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Nested case control (NCC) is a sampling method widely used for developing and evaluating risk models with expensive biomarkers on large prospective cohort studies. In a typical NCC design, biomarker values are obtained on a subcohort, where cases consist of all the events (subjects who experience the event during the follow-up). However, when the number of events is not small, due to the cost and limited availability of biospecimen, one may select only a subset of events as cases. We refer to such a variation as the untypical NCC. Unfortunately, existing inverse probability weighted (IPW) estimators for the untypical NCC are biased, and they only focus on relative risk parameters under the proportional hazards (PH) model. In this manuscript, we propose new weighting methods that produce consistent IPW estimators for not only relative risk parameters but also several metrics that evaluate a risk model's predictive performance. We also provide the inference procedure via perturbation resampling, which captures all the variance and between-subject covariance induced by the sampling processes for both case and control selections. In addition, our methods are not limited to the PH model, and they can be applied to the time-specific generalized linear model. Under the typical NCC design, our new weights are equivalent to the weight proposed by Samuelsen; under the untypical NCC, the IPW estimators using our weights have smaller bias and variance than the existing methods. We will demonstrate this improved performance via both analytical and numerical investigations.

Accurate risk assessment is critical in clinical decision-making. It entails the projected risk based on a risk prediction model agreeing with the observed risk in the target cohort. However, the model often over- or under-estimates the risk. Building a new model for the target cohort would be ideal but costly. It is therefore of great interest to recalibrate an existing model for the target cohort. Existing methods have been proposed to recalibrate the model by leveraging the disease incidence rates from the target cohort. However, they assume the same covariate distribution across cohorts and when the assumption is violated, the recalibrated model can be substantially biased. Further, recalibration is also complicated by the two-phase sampling design that is commonly used for developing risk prediction models. In this paper, we develop a weighted estimating-equation approach accounting for the two-phase design and combine it with a weighted empirical likelihood that leverages the summary information on both disease incidence rates and covariates from the target cohort. We provide a resampling-based inference procedure. Our extensive simulation results show that using the summary information from the target population, the proposed recalibration method yields nearly unbiased risk estimates under a wide range of scenarios. An application to a colorectal cancer study also illustrates that the proposed method yields a well-calibrated model in the target cohort.

The nested case-control (NCC) design has been widely adopted as a cost-effective sampling design for biomarker research. Under the NCC design, markers are only measured for the NCC subcohort consisting of all cases and a fraction of the controls selected randomly from the matched risk sets of the cases. Robust methods for evaluating prediction performance of risk models have been derived under the inverse probability weighting framework. The probabilities of samples being included in the NCC cohort can be calculated based on the study design ``a previous study'' or estimated non-parametrically ``a previous study''. Neither strategy works well due to model mis-specification and the curse of dimensionality in practical settings where the sampling does not entirely follow the study design or depends on many factors. In this paper, we propose an alternative strategy to estimate the sampling probabilities based on a varying coefficient model, which attains a balance between robustness and the curse of dimensionality. The complex correlation structure induced by repeated finite risk set sampling makes the standard resampling procedure for variance estimation fail. We propose a perturbation resampling procedure that provides valid interval estimation for the proposed estimators. Simulation studies show that the proposed method performs well in finite samples. We apply the proposed method to the Nurses' Health Study II to develop and evaluate prediction models using clinical biomarkers for cardiovascular risk.

