Medicare costs for endovascular abdominal aortic aneurysm treatment in the Vascular Quality Initiative.
Academic Article
Overview
abstract
BACKGROUND: The ability to make good choices relies on the quality of information available and on the manner in which it is presented. The highest-quality information that can be presented to patients is that which is untinged from bias that distorts the comparative effectiveness of 1 treatment or approach over that of another. Two important bodies of literature consider instrumental variable (IV) methods to account for unmeasured confounding in observational data and the use of survival analysis methods to account for censoring of time-to-event outcomes. However, there is minimal research at the intersection of these areas. Especially lacking are IV methods for the Cox (proportional hazards) regression model. After developing improved methods for attaining estimates of comparative effectiveness in observational data, there remains the problem of how best to communicate risks and comparative risks to patients. Established research in shared decision-making recognizes the importance of effective communication of risks of alternative treatments to physicians and patients. However, there is little research comparing different risk formats for communicating survival time data (eg, survival probabilities vs survival times), especially when treatment effects vary between short- and long-term follow-up. Any trade-off between short- and long-term risks is important for patients to understand. OBJECTIVES: To develop IV methodology for the Cox model and demonstrate its ability to overcome unmeasured confounding in observational data, such as the Vascular Quality Initiative (VQI) patient registry, including when treatment effect heterogeneity occurs over follow-up time and over baseline predictors. Another objective was to engage VQI patients with carotid artery disease to identify the best risk communication formats to present the results of IV Cox model analyses. METHODS: We used statistical derivations to develop the appropriate IV procedure for the Cox model with homogeneous and heterogeneous treatment effects. The resulting methods are compared using simulated data; because the true value of the quantity being estimated is known, this allows the performance of each method to be determined. We compare the specifications of the Cox model IV procedure and naive methods that ignore unmeasured confounding. In the analysis of VQI observational data, comparator methods include unadjusted analysis, Cox regression models that ignored unmeasured confounding, propensity score matching, and the direct adaptation of the standard IV procedure for nonlinear models to the Cox model. To determine how different representations of survival risk information are interpreted by patients, we conducted a qualitative survey of VQI patients needing to make treatment decisions about carotid artery disease in which we asked them to provide feedback on various formats. RESULTS: The key theoretical result is that an unmeasured confounder in the Cox model may be accounted for by adjusting for the residual from the treatment selection equation and introducing an individual-level parameter (this parameter is referred to as a frailty in survival analysis parlance, as it captures the extent to which an individual is more or less at risk of the outcome event due to unmeasured factors). In the absence of random error, the residual from the first-stage equation is proportional to the magnitude and direction of the unmeasured confounder, which if ignored leads to bias due to the noncollapsibility (the failure of a model to remain in the same family of models when a predictor is excluded) of the Cox model. The resulting 2-stage residual inclusion-frailty (2SRI-F) procedure is statistically consistent under standard regularity conditions, outperforms all statistical approaches compared in our simulation when the statistical model is correctly specified, and is robust to incorrect specification of the distribution of the frailty. Furthermore, when the treatment effect varies over follow-up time, only a single IV is needed, but the residual from the estimated treatment selection equation and the univariate frailty must have time-dependent coefficients in the second-stage equation. Related to patient communication, patients find it easier to understand risk information when it is communicated in the form of pie charts rather than icon arrays, which were consistently viewed as being too complex and visually confusing, especially when a time horizon is introduced. CONCLUSIONS: The strong robustness of 2SRI-F to model misspecification is attributed to the role of the frailty being able to account for noise from the treatment selection process. We recommend using 2SRI-F procedures when the proportional hazards assumption holds and when the treatment effect is time dependent. The improved performance of 2SRI-F was smaller in the latter case. In all cases, current statistical software only approximates estimates of individual frailties, biasing 2SRI-F performance assessments to underestimate the true performance gain over incumbent approaches. In the context of carotid artery stenosis treatment, patients preferred time-dependent risk of stroke and death to be displayed using pie charts rather than icon arrays, a result that requires further investigation. LIMITATIONS: Existing statistical software for estimating models with frailties relies on approximations that hinder the performance of 2SRI-F. In future work, customized frailty estimation procedures should be developed to improve on our easy-to-compute estimation procedure. In the qualitative risk communication study, we only studied 27 patients in a single disease group (ie, carotid artery disease). It is possible that patients with different diseases (eg, cancer), education, or socioeconomic status will have different risk communication preferences.
