Inference for treatment effect parameters in potentially misspecified high-dimensional models

Biometrika ◽  
2020 ◽  
Author(s):  
Oliver Dukes ◽  
Stijn Vansteelandt
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Treatment Effect ◽  
Observational Studies ◽  
Treatment Effects ◽  
Treatment Selection ◽  
High Dimensional ◽  
Selection Mechanism ◽  
Dimensional Models ◽  
Effect Parameter

Summary Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators, such as the lasso, or other regularization approaches. Naïve use of such estimators yields confidence intervals for the conditional treatment effect parameter that are not uniformly valid. Moreover, as the number of covariates grows with the sample size, correctly specifying a model for the outcome is nontrivial. In this article we deal with both of these concerns simultaneously, obtaining confidence intervals for conditional treatment effects that are uniformly valid, regardless of whether the outcome model is correct. This is done by incorporating an additional model for the treatment selection mechanism. When both models are correctly specified, we can weaken the standard conditions on model sparsity. Our procedure extends to multivariate treatment effect parameters and complex longitudinal settings.

SHARP BOUNDS ON THE DISTRIBUTION OF TREATMENT EFFECTS AND THEIR STATISTICAL INFERENCE

2009 ◽  
Vol 26 (3) ◽  
pp. 931-951 ◽  
Author(s):  
Yanqin Fan ◽  
Sang Soo Park
Keyword(s):  
Sample Size ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Simulation Study ◽  
Treatment Effect ◽  
Treatment Effects ◽  
Asymptotic Distributions ◽  
Finite Sample ◽  
Sharp Bounds ◽  
Nonparametric Estimators

In this paper, we propose nonparametric estimators of sharp bounds on the distribution of treatment effects of a binary treatment and establish their asymptotic distributions. We note the possible failure of the standard bootstrap with the same sample size and apply the fewer-than-nbootstrap to making inferences on these bounds. The finite sample performances of the confidence intervals for the bounds based on normal critical values, the standard bootstrap, and the fewer-than-nbootstrap are investigated via a simulation study. Finally we establish sharp bounds on the treatment effect distribution when covariates are available.

Randomized trials in oncology stopped early for benefit: A systematic review

2007 ◽  
Vol 25 (18_suppl) ◽  
pp. 6513-6513
Author(s):  
R. A. Wilcox ◽  
G. H. Guyatt ◽  
V. M. Montori
Keyword(s):  
Systematic Review ◽  
New England ◽  
Sample Size ◽  
Treatment Effect ◽  
Interim Analysis ◽  
Treatment Effects ◽  
Stopping Rules ◽  
Study Characteristics ◽  
Large Treatment Effect ◽  
True Treatment Effect

6513 Background: Investigators finding a large treatment effect in an interim analysis may terminate a randomized trial (RCT) earlier than planned. A systematic review (Montori et. al., JAMA 2005; 294: 2203–2209) found that RCTs stopped early for benefit are poorly reported and may overestimate the true treatment affect. The extent to which RCTs in oncology stopped early for benefit share similar concerns remains unclear. Methods: We selected RCTs in oncology which had been reported in the original systematic review and reviewed the study characteristics, features related to the decision to monitor and stop the study early (sample size, interim analyses, monitoring and stopping rules), and the number of events and the estimated treatment effects. Results: We found 29 RCTs in malignant hematology (n=6) and oncology (n=23), 52% published in 2000–2004 and 41% in 3 high-impact medical journals (New England Journal of Medicine, Lancet, JAMA). The majority (79%) of trials reported a planned sample size and, on average, recruited 67% of the planned sample size (SD 31%). RCTs reported (1) the planned sample size (n=20), (2) the interim analysis at which the study was terminated (n=16), and (3) whether the decision to stop the study prematurely was informed by a stopping rule (n=16); only 13 reported all three. There was a highly significant correlation between the number of events and the treatment effect (r=0.68, p=0.0007). The odds of finding a large treatment effect (a relative risk < median of 0.54, IQR 0.3–0.7) when studies stopped after a few events (no. events < median of 54 events, IQR 22–125) was 6.2 times greater than when studies stopped later. Conclusions: RCTs in oncology stopped early for benefit tend to report large treatment effects that may overestimate the true treatment effect, particularly when the number of events driving study termination is small. Also, information pertinent to the decision to stop early was inconsistently reported. Clinicians and policymakers should interpret such studies with caution, especially when information about the decision to stop early is not provided and few events occurred. No significant financial relationships to disclose.

