Raking and regression calibration: Methods to address bias from correlated covariate and time-to-event error.

Medical studies that depend on electronic health records (EHR) data are often subject to measurement error, as the data are not collected to support research questions under study. These data errors, if not accounted for in study analyses, can obscure or cause spurious associations between patient exposures and disease risk. Methodology to address covariate measurement error has been well developed; however, time-to-event error has also been shown to cause significant bias, but methods to address it are relatively underdeveloped. More generally, it is possible to observe errors in both the covariate and the time-to-event outcome that are correlated. We propose regression calibration (RC) estimators to simultaneously address correlated error in the covariates and the censored event time. Although RC can perform well in many settings with covariate measurement error, it is biased for nonlinear regression models, such as the Cox model. Thus, we additionally propose raking estimators which are consistent estimators of the parameter defined by the population estimating equation. Raking can improve upon RC in certain settings with failure-time data, require no explicit modeling of the error structure, and can be utilized under outcome-dependent sampling designs. We discuss features of the underlying estimation problem that affect the degree of improvement the raking estimator has over the RC approach. Detailed simulation studies are presented to examine the performance of the proposed estimators under varying levels of signal, error, and censoring. The methodology is illustrated on observational EHR data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.

Improved generalized raking estimators to address dependent covariate and failure-time outcome error.

Biomedical studies that use electronic health records (EHR) data for inference are often subject to bias due to measurement error. The measurement error present in EHR data is typically complex, consisting of errors of unknown functional form in covariates and the outcome, which can be dependent. To address the bias resulting from such errors, generalized raking has recently been proposed as a robust method that yields consistent estimates without the need to model the error structure. We provide rationale for why these previously proposed raking estimators can be expected to be inefficient in failure-time outcome settings involving misclassification of the event indicator. We propose raking estimators that utilize multiple imputation, to impute either the target variables or auxiliary variables, to improve the efficiency. We also consider outcome-dependent sampling designs and investigate their impact on the efficiency of the raking estimators, either with or without multiple imputation. We present an extensive numerical study to examine the performance of the proposed estimators across various measurement error settings. We then apply the proposed methods to our motivating setting, in which we seek to analyze HIV outcomes in an observational cohort with EHR data from the Vanderbilt Comprehensive Care Clinic.

Considerations for analysis of time-to-event outcomes measured with error: Bias and correction with SIMEX.

For time-to-event outcomes, a rich literature exists on the bias introduced by covariate measurement error in regression models, such as the Cox model, and methods of analysis to address this bias. By comparison, less attention has been given to understanding the impact or addressing errors in the failure time outcome. For many diseases, the timing of an event of interest (such as progression-free survival or time to AIDS progression) can be difficult to assess or reliant on self-report and therefore prone to measurement error. For linear models, it is well known that random errors in the outcome variable do not bias regression estimates. With nonlinear models, however, even random error or misclassification can introduce bias into estimated parameters. We compare the performance of 2 common regression models, the Cox and Weibull models, in the setting of measurement error in the failure time outcome. We introduce an extension of the SIMEX method to correct for bias in hazard ratio estimates from the Cox model and discuss other analysis options to address measurement error in the response. A formula to estimate the bias induced into the hazard ratio by classical measurement error in the event time for a log-linear survival model is presented. Detailed numerical studies are presented to examine the performance of the proposed SIMEX method under varying levels and parametric forms of the error in the outcome. We further illustrate the method with observational data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.

The carbon isotope ratios of nonessential amino acids identify sugar-sweetened beverage (SSB) consumers in a 12-wk inpatient feeding study of 32 men with varying SSB and meat exposures.