Panel current status data arise frequently in biomedical studies when the occurrence of a particular clinical condition is only examined at several prescheduled visit times. Existing methods for analyzing current status data have largely focused on regression modeling based on commonly used survival models such as the proportional hazards model and the accelerated failure time model. However, these procedures have the limitations of being difficult to implement and performing sub-optimally in relatively small sample sizes. The performance of these procedures is also unclear under model mis-specification. In addition, no methods currently exist to evaluate the prediction performance of estimated risk models with panel current status data. In this paper, we propose a simple estimator under a general class of non-parametric transformation (NPT) models by fitting a logistic regression working model and demonstrate that our proposed estimator is consistent for the NPT model parameter up to a scale multiplier. Furthermore, we propose non-parametric estimators for evaluating the prediction performance of the risk score derived from model fitting, which is valid regardless of the adequacy of the fitted model. Extensive simulation results suggest that our proposed estimators perform well in finite samples and the regression parameter estimators outperform existing estimators under various scenarios. We illustrate the proposed procedures using data from the Framingham Offspring Study.

Novel biomarkers, in combination with currently available clinical information, have been sought to improve clinical decision making in many branches of medicine, including screening, surveillance, and prognosis. Statistical methods are needed to integrate such diverse information to develop targeted interventions that balance benefit and harm. In the specific setting of disease detection, we propose novel approaches to construct a multiple-marker-based decision rule by directly optimizing a benefit function, while controlling harm at a maximally tolerable level. These new approaches include plug-in and direct-optimization-based algorithms, and they allow for the construction of both nonparametric and parametric rules. A study of asymptotic properties of the proposed estimators is provided. Simulation results demonstrate good clinical utilities for the resulting decision rules under various scenarios. The methods are applied to a biomarker study in prostate cancer surveillance.

Long-term follow-up is common in many medical investigations where the interest lies in predicting patients' risks for a future adverse outcome using repeatedly measured predictors over time. A key quantity is the likelihood of developing an adverse outcome among individuals who survived up to time s given their covariate information up to time s. Simple, yet reliable, methodology for updating the predicted risk of disease progression using longitudinal markers remains elusive. Two main approaches have been considered in the literature. One approach, based on joint modeling (JM) of failure time and longitudinal covariate process (Tsiatis and Davidian, 2004), derives such longitudinal predictive probability from the joint probability of a longitudinal marker and an event at a given time. A second approach, the partly conditional (PC) modeling (Zheng and Heagerty, 2005), directly models the predictive probability conditional on survival up to a landmark time and information accrued by that time. In this article, we propose new PC models for longitudinal prediction that are more flexible than joint modeling and improve the prediction accuracy over existing PC models. We provide procedures for making inference regarding future risk for an individual with longitudinal measures up to a given time. In addition, we conduct simulations to evaluate both JM and PC approaches in order to provide practical guidance on modeling choices. We use standard measures of predictive accuracy adapted to our setting to explore the predictiveness of the two approaches. We illustrate the performance of the two approaches on a dataset from the End Stage Renal Disease Study (ESRDS).

Accurate risk prediction models are needed to identify different risk groups for individualized prevention and treatment strategies. In the Nurses’ Health Study, to examine the effects of several biomarkers and genetic markers on the risk of rheumatoid arthritis (RA), a three-phase nested case-control (NCC) design was conducted, in which two sequential NCC subcohorts were formed with one nested within the other, and one set of new markers measured on each of the subcohorts. One objective of the study is to evaluate clinical values of novel biomarkers in improving upon existing risk models because of potential cost associated with assaying biomarkers. In this paper, we develop robust statistical procedures for constructing risk prediction models for RA and estimating the incremental value (IncV) of new markers based on three-phase NCC studies. Our method also takes into account possible time-varying effects of biomarkers in risk modeling, which allows us to more robustly assess the biomarker utility and address the question of whether a marker is better suited for short-term or long-term risk prediction. The proposed procedures are shown to perform well in finite samples via simulation studies.

