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Two stage least squares with time-varying instruments : an application to an evaluation of treatment intensification for type-2 diabetes

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Abstract
As routinely collected longitudinal data becomes more available in many settings, policy makers are increasingly interested in the effect of time-varying treatments (sustained treatment strategies). In settings such as this, many commonly used statistical approaches for estimating treatment effects, such as g-methods, often adopt the 'no unmeasured confounding' assumption. Instrumental variable (IV) methods aim to reduce biases due to unmeasured confounding, but have received limited attention in settings with time-varying treatments. This paper extends and critically evaluates a commonly used IV estimating approach, Two Stage Least Squares (2SLS), for evaluating time-varying treatments. Using a simulation study, we found that, unlike standard 2SLS, the extended 2SLS performs relatively well across a wide range of circumstances, including certain model misspecifications. 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.
Keywords
Instrumental variable, time-varying, two stage least squares, physician preference, diabetes, VARIABLE METHODS, METFORMIN, MODELS, SULFONYLUREA, EFFICACY, SAFETY, BIAS

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MLA
Tompsett, Daniel, et al. “Two Stage Least Squares with Time-Varying Instruments : An Application to an Evaluation of Treatment Intensification for Type-2 Diabetes.” STATISTICAL METHODS IN MEDICAL RESEARCH, vol. 35, no. 2, 2026, pp. 346–69, doi:10.1177/09622802251404064.
APA
Tompsett, D., Vansteelandt, S., Grieve, R., Robson, J., & Gomes, M. (2026). Two stage least squares with time-varying instruments : an application to an evaluation of treatment intensification for type-2 diabetes. STATISTICAL METHODS IN MEDICAL RESEARCH, 35(2), 346–369. https://doi.org/10.1177/09622802251404064
Chicago author-date
Tompsett, Daniel, Stijn Vansteelandt, Richard Grieve, John Robson, and Manuel Gomes. 2026. “Two Stage Least Squares with Time-Varying Instruments : An Application to an Evaluation of Treatment Intensification for Type-2 Diabetes.” STATISTICAL METHODS IN MEDICAL RESEARCH 35 (2): 346–69. https://doi.org/10.1177/09622802251404064.
Chicago author-date (all authors)
Tompsett, Daniel, Stijn Vansteelandt, Richard Grieve, John Robson, and Manuel Gomes. 2026. “Two Stage Least Squares with Time-Varying Instruments : An Application to an Evaluation of Treatment Intensification for Type-2 Diabetes.” STATISTICAL METHODS IN MEDICAL RESEARCH 35 (2): 346–369. doi:10.1177/09622802251404064.
Vancouver
1.
Tompsett D, Vansteelandt S, Grieve R, Robson J, Gomes M. Two stage least squares with time-varying instruments : an application to an evaluation of treatment intensification for type-2 diabetes. STATISTICAL METHODS IN MEDICAL RESEARCH. 2026;35(2):346–69.
IEEE
[1]
D. Tompsett, S. Vansteelandt, R. Grieve, J. Robson, and M. Gomes, “Two stage least squares with time-varying instruments : an application to an evaluation of treatment intensification for type-2 diabetes,” STATISTICAL METHODS IN MEDICAL RESEARCH, vol. 35, no. 2, pp. 346–369, 2026.
@article{01KEWRFH8RERX9943A86FK92BW,
  abstract     = {{As routinely collected longitudinal data becomes more available in many settings, policy makers are increasingly interested in the effect of time-varying treatments (sustained treatment strategies). In settings such as this, many commonly used statistical approaches for estimating treatment effects, such as g-methods, often adopt the 'no unmeasured confounding' assumption. Instrumental variable (IV) methods aim to reduce biases due to unmeasured confounding, but have received limited attention in settings with time-varying treatments. This paper extends and critically evaluates a commonly used IV estimating approach, Two Stage Least Squares (2SLS), for evaluating time-varying treatments. Using a simulation study, we found that, unlike standard 2SLS, the extended 2SLS performs relatively well across a wide range of circumstances, including certain model misspecifications. 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.}},
  author       = {{Tompsett, Daniel and Vansteelandt, Stijn and Grieve, Richard and Robson, John and Gomes, Manuel}},
  issn         = {{0962-2802}},
  journal      = {{STATISTICAL METHODS IN MEDICAL RESEARCH}},
  keywords     = {{Instrumental variable,time-varying,two stage least squares,physician preference,diabetes,VARIABLE METHODS,METFORMIN,MODELS,SULFONYLUREA,EFFICACY,SAFETY,BIAS}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{346--369}},
  title        = {{Two stage least squares with time-varying instruments : an application to an evaluation of treatment intensification for type-2 diabetes}},
  url          = {{http://doi.org/10.1177/09622802251404064}},
  volume       = {{35}},
  year         = {{2026}},
}

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