancer research, it is important to evaluate the performance of a biomarker (e.g., molecular, genetic, or imaging) that correlates patients' prognosis or predicts patients' response to treatment in a large prospective study. Due to overall budget constraint and high cost associated with bioassays, investigators often have to select a subset from all registered patients for biomarker assessment. To detect a potentially moderate association between the biomarker and the outcome, investigators need to decide how to select the subset of a fixed size such that the study efficiency can be enhanced. We show that, instead of drawing a simple random sample from the study cohort, greater efficiency can be achieved by allowing the selection probability to depend on the outcome and an auxiliary variable; we refer to such a sampling scheme as outcome and auxiliary-dependent subsampling (OADS). This article is motivated by the need to analyze data from a lung cancer biomarker study that adopts the OADS design to assess epidermal growth factor receptor (EGFR) mutations as a predictive biomarker for whether a subject responds to a greater extent to EGFR inhibitor drugs. We propose an estimated maximum-likelihood method that accommodates the OADS design and utilizes all observed information, especially those contained in the likelihood score of EGFR mutations (an auxiliary variable of EGFR mutations) that is available to all patients. We derive the asymptotic properties of the proposed estimator and evaluate its finite sample properties via simulation. We illustrate the proposed method with a data example.

Outcome- and auxiliary-dependent subsampling and its statistical inference

The performance of a biomarker predicting clinical outcome is often evaluated in a large prospective study. Due to high costs associated with bioassay, investigators need to select a subset from all available patients for biomarker assessment. We consider an outcome- and auxiliary-dependent subsampling (OADS) scheme, in which the probability of selecting a patient into the subset depends on the patient's clinical outcome and an auxiliary variable. We proposed a semiparametric empirical likelihood method to estimate the association between biomarker and clinical outcome. Asymptotic properties of the estimator are given. Simulation study shows that the proposed method outperforms alternative methods.

On semiparametric efficient inference for two-stage outcome-dependent sampling with a continuous outcome

Outcome-dependent sampling designs have been shown to be a cost effective way to enhance study efficiency. We show that the outcome-dependent sampling design with a continuous outcome can be viewed as an extension of the two-stage case-control designs to the continuous-outcome case. We further show that the two-stage outcome-dependent sampling has a natural link with the missing-data and biased-sampling framework. Through the use of semiparametric inference and missing-data techniques, we show that a certain semiparametric maximum likelihood estimator is computationally convenient and achieves the semiparametric efficient information bound. We demonstrate this both theoretically and through simulation.