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1.  Regression Calibration with Heteroscedastic Error Variance 
The problem of covariate measurement error with heteroscedastic measurement error variance is considered. Standard regression calibration assumes that the measurement error has a homoscedastic measurement error variance. An estimator is proposed to correct regression coefficients for covariate measurement error with heteroscedastic variance. Point and interval estimates are derived. Validation data containing the gold standard must be available. This estimator is a closed-form correction of the uncorrected primary regression coefficients, which may be of logistic or Cox proportional hazards model form, and is closely related to the version of regression calibration developed by Rosner et al. (1990). The primary regression model can include multiple covariates measured without error. The use of these estimators is illustrated in two data sets, one taken from occupational epidemiology (the ACE study) and one taken from nutritional epidemiology (the Nurses’ Health Study). In both cases, although there was evidence of moderate heteroscedasticity, there was little difference in estimation or inference using this new procedure compared to standard regression calibration. It is shown theoretically that unless the relative risk is large or measurement error severe, standard regression calibration approximations will typically be adequate, even with moderate heteroscedasticity in the measurement error model variance. In a detailed simulation study, standard regression calibration performed either as well as or better than the new estimator. When the disease is rare and the errors normally distributed, or when measurement error is moderate, standard regression calibration remains the method of choice.
doi:10.2202/1557-4679.1259
PMCID: PMC3404553  PMID: 22848187
measurement error; logistic regression; heteroscedasticity; regression calibration
2.  When to Start Treatment? A Systematic Approach to the Comparison of Dynamic Regimes Using Observational Data* 
Dynamic treatment regimes are the type of regime most commonly used in clinical practice. For example, physicians may initiate combined antiretroviral therapy the first time an individual’s recorded CD4 cell count drops below either 500 cells/mm3 or 350 cells/mm3. This paper describes an approach for using observational data to emulate randomized clinical trials that compare dynamic regimes of the form “initiate treatment within a certain time period of some time-varying covariate first crossing a particular threshold.” We applied this method to data from the French Hospital database on HIV (FHDH-ANRS CO4), an observational study of HIV-infected patients, in order to compare dynamic regimes of the form “initiate treatment within m months after the recorded CD4 cell count first drops below x cells/mm3” where x takes values from 200 to 500 in increments of 10 and m takes values 0 or 3. We describe the method in the context of this example and discuss some complications that arise in emulating a randomized experiment using observational data.
doi:10.2202/1557-4679.1212
PMCID: PMC3406513  PMID: 21972433
dynamic treatment regimes; marginal structural models; HIV infection; antiretroviral therapy

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