scholarly journals L2-Boosting for Economic Applications

2017 ◽  
Vol 107 (5) ◽  
pp. 270-273 ◽  
Author(s):  
Ye Luo ◽  
Martin Spindler
Keyword(s):  
Treatment Effect ◽  
Treatment Effects ◽  
High Dimensional ◽  
Economic Applications ◽  
Many Instruments ◽  
Low Dimensional

We present the L2Boosting algorithm and two variants, namely post-Boosting and orthogonal Boosting. Building on results in Ye and Spindler (2016), we demonstrate how boosting can be used for estimation and inference of low-dimensional treatment effects. In particular, we consider estimation of a treatment effect in a setting with very many controls and in a setting with very many instruments. We provide simulations and analyze two real applications. We compare the results with Lasso and find that boosting performs quite well. This encourages further use of boosting for estimation of treatment effects in high-dimensional settings.

scholarly journals Conditional Generative Adversarial Networks for Individualized Treatment Effect Estimation and Treatment Selection

2020 ◽  
Vol 11 ◽  
Author(s):  
Qiyang Ge ◽  
Xuelin Huang ◽  
Shenying Fang ◽  
Shicheng Guo ◽  
Yuanyuan Liu ◽  
...  
Keyword(s):  
Random Forest ◽  
Treatment Response ◽  
Treatment Effect ◽  
Treatment Effects ◽  
State Of The Art ◽  
Treatment Selection ◽  
Individualized Treatment ◽  
Generative Adversarial Networks ◽  
Precision Oncology ◽  
Adversarial Networks

Treatment response is heterogeneous. However, the classical methods treat the treatment response as homogeneous and estimate the average treatment effects. The traditional methods are difficult to apply to precision oncology. Artificial intelligence (AI) is a powerful tool for precision oncology. It can accurately estimate the individualized treatment effects and learn optimal treatment choices. Therefore, the AI approach can substantially improve progress and treatment outcomes of patients. One AI approach, conditional generative adversarial nets for inference of individualized treatment effects (GANITE) has been developed. However, GANITE can only deal with binary treatment and does not provide a tool for optimal treatment selection. To overcome these limitations, we modify conditional generative adversarial networks (MCGANs) to allow estimation of individualized effects of any types of treatments including binary, categorical and continuous treatments. We propose to use sparse techniques for selection of biomarkers that predict the best treatment for each patient. Simulations show that MCGANs outperform seven other state-of-the-art methods: linear regression (LR), Bayesian linear ridge regression (BLR), k-Nearest Neighbor (KNN), random forest classification [RF (C)], random forest regression [RF (R)], logistic regression (LogR), and support vector machine (SVM). To illustrate their applications, the proposed MCGANs were applied to 256 patients with newly diagnosed acute myeloid leukemia (AML) who were treated with high dose ara-C (HDAC), Idarubicin (IDA) and both of these two treatments (HDAC+IDA) at M. D. Anderson Cancer Center. Our results showed that MCGAN can more accurately and robustly estimate the individualized treatment effects than other state-of-the art methods. Several biomarkers such as GSK3, BILIRUBIN, SMAC are identified and a total of 30 biomarkers can explain 36.8% of treatment effect variation.

scholarly journals Assessing The Effectiveness of Empirical Calibration Under Different Bias Scenarios

2021 ◽  
Author(s):  
Hon Hwang ◽  
Juan C Quiroz ◽  
Blanca Gallego
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Observational Studies ◽  
Treatment Effects ◽  
Model Misspecification ◽  
Calibration Procedure ◽  
Negative Control ◽  
Unmeasured Confounding ◽  
Empirical Calibration ◽  
Negative Controls

Abstract Background: Estimations of causal effects from observational data are subject to various sources of bias. These biases can be adjusted by using negative control outcomes not affected by the treatment. The empirical calibration procedure uses negative controls to calibrate p-values and both negative and positive controls to calibrate coverage of the 95% confidence interval of the outcome of interest. Although empirical calibration has been used in several large observational studies, there is no systematic examination of its effect under different bias scenarios. Methods: The effect of empirical calibration of confidence intervals was analyzed using simulated datasets with known treatment effects. The simulations were for binary treatment and binary outcome, with simulated biases resulting from unmeasured confounder, model misspecification, measurement error, and lack of positivity. The performance of empirical calibration was evaluated by determining the change of the confidence interval coverage and bias of the outcome of interest. Results: Empirical calibration increased coverage of the outcome of interest by the 95% confidence interval under most settings but was inconsistent in adjusting the bias of the outcome of interest. Empirical calibration was most effective when adjusting for unmeasured confounding bias. Suitable negative controls had a large impact on the adjustment made by empirical calibration, but small improvements in the coverage of the outcome of interest was also observable when using unsuitable negative controls. Conclusions: This work adds evidence to the efficacy of empirical calibration on calibrating the confidence intervals of treatment effects in observational studies. We recommend empirical calibration of confidence intervals, especially when there is a risk of unmeasured confounding.