BACKGROUND Investigations of folate-mediated one-carbon metabolism (FOCM) genes and gene-nutrient interactions with respect to colorectal cancer (CRC) risk are limited to candidate polymorphisms and dietary folate. This study comprehensively investigated associations between genetic variants in FOCM and CRC risk and whether the FOCM nutrient status modified these associations. METHODS Two hundred eighty-eight candidate and tagging single-nucleotide polymorphisms (SNPs) in 30 FOCM genes were genotyped for 821 incident CRC case-control matched pairs in the Women's Health Initiative Observational Study cohort. FOCM biomarkers (red blood cell [RBC] folate, plasma folate, pyridoxal-5′-phosphate [PLP], vitamin B12, and homocysteine) and self-reported alcohol consumption were measured at the baseline. Conditional logistic regression was implemented; effect modification was examined on the basis of known enzyme-nutrient relations. RESULTS Statistically significant associations were observed between CRC risk and functionally defined candidate SNPs of methylenetetrahydrofolate dehydrogenase 1 (MTHFD1; K134R), 5-methyltetrahydrofolate-homocysteine methyltransferase reductase (MTRR; P450R), and PR domain containing 2 with ZNF domain (PRDM2; S450N) and a literature candidate SNP of thymidylate synthase (TYMS; g.676789A>T; nominal P

The relationship between folate and colorectal cancer (CRC) risk is unclear. We investigated the association of two biomarkers of folate status, plasma folate and red blood cell (RBC) folate, with CRC risk using a nested case-control design in the Women's Health Initiative Observational Study. Postmenopausal women (n = 93,676) aged 50-79 years were enrolled in the Women's Health Initiative Observational Study (1993-1998). A fasting blood draw and extensive health, dietary and lifestyle data were collected upon enrollment. Through 2008, 988 incident CRC cases were reported and confirmed with medical records adjudication. Cases and controls were matched on age (± 3 years), enrollment date (± 1 year), race/ethnicity, blood draw date (± 6 months) and hysterectomy status. Plasma and RBC folate were determined by radio assay. Folate biomarker values were divided into quartiles, and conditional logistic regression estimated odds ratios (ORs) and 95% confidence intervals (CI) for the associations of folate with total CRC, by tumor site and by stage at diagnosis. Additional analyses examined whether risks varied across time periods corresponding to the United States folic acid fortification policy: prefortification (1994-1995), perifortification (1996-1997) and postfortification (1998). ORs for overall CRC risk comparing Q4 vs. Q1 were 0.91 (95% CI 0.67-1.24) and 0.91 (95% CI 0.67-1.23) for RBC and plasma folate, respectively. There were no changes in risk attributable to food supply fortification. These results do not support an overall association of folate with CRC risk and suggest that folic acid fortification of the US food supply did not alter the associations in these postmenopausal women.

Data are very limited on vitamin D and lung cancer prevention in high-risk populations. The authors investigated whether estimated vitamin D intake was associated with lung cancer risk and whether effect modification by vitamin A existed among current/former heavy smokers and workers with occupational exposure to asbestos. A case-cohort study selected 749 incident lung cancers and 679 noncases from the Carotene and Retinol Efficacy Trial (CARET), 1988-2005. The active intervention was supplementation of 30 mg β-carotene + 25,000 IU retinyl palmitate/day. Baseline total intake including both diet (from food frequency questionnaire) and personal supplements (from brand names linked to the labeled potencies) was assessed. Hazard ratios (HRs) were estimated by Cox proportional hazard models. No significant association of total vitamin D intake with lung cancer was observed overall. However, total vitamin D intake ≥600 versus

For rare-variant association analysis, due to extreme low frequencies of these variants, it is necessary to aggregate them by a prior set (e.g., genes and pathways) in order to achieve adequate power. In this paper, we consider hierarchical models to relate a set of rare variants to phenotype by modeling the effects of variants as a function of variant characteristics while allowing for variant-specific effect (heterogeneity). We derive a set of two score statistics, testing the group effect by variant characteristics and the heterogeneity effect. We make a novel modification to these score statistics so that they are independent under the null hypothesis and their asymptotic distributions can be derived. As a result, the computational burden is greatly reduced compared with permutation-based tests. Our approach provides a general testing framework for rare variants association, which includes many commonly used tests, such as the burden test [Li and Leal, 2008] and the sequence kernel association test [Wu et al., 2011], as special cases. Furthermore, in contrast to these tests, our proposed test has an added capacity to identify which components of variant characteristics and heterogeneity contribute to the association. Simulations under a wide range of scenarios show that the proposed test is valid, robust, and powerful. An application to the Dallas Heart Study illustrates that apart from identifying genes with significant associations, the new method also provides additional information regarding the source of the association. Such information may be useful for generating hypothesis in future studies.

