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

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.

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

Journal of Causal Inference ◽

10.1515/jci-2020-0012 ◽

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.

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Sensitivity analysis for unmeasured confounding in meta-analyses

10.31219/osf.io/jkhfg ◽

2017 ◽

Cited By ~ 2

Author(s):

Maya B Mathur ◽

Tyler VanderWeele

Keyword(s):

Random Effects ◽

Observational Studies ◽

R Package ◽

Sensitivity Analyses ◽

Unmeasured Confounding ◽

Confounding Bias ◽

Point Estimates ◽

Bias Factor ◽

Meta Analyses ◽

Biased Estimates

Random-effects meta-analyses of observational studies can produce biased estimates if the synthesized studies are subject to unmeasured confounding. We propose sensitivity analyses quantifying the extent to which unmeasured confounding of specified magnitude could reduce to below a certain threshold the proportion of true effect sizes that are scientifically meaningful. We also develop converse methods to estimate the strength of confounding capable of reducing the proportion of scientifically meaningful true effects to below a chosen threshold. These methods apply when a "bias factor'' is assumed to be normally distributed across studies or is assessed across a range of fixed values. Our estimators are derived using recently proposed sharp bounds on confounding bias within a single study that do not make assumptions regarding the unmeasured confounders themselves or the functional form of their relationships to the exposure and outcome of interest. We provide an R package, EValue, and a free website that compute point estimates and inference and produce plots for conducting such sensitivity analyses. These methods facilitate principled use of random-effects meta-analyses of observational studies to assess the strength of causal evidence for a hypothesis.

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Bias factor, maximum bias and the E-value: insight and extended applications

International Journal of Epidemiology ◽

10.1093/ije/dyaa127 ◽

2020 ◽

Vol 49 (5) ◽

pp. 1509-1516

Author(s):

Alexandre Cusson ◽

Claire Infante-Rivard

Keyword(s):

Odds Ratio ◽

Sensitivity Analyses ◽

Unmeasured Confounding ◽

Unmeasured Confounder ◽

Maximum Value ◽

Bias Factor ◽

Maximum Bias ◽

The Relationship ◽

Value Measure ◽

Insight Into

Abstract Background Unmeasured confounding can bias the relationship between exposure and outcome. Sensitivity analyses generate bias-adjusted measures but these are not much used; this may change with the availability of the E-value (for evidence for causality in observational studies), appealing for its ease of calculation. However, as currently proposed, the E-value has some practical limitations that may reduce its use. Methods We first provide some insight into the relationship between two established measures for unmeasured confounding: ‘the bias factor’ and the maximum value this bias factor can take (‘the B bias’). These measures are the statistical foundation for the E-value. We use them to develop new E-value formulas for situations when it is not currently applicable such as e.g. when, not unusually, a negative relation between unmeasured confounder and outcome and a positive one with exposure are postulated. We also provide E-values on the odds ratio scale because, currently, even when using the odds ratio as the study measure in the calculation of E-value, the result is to be interpreted as a relative risk, which is somewhat inconvenient. Results The additional formulas for the E-value measure make it applicable in all possible scenarios defined by the combined directions between unmeasured confounder and both the exposure and outcome. In addition, E-value measures can now be interpreted as odds ratios if the observed results are reported on the same scale. Conclusions The E-value is part of newer sensitivity analyses methods for unmeasured confounding. We provide insight into its structure, underscoring its advantages and limitations, and expand its applications.

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

10.31219/osf.io/fe4gs ◽

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.

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Oral splints for temporomandibular disorder or bruxism: a systematic review

BDJ ◽

10.1038/s41415-020-1250-2 ◽

2020 ◽

Vol 228 (3) ◽

pp. 191-197 ◽

Cited By ~ 3

Author(s):

Philip Riley ◽

Anne-Marie Glenny ◽

Helen V. Worthington ◽

Elisabet Jacobsen ◽

Clare Robertson ◽

...

Keyword(s):

Temporomandibular Disorder ◽

Cochrane Review ◽

Clinical Effectiveness ◽

Tooth Wear ◽

Sensitivity Analyses ◽

Data Synthesis ◽

Random Effects Models ◽

Minimal Treatment ◽

Mean Differences ◽

Randomised Controlled

AbstractObjectives To evaluate the clinical-effectiveness of oral splints for patients with TMD or bruxism for the primary outcomes: pain (TMD) and tooth wear (bruxism).Data sources Four databases including MEDLINE and EMBASE were searched from inception until 1 October 2018.Data selection and extraction Randomised controlled trials comparing all types of splints versus no/minimal treatment for patients with TMD or bruxism were eligible. Standard Cochrane review methods were used. Standardised mean differences (SMD) were pooled for the primary outcome of pain, using random effects models in TMD patients.Data synthesis Thirty-seven trials were included and the evidence identified was of very low certainty using GRADE assessments. When all subtypes of TMD were pooled into one global TMD group, there was no evidence that splints reduced pain: SMD (up to 3 months) -0.18 (95% CI -0.42 to 0.06); 13 trials, 1,076 participants. There was no evidence that any other outcomes improved when using splints. There was no evidence of adverse events associated with splints, but reporting was poor regarding this outcome. No trials measured tooth wear in patients with bruxism. There was a large variation in diagnostic criteria, splint types and outcome measures used and reported. Sensitivity analyses based on these factors did not indicate a reduction in pain.Conclusions The very low-certainty evidence identified did not demonstrate that splints reduced pain in TMD as a group of conditions. There is insufficient evidence to determine whether splints reduce tooth wear in patients with bruxism.