scholarly journals Conditional Generative Adversarial Networks for Individualized Treatment Effect Estimation and Treatment Selection

2020 ◽  
Author(s):  
Qiyang Ge ◽  
Xuelin Huang ◽  
Shenying Fang ◽  
Shihcheng Guo ◽  
yuanyuan Liu ◽  
...  
Keyword(s):  
Random Forest ◽  
Treatment Response ◽  
Treatment Effect ◽  
Treatment Effects ◽  
State Of The Art ◽  
Treatment Selection ◽  
Individualized Treatment ◽  
Generative Adversarial Networks ◽  
Precision Oncology ◽  
Adversarial Networks

Treatment response is heterogeneous. However the classical methods treat the treatment response as homogeneous and estimate the average treatment effects. The traditional methods are difficult to apply to precision oncology. The artificial intelligence (AI) is a powerful tool for precision oncology. It can accurately estimate the individualized treatment effects and learn optimal treatment choices. Therefore, the AI approach can substantially improve progress and treatment outcomes of patients. As one of AI approach, conditional generative adversarial nets for inference of individualized treatment effects (GANITE) have been developed. However, the GANITE can only deal with binary treatment and does not provide a tool for optimal treatment selection. To overcome these limitations, we modify conditional generative adversarial networks (MCGANs) to allow estimation of individualized effects of any types of treatments including binary, categorical and continuous treatments. We propose to use sparse techniques for selection of biomarkers that predict the best treatment for each patient. Simulations show that the CGANs outperform seven other state-of-the-art methods: linear regression (LR), Bayesian linear ridge regression (BLR), KNN, random forest classification (RF (C)), random forest regression (RF (R)), logistic regression (LogR) and support vector machine (SVM). To illustrate their applications, the proposed CGANs were applied to 256 patients with newly diagnosed acute myeloid leukemia (AML) who were treated with high dose ara-C (HDAC), Idarubicin (IDA) and both of these two treatments (HDAC+IDA) at M. D. Anderson Cancer Center. Our results showed that the MCGAN can more accurately and robustly estimate the individualized treatment effects than other state-of-the art methods. Several biomarkers such as GSK3, BILIRUBIN, SMAC are identified and a total of 30 biomarkers can explain 36.8% of treatment effect variation.

scholarly journals Recursive partitioning for heterogeneous causal effects

2016 ◽  
Vol 113 (27) ◽  
pp. 7353-7360 ◽  
Author(s):  
Susan Athey ◽  
Guido Imbens
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Treatment Effects ◽  
Mean Squared Error ◽  
Causal Effect ◽  
Selection Criterion ◽  
Regression Tree ◽  
Ground Truth ◽  
Causal Effects

In this paper we propose methods for estimating heterogeneity in causal effects in experimental and observational studies and for conducting hypothesis tests about the magnitude of differences in treatment effects across subsets of the population. We provide a data-driven approach to partition the data into subpopulations that differ in the magnitude of their treatment effects. The approach enables the construction of valid confidence intervals for treatment effects, even with many covariates relative to the sample size, and without “sparsity” assumptions. We propose an “honest” approach to estimation, whereby one sample is used to construct the partition and another to estimate treatment effects for each subpopulation. Our approach builds on regression tree methods, modified to optimize for goodness of fit in treatment effects and to account for honest estimation. Our model selection criterion anticipates that bias will be eliminated by honest estimation and also accounts for the effect of making additional splits on the variance of treatment effect estimates within each subpopulation. We address the challenge that the “ground truth” for a causal effect is not observed for any individual unit, so that standard approaches to cross-validation must be modified. Through a simulation study, we show that for our preferred method honest estimation results in nominal coverage for 90% confidence intervals, whereas coverage ranges between 74% and 84% for nonhonest approaches. Honest estimation requires estimating the model with a smaller sample size; the cost in terms of mean squared error of treatment effects for our preferred method ranges between 7–22%.

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