Initial studies have investigated the association between inflammation and colorectal cancer (CRC) using C-reactive protein (CRP) as a proinflammatory biomarker and have noted inconsistent results among women. We here report the findings from a large prospective study with repeat measurements of CRP, as well as serum amyloid A (SAA), an additional biomarker of inflammation, and risk of CRC. In the Women's Health Initiative Observational Study, we examined associations of CRP and SAA with CRC using repeat assessments (baseline and 3-year follow-up) among 953 matched case-control pairs for CRP and 966 pairs for SAA. Multivariate-adjusted conditional-logistic regression models were used with two-sided tests of significance. Receiver operating characteristic (ROC) curve analysis assessed their utility as early detection markers. Colon cancer risk (odds ratio [OR] and 95% confidence intervals) among women in the highest quintiles of CRP or SAA compared to those in the lowest quintiles was ORcolon/CRP = 1.37 (0.95-1.97, p-trend = 0.04) and ORcolon/SAA = 1.26 (0.88-1.80, p-trend = 0.10), respectively. Women with elevated concentrations of both CRP and SAA had an increased risk of ORcolon = 1.50 (1.12-2.00, p-value = 0.006) compared to those with low concentrations. No positive associations were observed with rectal cancer and weaker associations for CRC overall. Temporal changes in biomarkers more than 3 years did not predict risk. The area under the 6-month ROC curve for CRP+SAA was 0.62 (95% confidence interval = 0.55-0.68). Elevated inflammatory biomarkers are associated with an increased risk of CRC, mainly colon cancer. Nevertheless, changes in the biomarkers over time do not suggest that they merit consideration as early detection markers for CRC.

Identification of novel biomarkers for risk assessment is important for both effective disease prevention and optimal treatment recommendation. Discovery relies on the precious yet limited resource of stored biological samples from large prospective cohort studies. Case-cohort sampling design provides a cost-effective tool in the context of biomarker evaluation, especially when the clinical condition of interest is rare. Existing statistical methods focus on making efficient inference on relative hazard parameters from the Cox regression model. Drawing on recent theoretical development on the weighted likelihood for semiparametric models under two-phase studies (Breslow and Wellner, 2007), we propose statistical methods to evaluate accuracy and predictiveness of a risk prediction biomarker, with censored time-to-event outcome under stratified case-cohort sampling. We consider nonparametric methods and a semiparametric method. We derive large sample properties of proposed estimators and evaluate their finite sample performance using numerical studies. We illustrate new procedures using data from Framingham Offspring study to evaluate the accuracy of a recently developed risk score incorporating biomarker information for predicting cardiovascular disease.

Recently meta-analysis has been widely utilized to combine information across multiple studies to evaluate a common effect. Integrating data from similar studies is particularly useful in genomic studies where the individual study sample sizes are not large relative to the number of parameters of interest. In this article, we are interested in developing robust prognostic rules for the prediction of t-year survival based on multiple studies. We propose to construct a composite score for prediction by fitting a stratified semiparametric transformation model that allows the studies to have related but not identical outcomes. To evaluate the accuracy of the resulting score, we provide point and interval estimators for the commonly used accuracy measures including the time-specific receiver operating characteristic curves, and positive and negative predictive values. We apply the proposed procedures to develop prognostic rules for the 5-year survival of breast cancer patients based on five breast cancer genomic studies.

