scholarly journals A note on a sensitivity analysis for unmeasured confounding, and the related E-value

2020 ◽  
Vol 8 (1) ◽  
pp. 229-248
Author(s):  
Arvid Sjölander
Keyword(s):  
Sensitivity Analysis ◽  
Observational Studies ◽  
Real Data ◽  
Feasible Region ◽  
Maximal Strength ◽  
Unmeasured Confounding ◽  
Unmeasured Confounder ◽  
Two Parameters ◽  
Strength Of Association

Abstract Unmeasured confounding is one of the most important threats to the validity of observational studies. In this paper we scrutinize a recently proposed sensitivity analysis for unmeasured confounding. The analysis requires specification of two parameters, loosely defined as the maximal strength of association that an unmeasured confounder may have with the exposure and with the outcome, respectively. The E-value is defined as the strength of association that the confounder must have with the exposure and the outcome, to fully explain away an observed exposure-outcome association. We derive the feasible region of the sensitivity analysis parameters, and we show that the bounds produced by the sensitivity analysis are not always sharp. We finally establish a region in which the bounds are guaranteed to be sharp, and we discuss the implications of this sharp region for the interpretation of the E-value. We illustrate the theory with a real data example and a simulation.

scholarly journals Conducting sensitivity analysis for unmeasured confounding in observational studies using E-values: The evalue package

2020 ◽  
Vol 20 (1) ◽  
pp. 162-175 ◽  
Author(s):  
Ariel Linden ◽  
Maya B. Mathur ◽  
Tyler J. VanderWeele
Keyword(s):  
Observational Studies ◽  
Specific Treatment ◽  
Sensitivity Analyses ◽  
Unmeasured Confounding ◽  
Unmeasured Confounder ◽  
Point Estimates ◽  
Hazard Ratios ◽  
Mean Differences ◽  
Rate Ratios ◽  
Strength Of Association

In this article, we introduce the evalue package, which performs sensitivity analyses for unmeasured confounding in observational studies using the methodology proposed by VanderWeele and Ding (2017, Annals of Internal Medicine 167: 268–274). evalue reports E-values, defined as the minimum strength of association on the risk-ratio scale that an unmeasured confounder would need to have with both the treatment assignment and the outcome to fully explain away a specific treatment-outcome association, conditional on the measured covariates. evalue computes E-values for point estimates (and optionally, confidence limits) for several common outcome types, including risk and rate ratios, odds ratios with common or rare outcomes, hazard ratios with common or rare outcomes, standardized mean differences in outcomes, and risk differences.

scholarly journals Novel bounds for causal effects based on sensitivity parameters on the risk difference scale

2021 ◽  
Vol 9 (1) ◽  
pp. 190-210
Author(s):  
Arvid Sjölander ◽  
Ola Hössjer
Keyword(s):  
Risk Ratio ◽  
Simulation Study ◽  
Observational Studies ◽  
Causal Effect ◽  
Real Data ◽  
Risk Difference ◽  
Causal Effects ◽  
Ratio Scale ◽  
Unmeasured Confounding ◽  
Range Of Values

Abstract Unmeasured confounding is an important threat to the validity of observational studies. A common way to deal with unmeasured confounding is to compute bounds for the causal effect of interest, that is, a range of values that is guaranteed to include the true effect, given the observed data. Recently, bounds have been proposed that are based on sensitivity parameters, which quantify the degree of unmeasured confounding on the risk ratio scale. These bounds can be used to compute an E-value, that is, the degree of confounding required to explain away an observed association, on the risk ratio scale. We complement and extend this previous work by deriving analogous bounds, based on sensitivity parameters on the risk difference scale. We show that our bounds can also be used to compute an E-value, on the risk difference scale. We compare our novel bounds with previous bounds through a real data example and a simulation study.

Sensitivity Analysis for Unmeasured Confounding: E-Values for Observational Studies

2017 ◽  
Vol 167 (4) ◽  
pp. 285 ◽  
Author(s):  
A. Russell Localio ◽  
Catherine B. Stack ◽  
Michael E. Griswold
Keyword(s):  
Sensitivity Analysis ◽  
Observational Studies ◽  
Unmeasured Confounding

scholarly journals Assess the Application of the E-Value in the Unmeasured Confounder Evaluation of Observational Pharmaceutical Studies

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Lihong Huang ◽  
Jianbing Ma ◽  
Xiaochun Qiu ◽  
Tao Suo
Keyword(s):  
Public Health ◽  
Sensitivity Analysis ◽  
Lower Bound ◽  
Confidence Interval ◽  
Effect Size ◽  
Observational Studies ◽  
Relative Effect ◽  
Analysis Tool ◽  
Unmeasured Confounder ◽  
Unmeasured Confounders

