Abstract:
Two-stage regression is a common tool for instrumental variable analysis in applied research. This thesis introduces additional uses of two-stage regression models that enable researchers to make inferences that are unavailable in one-stage models.
The first part of the thesis explores recent methodology that examines whether the predicted response to control affects the magnitude of the treatment effect. The method is a two-stage variation of the Peters-Belson method, studying the interaction between the treatment and some prognostic score. We expand this method into a full two-stage regression method we call Peters-Belson with Prognostic Heterogeneity. PBPH carefully considers the standard error calculation in the second stage, accounting for measurement error introduced in the first stage. A Wald-style confidence interval for the second stage coefficients, even with the corrected standard error, is insufficient to provide proper coverage. We find that a method based on estimating equations and hypothesis test inversion addresses these inference concerns that researchers haven't been aware of.
Following this, we enhance the PBPH methodology, enabling complications that the applied researcher may encounter. First, we allow a generalized linear first stage model to permit the error to have a non-normal distribution. Secondly, clustered random trials can ease data collection, but generate intra-cluster correlation which must be adjusted for. We the analysis of clustered random trials in the PBPH framework.
The final chapter examines treatment effect estimation with a binary response. We show simulationally that using two-stage regression models allows us to test whether a treatment effect is linear on the logit scale (logistic regression) or linear on the probability scale (linear regression). Often, matching is performed on observational data to aid in treatment effect estimation. Conditional logistic regression is a typical approach to matched data with binary response; however, we show that two-stage regression in this setting offers benefits not available to a one-stage conditional logistic model.
Two-stage regression is a common tool for instrumental variable analysis in applied research. This thesis introduces additional uses of two-stage regression models that enable researchers to make inferences that are unavailable in one-stage models.
The first part of the thesis explores recent methodology that examines whether the predicted response to control affects the magnitude of the treatment effect. The method is a two-stage variation of the Peters-Belson method, studying the interaction between the treatment and some prognostic score. We expand this method into a full two-stage regression method we call Peters-Belson with Prognostic Heterogeneity. PBPH carefully considers the standard error calculation in the second stage, accounting for measurement error introduced in the first stage. A Wald-style confidence interval for the second stage coefficients, even with the corrected standard error, is insufficient to provide proper coverage. We find that a method based on estimating equations and hypothesis test inversion addresses these inference concerns that researchers haven't been aware of.
Following this, we enhance the PBPH methodology, enabling complications that the applied researcher may encounter. First, we allow a generalized linear first stage model to permit the error to have a non-normal distribution. Secondly, clustered random trials can ease data collection, but generate intra-cluster correlation which must be adjusted for. We the analysis of clustered random trials in the PBPH framework.
The final chapter examines treatment effect estimation with a binary response. We show simulationally that using two-stage regression models allows us to test whether a treatment effect is linear on the logit scale (logistic regression) or linear on the probability scale (linear regression). Often, matching is performed on observational data to aid in treatment effect estimation. Conditional logistic regression is a typical approach to matched data with binary response; however, we show that two-stage regression in this setting offers benefits not available to a one-stage conditional logistic model.
| Building: | West Hall |
|---|---|
| Event Type: | Lecture / Discussion |
| Tags: | Dissertation |
| Source: | Happening @ Michigan from Department of Statistics |
