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1.  Observational studies analyzed like randomized experiments: an application to postmenopausal hormone therapy and coronary heart disease 
Epidemiology (Cambridge, Mass.)  2008;19(6):766-779.
Background
The Women’s Health Initiative randomized trial found greater coronary heart disease (CHD) risk in women assigned to estrogen/progestin therapy than in those assigned to placebo. Observational studies had previously suggested reduced CHD risk in hormone users.
Methods
Using data from the observational Nurses’ Health Study, we emulated the design and intention-to-treat (ITT) analysis of the randomized trial. The observational study was conceptualized as a sequence of “trials” in which eligible women were classified as initiators or noninitiators of estrogen/progestin therapy.
Results
The ITT hazard ratios (95% confidence intervals) of CHD for initiators versus noninitiators were 1.42 (0.92 – 2.20) for the first 2 years, and 0.96 (0.78 – 1.18) for the entire follow-up. The ITT hazard ratios were 0.84 (0.61 – 1.14) in women within 10 years of menopause, and 1.12 (0.84 – 1.48) in the others (P value for interaction = 0.08). These ITT estimates are similar to those from the Women’s Health Initiative. Because the ITT approach causes severe treatment misclassification, we also estimated adherence-adjusted effects by inverse probability weighting. The hazard ratios were 1.61 (0.97 – 2.66) for the first 2 years, and 0.98 (0.66 – 1.49) for the entire follow-up. The hazard ratios were 0.54 (0.19 – 1.51) in women within 10 years after menopause, and 1.20 (0.78 – 1.84) in others (P value for interaction = 0.01). Finally, we also present comparisons between these estimates and previously reported NHS estimates.
Conclusions
Our findings suggest that the discrepancies between the Women’s Health Initiative and Nurses’ Health Study ITT estimates could be largely explained by differences in the distribution of time since menopause and length of follow-up.
doi:10.1097/EDE.0b013e3181875e61
PMCID: PMC3731075  PMID: 18854702
2.  Observational data for comparative effectiveness research: an emulation of randomised trials to estimate the effect of statins on primary prevention of coronary heart disease 
This article reviews methods to estimate treatment effectiveness research using observational data. The basic idea is using an observational study to emulate a hypothetical randomised trial by comparing initiators vs. non-initiators of treatment. After adjustment for baseline confounders, one can estimate the analogue of the intention-to-treat effect. We also explain two approaches to adjust for imperfect adherence using the per-protocol and as-treated analyses after adjusting for measured time-varying confounding and selection bias using inverse probability weighting of marginal structural models.
As an example, we implemented these methods to estimate the effect of statins for primary prevention of coronary heart disease (CHD) using data from electronic medical records in the United Kingdom. Despite strong confounding by indication, our approach detected a potential benefit of statin therapy. The analogue of the intention-to-treat hazard ratio of CHD was 0.89 (0.73, 1.09) for statin initiators vs. noninitiators. The hazard ratio of CHD was 0.84 (0.54, 1.30) in the per-protocol analysis and 0.79 (0.41, 1.41) in the as-treated analysis for 2-years of use vs. no use. In contrast, a conventional comparison of current users vs. never users of statin therapy resulted in a hazard ratio of 1.31 (1.04, 1.66). We provide a flexible and annotated SAS program to implement the proposed analyses.
doi:10.1177/0962280211403603
PMCID: PMC3613145  PMID: 22016461
comparative effectiveness; confounding; intention-to-treat analysis; per-protocol analysis; as-treated analysis; selection bias; inverse-probability weighting
3.  Estimating absolute risks in the presence of nonadherence: An application to a follow-up study with baseline randomization 
Epidemiology (Cambridge, Mass.)  2010;21(4):528-539.
The intention-to-treat (ITT) analysis provides a valid test of the null hypothesis and naturally results in both absolute and relative measures of risk. However, this analytic approach may miss the occurrence of serious adverse effects that would have been detected under full adherence to the assigned treatment. Inverse probability weighting of marginal structural models has been used to adjust for nonadherence, but most studies have provided only relative measures of risk. In this study, we used inverse probability weighting to estimate both absolute and relative measures of risk of invasive breast cancer under full adherence to the assigned treatment in the Women’s Health Initiative estrogen-plus-progestin trial. In contrast to an ITT hazard ratio (HR) of 1.25 (95% confidence interval [CI] = 1.01 to 1.54), the HR for 8-year continuous estrogen-plus-progestin use versus no use was 1.68 (1.24 to 2.28). The estimated risk difference (cases/100 women) at year 8 was 0.83 (−0.03 to 1.69) in the ITT analysis, compared with 1.44 (0.52 to 2.37) in the adherence-adjusted analysis. Results were robust across various dose-response models. We also compared the dynamic treatment regime “take hormone therapy until certain adverse events become apparent, then stop taking hormone therapy” with no use (HR= 1.64; 95% CI = 1.24 to 2.18). The methods described here are also applicable to observational studies with time-varying treatments.
doi:10.1097/EDE.0b013e3181df1b69
PMCID: PMC3315056  PMID: 20526200
4.  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
5.  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
6.  Coronary heart disease in postmenopausal recipients of estrogen plus progestin therapy: Does the increased risk ever disappear? A randomized trial 
Annals of internal medicine  2010;152(4):211-217.
Background
Estrogen-plus-progestin therapy increases the risk of coronary heart disease (CHD) in postmenopausal women. However, this increased risk might be limited to the first years of use and to women who start therapy late in menopause.
Objective
To estimate the effect of continuous estrogen-plus-progestin therapy on CHD risk over time and stratified by years since menopause, i.e., to estimate an adherence-adjusted effect.
Design
The Women's Health Initiative randomized, double-blinded, placebo-controlled trial.
Setting
40 US clinical centers.
Patients
16,608 postmenopausal women with an intact uterus at baseline in 1993-1998
Intervention
Conjugated equine estrogens, 0.625 mg/d, plus medroxyprogesterone acetate, 2.5 mg/d or placebo.
Measurements
Adherence-adjusted hazard ratios (HRs) estimated via inverse probability weighting and CHD-free survival curves.
Results
Compared with no use of hormone therapy, the HR (95% confidence interval [CI]) for continuous use of estrogen-plus-progestin was 2.36 (1.55-3.62) for the first 2 years and 1.69 (0.98-2.89) for the first 8 years. For women within 10 years after menopause, the HRs (95% CI) were 1.29 (0.52-3.18) for the first 2 years and 0.64 (0.21-1.99) for the first 8 years, and the CHD-free survival curves for continuous use and no use of estrogen-plus-progestin crossed at about 6 (95% CI: 2-10) years.
Limitations
The analysis may have not fully adjusted for joint determinants of adherence and CHD risk. Sample sizes for some subgroup analyses were small.
Conclusions
There was no suggestion of a decreased risk of CHD from estrogen-plus-progestin within the first 2 years after randomization, including women who initiated therapy within 10 years after menopause, and a cardioprotective effect became apparent only after 6 years of use.
doi:10.1059/0003-4819-152-4-201002160-00005
PMCID: PMC2936769  PMID: 20157135

Results 1-6 (6)