Public health is very important in big cities, and data analysis on public health studies is always a demanding issue that determines the study effectiveness. E-value was proposed as a standard sensitivity analysis tool to assess unmeasured confounders in observational studies, but its value is doubted. To evaluate the usefulness of E-value, in this paper, we collected 368 observational studies on drug effectiveness evaluation published from 1998 to September 2019 (out of 3426 searched studies) and evaluated the features of E-value. We selected the effects of primary outcomes or the largest effects in terms of hazard ratio, risk ratio, or odds ratio. Effects were transformed into estimated effect sizes following a standard E-value computation. In all 368 studies, the disease with the highest percentage was infections and infestations, at 21.7% (80/368). Our results showed that the median relative effect size was 1.89 (Q1-Q3: 1.41–2.95), and the corresponding median E-value was 3.19 with 95% confidence interval lower bound 1.77. Smaller studies yielded larger E-values for the effect size estimate and the relationship was considerably attenuated when considering the E-value for the lower bound of 95% confidence interval on the effect size. Notably, E-values have a monotonic, almost linear relationship with effect estimates. We found that E-value may cause misimpressions on the unmeasured confounder, and the same E-value does not reflect the varying nature of the unmeasured confounders in different studies, and there lacks a guidance on how E-value can be deemed as small or large, all of which limits the capability of E-value as a standard sensitivity analysis tool in real applications.

Bayesian sensitivity analysis for unmeasured confounding in observational studies

2007 ◽  
Vol 26 (11) ◽  
pp. 2331-2347 ◽  
Author(s):  
Lawrence C. McCandless ◽  
Paul Gustafson ◽  
Adrian Levy
Keyword(s):  
Sensitivity Analysis ◽  
Observational Studies ◽  
Unmeasured Confounding

scholarly journals Sensitivity analysis for an unmeasured confounder: a review of two independent methods

2010 ◽  
Vol 13 (2) ◽  
pp. 188-198 ◽  
Author(s):  
Ronir Raggio Luiz ◽  
Maria Deolinda Borges Cabral
Keyword(s):  
Sensitivity Analysis ◽  
Causal Inference ◽  
Observational Studies ◽  
Experimental Studies ◽  
Epidemiological Studies ◽  
Strong Constraint ◽  
Unmeasured Confounder ◽  
Direct Sensitivity ◽  
Hidden Biases ◽  
The Impact

One of the main purposes of epidemiological studies is to estimate causal effects. Causal inference should be addressed by observational and experimental studies. A strong constraint for the interpretation of observational studies is the possible presence of unobserved confounders (hidden biases). An approach for assessing the possible effects of unobserved confounders may be drawn up through the use of a sensitivity analysis that determines how strong the effects of an unmeasured confounder should be to explain an apparent association, and which should be the characteristics of this confounder to exhibit such an effect. The purpose of this paper is to review and integrate two independent sensitivity analysis methods. The two methods are presented to assess the impact of an unmeasured confounder variable: one developed by Greenland under an epidemiological perspective, and the other developed from a statistical standpoint by Rosenbaum. By combining (or merging) epidemiological and statistical issues, this integration became a more complete and direct sensitivity analysis, encouraging its required diffusion and additional applications. As observational studies are more subject to biases and confounding than experimental settings, the consideration of epidemiological and statistical aspects in sensitivity analysis strengthens the causal inference.

scholarly journals Assessing the impact of unmeasured confounders for credible and reliable real-world evidence

2020 ◽  
Author(s):  
Xiang Zhang ◽  
James Stamey ◽  
Maya B Mathur
Keyword(s):  
Sensitivity Analysis ◽  
Statistical Methods ◽  
Real World ◽  
Sensitivity Analyses ◽  
Real World Data ◽  
Unmeasured Confounding ◽  
Suggested Approach ◽  
Unmeasured Confounder ◽  
The Impact ◽  
Unmeasured Confounders

Purpose: We review statistical methods for assessing the possible impact of bias due to unmeasured confounding in real world data analysis and provide detailed recommendations for choosing among the methods. Methods: By updating an earlier systematic review, we summarize modern statistical best practices for evaluating and correcting for potential bias due to unmeasuredconfounding in estimating causal treatment effect from non-interventional studies. Results: We suggest a hierarchical structure for assessing unmeasured confounding.First, for initial sensitivity analyses, we strongly recommend applying a recently developed method, the E-value, that is straightforward to apply and does not require prior knowledge or assumptions about the unmeasured confounder(s). When some such knowledge is available, the E-value could be supplemented by the rule-out or array method at this step. If these initial analyses suggest results may not be robust to unmeasured confounding, subsequent analyses could be conducted using more specialized statistical methods, which we categorize based on whether they requireaccess to external data on the suspected unmeasured confounder(s), internal data, or no data. Other factors for choosing the subsequent sensitivity analysis methods arealso introduced and discussed, including the types of unmeasured confounders and whether the subsequent sensitivity analysis is intended to provide a corrected causaltreatment effect. Conclusion: Various analytical methods have been proposed to address unmeasured confounding, but little research has discussed a structured approach to select appropriate methods in practice. In providing practical suggestions for choosing appropriate initial and, potentially, more specialized subsequent sensitivity analyses, we hopeto facilitate the widespread reporting of such sensitivity analyses in non-interventional studies. The suggested approach also has the potential to inform pre-specificationof sensitivity analyses before executing the analysis, and therefore increase the transparency and limit selective study reporting.

scholarly journals A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 62
Author(s):  
Zhengwei Liu ◽  
Fukang Zhu
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Models ◽  
Superior Performance ◽  
Data Sets ◽  
Binomial Thinning ◽  
Free Case ◽  
Two Parameters ◽  
Conditional Maximum ◽  
Thinning Operator

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

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