BACKGROUND: The carbon isotope ratios (CIRs) of individual amino acids (AAs) may provide more sensitive and specific biomarkers of sugar-sweetened beverages (SSBs) than total tissue CIR. Because CIRs turn over slowly, long-term controlled-feeding studies are needed in their evaluation. OBJECTIVE: We assessed the responses of plasma and RBC CIRAA's to SSB and meat intake in a 12-wk inpatient feeding study. METHODS: Thirty-two men (aged 46.2 ± 10.5 y) completed the feeding study at the National Institute of Diabetes and Digestive and Kidney Diseases in Phoenix, Arizona. The effects of SSB, meat, and fish intake on plasma and RBC CIRAA's were evaluated in a balanced factorial design with each dietary variable either present or absent in a common weight-maintaining, macronutrient-balanced diet. Fasting blood samples were collected biweekly from baseline. Dietary effects on the postfeeding CIR of 5 nonessential AAs (CIRNEAA's) and 4 essential AAs (CIREAA's) were analyzed using multivariable regression. RESULTS: In plasma, 4 of 5 CIRNEAA's increased with SSB intake. Of these, the CIRAla was the most sensitive (ß = 2.81, SE = 0.38) to SSB intake and was not affected by meat or fish intake. In RBCs, all 5 CIRNEAA's increased with SSBs but had smaller effect sizes than in plasma. All plasma CIREAA's increased with meat intake (but not SSB or fish intake), and the CIRLeu was the most sensitive (ß = 1.26, SE = 0.23). CIRs of leucine and valine also increased with meat intake in RBCs. Estimates of turnover suggest that CIRAA's in plasma, but not RBCs, were in equilibrium with the diets by the end of the study. CONCLUSIONS: The results of this study in men support CIRNEAA's as potential biomarkers of SSB intake and suggest CIREAA's as potential biomarkers of meat intake in US diets. This trial was registered at clinicaltrials.gov/ct2/show/NCT01237093 as NCT01237093.

Associations of plasma, RBCs, and hair carbon and nitrogen isotope ratios with fish, meat, and sugar-sweetened beverage intake in a 12-wk inpatient feeding study.

BACKGROUND: Naturally occurring carbon and nitrogen stable isotope ratios [13C/12C (CIR) and 15N/14N (NIR)] are promising dietary biomarkers. As these candidate biomarkers have long tissue residence times, long-term feeding studies are needed for their evaluation. OBJECTIVE: Our aim was to evaluate plasma, RBCs, and hair CIR and NIR as biomarkers of fish, meat, and sugar-sweetened beverage (SSB) intake in a 12-wk dietary intervention. METHODS: Thirty-two men (aged 46.2 ± 10.5 y; BMI: 27.2 ± 4.0 kg/m2) underwent a 12-wk inpatient dietary intervention at the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) in Phoenix, Arizona. The effects of fish, meat, and SSB intake on CIR and NIR were evaluated using a balanced factorial design, with each intake factor at 2 levels (present/absent) in a common, background diet (50% carbohydrate, 30% fat, 20% protein). Fasting blood samples were taken biweekly from baseline, and hair samples were collected at baseline and postintervention. Data were analyzed using multivariable regression. RESULTS: The postintervention CIR of plasma was elevated when diets included meat (ß = 0.89, 95% CI: 0.73,1.05) and SSBs (ß = 0.48, 95% CI: 0.32, 0.64). The postintervention NIR of plasma was elevated when diets included fish (ß = 0.85, 95% CI: 0.64, 1.05) and meat (ß = 0.61, 95% CI: 0.42, 0.8). Results were similar for RBCs and hair. Postintervention RBC CIR and NIR had strong associations with baseline, suggesting that turnover to the intervention diets was incomplete after 12 wk. Estimates of isotopic turnover rate further confirmed incomplete turnover of RBCs. CONCLUSIONS: CIR was associated with meat and SSBs, and more strongly with meat. NIR was associated with fish and meat, and more strongly with fish. Overall, CIR and NIR discriminated between dietary fish and meat, and to a lesser extent SSBs, indicating their potential utility as biomarkers of intake in US diets. Approaches to make these biomarkers more specific are needed. This trial was registered at clinicaltrials.gov as NCT01237093.