An approximate quasi‐likelihood approach for error‐prone failure time outcomes and exposures

Abstract

Measurement error arises commonly in clinical research settings that rely on data from electronic health records or large observational cohorts. In particular, self-reported outcomes are typical in cohort studies for chronic diseases such as diabetes in order to avoid the burden of expensive diagnostic tests.Dietary intake, which is also commonly collected by self-report and subject to measurement error, is a major factor linked to diabetes and other chronic diseases. These errors can bias exposure-disease associations that ultimately can mislead clinical decision-making. We have extended an existing semiparametric likelihood-based method for handling error-prone, discrete failure time outcomes to also address covariate error. We conduct an extensive numerical study to compare the proposed method to the naive approach that ignores measurement error in terms of bias and efficiency in the estimation of the regression parameter of interest. In all settings considered, the proposed method showed minimal bias and maintained coverage probability, thus outperforming the naive analysis which showed extreme bias and low coverage. This method is applied to data from the Women's Health Initiative to assess the association between energy and protein intake and the risk of incident diabetes mellitus. Our results show that correcting for errors in both the self-reported outcome and dietary exposures leads to considerably different hazard ratio estimates than those from analyses that ignore measurement error, which demonstrates the importance of correcting for both outcome and covariate error.

An augmented likelihood approach for the Cox proportional hazards model with interval-censored auxiliary and validated outcome data—with application to the Hispanic Community Health Study/Study of Latinos

“…Following previous work to address misclassified interval-censored outcomes in the proportional hazards model, 9,1,10 we assume the n i error-prone outcomes Y i j * are conditionally independent given the true disease status and event time T i, such that P false( boldY boldi bold∗ | T i , boldT boldi bold∗ , Δ i , V i false) = ∏ l = 1 n i P false( Y i l * | T i , T i l * , Δ i , V i false). Note, in our setting, this “conditional independence” assumption is weaker than full conditional independence as the self-reported outcome is only collected through the first self-reported positive result.…”

“…13,18 Additionally, regression calibration has been shown to work well under these same settings when also correcting for errors in time-to-event outcomes. 9…”

“…13,18 Additionally, regression calibration has been shown to work well under these same settings when also correcting for errors in time-toevent outcomes. 9 As we described in Section 2.2, variance estimation for data from a complex survey design often requires extra steps to address within-cluster correlation. When regression calibration is applied, variance estimates from the outcome model need to be adjusted further to account for the extra uncertainty added by the calibration model step.…”

“…Gu et al 1 developed a likelihood-based method that models the association of a covariate with an interval-censored time-to-event outcome recorded by error-prone self-reports or imperfect diagnostic tests, assuming the proportional hazards model. Boe et al 9 extended this work by incorporating regression calibration to additionally adjust for covariate measurement error for cases in which one or more exposure variables of interest are also recorded with error. Each of these methods addressed the misclassification by incorporating externally estimated sensitivity and specificity into the estimation.…”