Table 3, Summary of Results for Estimation of θ1a - Developing and Testing New Methods for Estimating Treatment Effectiveness in Observational Studies Using High-Dimension Data

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Table 3Summary of Results for Estimation of θ₁^a

	(C1) cor IPS, more cor OR			(C2) cor IPS, less cor OR			(C3) mis IPS, more cor OR
	RCAL	RML	RML2	RCAL	RML	RML2	RCAL	RML	RML2
	(M1) n = 800 and p = 400
Bias	−0.146	−0.195	−0.007	−0.054	−0.208	−0.118	0.043	−0.022	0.119
$\sqrt{V a r}$	0.433	0.435	0.896	0.518	0.521	1.231	0.429	0.434	0.804
$\sqrt{E V a r}$	0.418	0.400	2.533	0.510	0.486	11.410	0.418	0.422	0.957
Cov90	0.854	0.811	0.868	0.889	0.830	0.848	0.886	0.876	0.885
Cov95	0.908	0.889	0.930	0.935	0.897	0.898	0.932	0.933	0.939
	(M2) n = 800 and p = 400
Bias	−0.155	−0.201	−0.026	−0.056	−0.210	−0.143	0.025	−0.026	0.120
$\sqrt{V a r}$	0.432	0.438	0.752	0.522	0.521	1.301	0.427	0.433	0.784
$\sqrt{E V a r}$	0.415	0.401	1.290	0.509	0.486	11.804	0.415	0.422	0.790
Cov90	0.848	0.803	0.872	0.884	0.832	0.851	0.884	0.877	0.883
Cov95	0.909	0.882	0.928	0.933	0.895	0.894	0.937	0.929	0.941
	(M1) n = 800 and p = 1000
Bias	−0.198	−0.239	−0.145	−0.087	−0.227	−0.204	0.047	−0.028	0.092
$\sqrt{V a r}$	0.428	0.424	0.632	0.518	0.521	0.749	0.438	0.451	0.961
$\sqrt{E V a r}$	0.411	0.393	0.600	0.439	0.477	0.742	0.411	0.413	0.816
Cov90	0.837	0.808	0.832	0.879	0.831	0.833	0.882	0.864	0.857
Cov95	0.900	0.869	0.901	0.933	0.888	0.899	0.945	0.924	0.920
	(M2) n = 800 and p = 1000
Bias	−0.223	−0.242	−0.146	−0.099	−0.227	−0.205	0.011	−0.030	0.068
$\sqrt{V a r}$	0.430	0.424	0.632	0.515	0.520	0.759	0.441	0.450	0.714
$\sqrt{E V a r}$	0.407	0.393	0.605	0.491	0.476	0.744	0.407	0.412	0.677
Cov90	0.820	0.803	0.831	0.874	0.824	0.828	0.875	0.862	0.858
Cov95	0.880	0.868	0.900	0.929	0.888	0.894	0.939	0.928	0.917

: Abbreviations: cor, correct; Cov90, coverage proportion of the 90% CI; Cov95, coverage proportion of the 95% CI; EVar, estimated variance; IPS, instrument propensity score model; M, model; mis, misspecified; OR, outcome and treatment regression models; Var, variance.
: ^aRCAL denotes ${\hat{θ}}_{1, R C A L}$ , RM L denotes ${\hat{θ}}_{1, R C A L}$ , and RML2 denotes the variant where the nuisance parameters are estimated by refitting models with only the variables selected from the corresponding Lasso estimation. Bias and $\sqrt{Var}$ are the Monte Carlo bias and SD of the point estimates, and $\sqrt{EVar}$ is the square root of the mean of the variance estimates. Cov90 and Cov95 are based on 1000 repeated simulations. The true values of ${\hat{θ}}_{1}$ under (C1) to (C3) are calculated using Monte Carlo integration with 100 repeated samples each of size 10⁷.

From: Developing and Testing New Methods for Estimating Treatment Effectiveness in Observational Studies Using High-Dimension Data

Cover of Developing and Testing New Methods for Estimating Treatment Effectiveness in Observational Studies Using High-Dimension Data

Developing and Testing New Methods for Estimating Treatment Effectiveness in Observational Studies Using High-Dimension Data [Internet].

Tan Z, Gerhard T, Sun B.

Washington (DC): Patient-Centered Outcomes Research Institute (PCORI); 2021 Nov.

This book is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License which permits noncommercial use and distribution provided the original author(s) and source are credited. (See https://creativecommons.org/licenses/by-nc-nd/4.0/

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Table 3Summary of Results for Estimation of θ1a

Table 3Summary of Results for Estimation of θ₁^a