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Use of Statins and Breast Cancer: A Meta-Analysis of Seven Randomized Clinical Trials and Nine Observational Studies

Journal of Clinical Oncology ◽

10.1200/jco.2005.02.7045 ◽

2005 ◽

Vol 23 (34) ◽

pp. 8606-8612 ◽

Cited By ~ 139

Author(s):

Stefanos Bonovas ◽

Kalitsa Filioussi ◽

Nikolaos Tsavaris ◽

Nikolaos M. Sitaras

Keyword(s):

Breast Cancer ◽

Breast Cancer Risk ◽

Cancer Risk ◽

Publication Bias ◽

Observational Studies ◽

Fixed Effects ◽

Randomized Clinical Trials ◽

Meta Analysis ◽

Sensitivity Analyses ◽

Fixed Effects Model

Purpose A growing body of evidence suggests that statins may have chemopreventive potential against breast cancer. Laboratory studies demonstrate that statins induce apoptosis and reduce cell invasiveness in various cell lines, including breast carcinoma cells. However, the clinical relevance of these data remains unclear. The nonconclusive nature of the epidemiologic data prompted us to conduct a detailed meta-analysis of the studies published on the subject in peer-reviewed literature. Patients and Methods A comprehensive search for articles published up until 2005 was performed; reviews of each study were conducted; and data were abstracted. Before meta-analysis, the studies were evaluated for publication bias and heterogeneity. Pooled relative risk (RR) estimates and 95% CIs were calculated using the random and the fixed-effects models. Subgroup and sensitivity analyses were also performed. Results Seven large randomized trials and nine observational studies (five case-control and four cohort studies) contributed to the analysis. We found no evidence of publication bias or heterogeneity among the studies. Statin use did not significantly affect breast cancer risk (fixed effects model: RR = 1.03; 95% CI, 0.93 to 1.14; random effects model: RR = 1.02; 95% CI, 0.89 to 1.18). When the analyses were stratified into subgroups, there was no evidence that study design substantially influenced the estimate of effects. Furthermore, the sensitivity analysis confirmed the stability of our results. Conclusion Our meta-analysis findings do not support a protective effect of statins against breast cancer. However, this conclusion is limited by the relatively short follow-up times of the studies analyzed. Further studies are required to investigate the potential decrease in breast cancer risk among long-term statin users.

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Leishmanicidal effects of resveratrol and its derivatives: a systematic review and meta-Analysis

10.21203/rs.3.rs-25274/v1 ◽

2020 ◽

Author(s):

Nasrin Amiri Dashatan ◽

Marzieh Ashrafmansouri ◽

Mehdi Koushki ◽

Nayebali Ahmadi

Keyword(s):

Systematic Review ◽

Publication Bias ◽

Data Extraction ◽

Meta Analysis ◽

Sensitivity Analyses ◽

Protective Effects ◽

Random Effects Models ◽

Important Health ◽

Mean Differences ◽

Meta Analyses

Abstract Background Leishmaniasis is one of the most important health problems worldwide. The evidence has suggested that resveratrol and its derivatives have anti-leishmanial effects; however, the results are inconsistent and inconclusive. The aim of this study was to assess the effect of resveratrol and its derivatives on the Leishmania viability through a systematic review and meta-analysis of available relevant studies. Methods The electronic databases PubMed, ScienceDirect, Embase, Web of Science and Scopus were queried between October 2000 and April 2020 using a comprehensive search strategy. The eligible articles selected and data extraction conducted by two reviewers. Mean differences of IC50 (concentration leading to reduction of 50% of Leishmania) for each outcome was calculated using random-effects models. Sensitivity analyses and prespecified subgroup were conducted to evaluate potential heterogeneity and the stability of the pooled results. Publication bias was evaluated using the Egger’s and Begg’s tests. We also followed the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) guidelines for this review. Results Ten studies were included in the meta-analysis. We observed that RSV and its derivatives had significant reducing effects on Leishmania viability in promastigote [24.02 µg/ml; (95% CI 17.1, 30.8); P < 0.05; I2 = 99.8%; P heterogeneity = 0.00] and amastigote [18.3 µg/ml; (95% CI 13.5, 23.2); P < 0.05; I2 = 99.6%; P heterogeneity = 0.00] stages of Leishmania. A significant publication bias was observed in the meta-analysis. Sensitivity analyses showed a similar effect size while reducing the heterogeneity. Subgroup analysis indicated that the pooled effects of leishmanicidal of resveratrol and its derivatives were affected by type of stilbenes and Leishmania species. Conclusions Our findings clearly suggest that the strategies for the treatment of leishmaniasis should be focused on natural products such as RSV and its derivatives. Further study is needed to identify the mechanisms mediating this protective effects of RSV and its derivatives in leishmaniasis.

