Generalizations to Corrections of Measurement Error Effects for Dynamic Treatment Regimes

Abstract

Measurement error is a pervasive issue in questions of estimation and inference. Generally, any data which are measured with error will render the results of an analysis which ignores this error unreliable. This is a particular concern in health research, where many quantities of interest are typically subject to measurement error. One particular field of health research, precision medicine, has not yet seen a substantive attempt to account for measurement error. Dynamic treatment regimes (DTRs), which can be used to represent sequences of treatment decisions in a medical setting, have historically been analyzed assuming, implicitly, that all quantities are perfectly observable.

We consider the problem of optimal DTR estimation where quantities of interest may be subject to measurement error. The nature of this problem is such that many existing techniques to account for the effects of measurement error need to be expanded in order to accommodate the data which are available in practice. This expansion further highlights theoretical shortcomings in the existing methodologies.

This thesis begins by expanding existing methods for correcting for the effects of measurement error to accommodate issues which are frequently observed in real-world data. We expand the most commonly applied measurement error corrections (regression calibration and simulation extrapolation), demonstrating how they are able to be conducted with non-identically distributed replicate measurements. We further expand simulation extrapolation, which typically assumes normality of the underlying error terms, proposing a nonparametric simulation extrapolation. These expansions are conducted generally, separate from the specific context of optimal DTR estimation.

Following the expansion of these extant techniques, we consider the problem of errors in covariates within the DTR framework. We apply the aforementioned generalized error correction techniques to this setting, and demonstrate how valid estimation and inference can proceed. Finally, we consider problems which are present when there is treatment misclassification in DTRs, proposing techniques to restore consistency and perform valid inference. To our knowledge this work represents the first substantive attempt to explore these problems. Thus, in addition to proposing methodological solutions, we also elucidate the particular challenges of estimation in this setting. All proposed techniques are explored theoretically, using simulation studies, and through real-world data analyses.