Two Stage Least Squares with Time-Varying Instruments: An Application to an Evaluation of Treatment Intensification for Type-2 Diabetes

TL;DR

This paper develops a robust two-stage least squares method for evaluating time-varying treatments using longitudinal data, addressing unmeasured confounding and demonstrating improved performance over existing methods through simulations and an application to diabetes treatment.

Contribution

It extends the two-stage least squares approach to handle time-varying treatments and instruments, providing a more reliable analysis in longitudinal observational studies.

Findings

The proposed method performs well across various scenarios, including model misspecification.

It compares favorably with recent g-estimation approaches for time-varying instruments.

Application to diabetes treatment shows practical utility in health policy evaluation.

Abstract

As longitudinal data becomes more available in many settings, policy makers are increasingly interested in the effect of time-varying treatments (e.g. sustained treatment strategies). In settings such as this, the preferred analysis techniques are the g-methods, however these require the untestable assumption of no unmeasured confounding. Instrumental variable analyses can minimise bias through unmeasured confounding. Of these methods, the Two Stage Least Squares technique is one of the most well used in Econometrics, but it has not been fully extended, and evaluated, in full time-varying settings. This paper proposes a robust two stage least squares method for the econometric evaluation of time-varying treatment. Using a simulation study we found that, unlike standard two stage least squares, it performs relatively well across a wide range of circumstances, including model misspecification. It compares well with recent time-varying instrument approaches via g-estimation. We illustrate the methods in an evaluation of treatment intensification for Type-2 Diabetes Mellitus, exploring the exogeneity in prescribing preferences to operationalise a time-varying instrument.