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

Journal of Causal Inference ◽

10.1515/jci-2021-0024 ◽

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.

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The evaluation of the reporting quality of observational studies in Master of Public Health’s dissertations in China

10.21203/rs.2.15451/v4 ◽

2020 ◽

Author(s):

ShuangYang Dai ◽

Xiaobin Zhou ◽

Hong Xu ◽

Beibei Li ◽

JinGao Zhang

Keyword(s):

Cohort Studies ◽

Observational Studies ◽

Absolute Risk ◽

Controlled Trial ◽

Reporting Quality ◽

Sensitivity Analyses ◽

Flow Diagram ◽

Case Control Studies ◽

Strobe Statement

Abstract Backgrounds Master of public health (MPH) plays an important role in Chinese medical education, and the dissertations is an important part of MPH education. In MPH dissertations, most are observational studies. Compared with randomized controlled trial (RCT), observational studies are more prone to information bias. So, the reporting of the observational studies should be transparent and standard. But, no research on evaluating the reporting quality of the MPH dissertation has been found.Methods A systematic literature search was performed in the Wanfang database from January 1, 2014 to May 31, 2019. The Strengthening the Reporting of Observation Studies in Epidemiology (STROBE) statement was adopted to evaluate the reporting quality of the selected studies. Articles that met the following criteria were selected: (1) observational studies, including cross-sectional studies, case-control studies, and cohort studies; (2) original articles; (3) studies on humans, including both adults and children.Results The Median of compliance to individual STROBE items was 74.79%. The mean (standard deviation) of STROBE score was 14.29 (1.84). Five items/sub-items were 100% reported (“reported” and “partly reported” were combined): background, objectives, study design, report numbers of individuals at each stage, and key result. Fifteen items/sub-items were reported by 75% or more. Reporting of methods and results was often omitted: missing data (6.67%), sensitivity analyses (3.63%), flow diagram (15.15%), and absolute risk (0%). Logistic regression analysis indicated that cohort studies (OR=3.41, 95% CI=1.27-9.16), funding support (OR=4.37, 95% CI=1.27-9.16) and more published papers during postgraduate period (OR=3.46, 95% CI=1.40-8.60) were related to high reporting quality.Conclusion In short, the reporting quality of observational studies in MPH’s dissertations in China is suboptimal. However, it’s necessary to improve the reporting of method and results sections. We recommend that authors should be stricter to adhere STROBE statement when conducting observational studies.

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Noncompliance and Missing Data in Health Economic Evaluation

Oxford Research Encyclopedia of Economics and Finance ◽

10.1093/acrefore/9780190625979.013.94 ◽

2019 ◽

Author(s):

Karla DiazOrdaz ◽

Richard Grieve

Keyword(s):

Health Economic ◽

Economic Evaluation ◽

Missing Data ◽

Causal Effect ◽

Health Economic Evaluation ◽

Specific Treatment ◽

Model Specification ◽

Sensitivity Analyses ◽

Economic Evaluations ◽

Random Assignment

Health economic evaluations face the issues of noncompliance and missing data. Here, noncompliance is defined as non-adherence to a specific treatment, and occurs within randomized controlled trials (RCTs) when participants depart from their random assignment. Missing data arises if, for example, there is loss-to-follow-up, survey non-response, or the information available from routine data sources is incomplete. Appropriate statistical methods for handling noncompliance and missing data have been developed, but they have rarely been applied in health economics studies. Here, we illustrate the issues and outline some of the appropriate methods with which to handle these with application to health economic evaluation that uses data from an RCT. In an RCT the random assignment can be used as an instrument-for-treatment receipt, to obtain consistent estimates of the complier average causal effect, provided the underlying assumptions are met. Instrumental variable methods can accommodate essential features of the health economic context such as the correlation between individuals’ costs and outcomes in cost-effectiveness studies. Methodological guidance for handling missing data encourages approaches such as multiple imputation or inverse probability weighting, which assume the data are Missing At Random, but also sensitivity analyses that recognize the data may be missing according to the true, unobserved values, that is, Missing Not at Random. Future studies should subject the assumptions behind methods for handling noncompliance and missing data to thorough sensitivity analyses. Modern machine-learning methods can help reduce reliance on correct model specification. Further research is required to develop flexible methods for handling more complex forms of noncompliance and missing data.

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