Combining data collected from different sources can potentially enhance statistical efficiency in estimating effects of environmental or genetic factors or gene-environment interactions. However, combining data across studies becomes complicated when data are collected under different study designs, such as family-based and unrelated individual-based case-control design. In this article, we describe likelihood-based approaches that permit the joint estimation of covariate effects on disease risk under study designs that include cases, relatives of cases, and unrelated individuals. Our methods accommodate familial residual correlation and a variety of ascertainment schemes. Extensive simulation experiments demonstrate that the proposed methods for estimation and inference perform well in realistic settings. Efficiencies of different designs are contrasted in the simulation. We applied the methods to data from the Colorectal Cancer Family Registry.

Rigorous statistical evaluation of the predictive values of novel biomarkers is critical prior to applying novel biomarkers into routine standard care. It is important to identify factors that influence the performance of a biomarker in order to determine the optimal conditions for test performance. We propose a covariate-specific time-dependent positive predictive values curve to quantify the predictive accuracy of a prognostic marker measured on a continuous scale and with censored failure time outcome. The covariate effect is accommodated with a semiparametric regression model framework. In particular, we adopt a smoothed survival time regression technique (Dabrowska, 1997, The Annals of Statistics 25, 1510-1540) to account for the situation where risk for the disease occurrence and progression is likely to change over time. In addition, we provide asymptotic distribution theory and resampling-based procedures for making statistical inference on the covariate-specific positive predictive values. We illustrate our approach with numerical studies and a dataset from a prostate cancer study.

The receiver operating characteristic (ROC) curve is a prominent tool for characterizing the accuracy of a continuous diagnostic test. To account for factors that might influence the test accuracy, various ROC regression methods have been proposed. However, as in any regression analysis, when the assumed models do not fit the data well, these methods may render invalid and misleading results. To date, practical model-checking techniques suitable for validating existing ROC regression models are not yet available. In this article, we develop cumulative residual-based procedures to graphically and numerically assess the goodness of fit for some commonly used ROC regression models, and show how specific components of these models can be examined within this framework. We derive asymptotic null distributions for the residual processes and discuss resampling procedures to approximate these distributions in practice. We illustrate our methods with a dataset from the cystic fibrosis registry.

Summary The rapid advancement in molecule technology has led to the discovery of many markers that have potential applications in disease diagnosis and prognosis. In a prospective cohort study, information on a panel of biomarkers as well as the disease status for a patient are routinely collected over time. Such information is useful to predict patients' prognosis and select patients for targeted therapy. In this article, we develop procedures for constructing a composite test with optimal discrimination power when there are multiple markers available to assist in prediction and characterize the accuracy of the resulting test by extending the time-dependent receiver operating characteristic (ROC) curve methodology (Heagerty, Lumley, and Pepe, 2000, Biometrics56, 337–344). We employ a modified logistic regression model to derive optimal linear composite scores such that their corresponding ROC curves are maximized at every false positive rate. We provide theoretical justification for using such a model for prognostic accuracy. The proposed method allows for time-varying marker effects and accommodates censored failure time outcome. When the effects of markers are approximately constant over time, we propose a more efficient estimating procedure under such models. We conduct numerical studies to evaluate the performance of the proposed procedures. Our results indicate the proposed methods are both flexible and efficient. We contrast these methods with an application concerning the prognostic accuracies of expression levels of six genes.

Aberrant methylation of 5'gene promoter regions associated with gene silencing is an epigenetic phenomenon responsible for silencing of tumor suppressor genes in many cancer types. The aims of our study were to study the role of methylation of a large panel of genes during multistage pathogenesis and to correlate our findings with patient age and other clinico-pathological features. We investigated the aberrant promoter methylation profile of 19 genes in 92 colorectal cancers (CRCs) and corresponding nonmalignant epithelia (NME) (n = 57), and selected 15 genes for studying 26 colorectal adenomas (CAs). On the Basis of our results, the genes could be divided into 3 groups. Group 1 consisted of 13 genes whose methylation was tumor-specific. For 8 of these genes, the methylation frequencies in CAs were similar to those of CRCs, but significantly different from the frequencies in NME. Group 2, consisting of 2 genes demonstrating little or no methylation, were present in any sample type. In Group 3, consisting of 4 genes, relatively frequent methylation was present in both CRCs and NME, and the differences between these specimen types were not significant. Methylation of Group 1 genes were tightly correlated with each other, and these genes demonstrated increased methylation frequencies in CRCs with increasing age. Methylation was not correlated with other clinico-pathological features. In general, methylation frequencies of CAs were intermediate between CRCs and NME. Our study constitutes the most comprehensive methylation profile of CRCs, demonstrates that methylation commences early during CRC pathogenesis and is an age-related phenomenon.

La performance des tests diagnostiques medicaux est souvent evaluee en comparant le resultat du test au vrai etat de la maladie du patient. L'analyse des courbes de caracteristiques de fonctionnement (ROC) peut etre utilisee pour resumer la precision du test. Cependant une telle analyse peut rencontrer plusieurs difficultes dans la pratique reelle. Une difficulte est la verification du biais, c'est-a-dire que l'evaluation de l'etat de la maladie peut etre partiellement disponible et la probabilite de determination de la maladie peut dependre aussi bien du resultat du test que des caracteristiques du sujet. Une deuxieme difficulte est que les tests interpretes par le meme lecteur peuvent ne pas etre independants. A l'aide des equations d'estimation nous generalisons des methodes proposees pour prendre en compte ces problemes. Nous comparons la performance de differents estimateurs de la precision en utilisant les estimateurs robustes de la variance sandwich pour permettre une inference asymptotique valide. Nous montrons que dans le contexte d'une cohorte d'observation ou de bonnes informations sur les covariables sont disponibles, une approche par des equations d'estimations ponderees (WEE) peut etre preferable pour sa robustesse a un modele mal specifie. Nous appliquons la methodologie a la mammographie comme realisee dans la communaute des radiologues.

Summary The predictive accuracy of a survival model can be summarized using extensions of the proportion of variation explained by the model, or R2, commonly used for continuous response models, or using extensions of sensitivity and specificity, which are commonly used for binary response models. In this article we propose new time-dependent accuracy summaries based on time-specific versions of sensitivity and specificity calculated over risk sets. We connect the accuracy summaries to a previously proposed global concordance measure, which is a variant of Kendall's tau. In addition, we show how standard Cox regression output can be used to obtain estimates of time-dependent sensitivity and specificity, and time-dependent receiver operating characteristic (ROC) curves. Semiparametric estimation methods appropriate for both proportional and nonproportional hazards data are introduced, evaluated in simulations, and illustrated using two familiar survival data sets.

This study assessed associations between plasma biomarkers of choline metabolism [choline, betaine, dimethylglycine, trimethylamine N-oxide (TMAO)] and CRC risk in postmenopausal women. We selected 835 matched case-control pairs within the WHI-OS and measured baseline choline metabolites by liquid chromatography-tandem mass spectrometry. CRC was assessed by self-report and confirmed by medical records over the mean 5.2 y of follow-up. In multivariate-adjusted conditional logistic regression models, plasma choline tended to be positively related to rectal cancer risk [OR (95% CI) for the highest vs. lowest quartile: 2.44 (0.93, 6.40); P-trend=0.08], while plasma betaine was inversely related to CRC risk [0.68 (0.47, 0.99); P-trend=0.01]. The ratio of plasma betaine to choline was a stronger predictor of CRC risk than either metabolite alone [0.56 (0.39, 0.82); P-trend=0.004 for total CRC and 0.27 (0.10, 0.78); P-trend=0.02 for rectal tumors]. Plasma TMAO was positively related to rectal cancer [3.38 (1.25,...