Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes

Toward a clearer understanding of what works to reduce gun violence: the role of falsification strategies

Strong epidemiologic evidence from ecological and individual-level studies in the United States supports the claim that access to firearms substantially increases the risk of dying by suicide, homicide, and firearm accidents. Less certain is how well particular interventions work to prevent these deaths and other firearm-related harms. Given the limits of existing data to study firearm violence and the infeasibility of conducting randomized trials of firearm access, it is important to do the best we can with the data we already have. We argue that falsification strategies are a critical-yet underutilized-component of any such analytical approach. The falsification strategies we focus on are versions of "negative controls" analyses in which we expect that an analysis should yield a null causal effect, and thus where not obtaining a null effect estimate raises questions about the assumptions underlying causal interpretation of a study's findings. We illustrate the saliency of this issue today with examples drawn from studies published in leading peer-reviewed journals within the last 5 years. Collecting rich, high-quality data always takes time, urgent as the need may be. On the other hand, doing better with the data we already have can start right now.

The Causal Roadmap and Simulations to Improve the Rigor and Reproducibility of Real-data Applications

The Causal Roadmap outlines a systematic approach to asking and answering questions of cause and effect: define the quantity of interest, evaluate needed assumptions, conduct statistical estimation, and carefully interpret results. To protect research integrity, it is essential that the algorithm for statistical estimation and inference be prespecified prior to conducting any effectiveness analyses. However, it is often unclear which algorithm will perform optimally for the real-data application. Instead, there is a temptation to simply implement one's favorite algorithm, recycling prior code or relying on the default settings of a computing package. Here, we call for the use of simulations that realistically reflect the application, including key characteristics such as strong confounding and dependent or missing outcomes, to objectively compare candidate estimators and facilitate full specification of the statistical analysis plan. Such simulations are informed by the Causal Roadmap and conducted after data collection but prior to effect estimation. We illustrate with two worked examples. First, in an observational longitudinal study, we use outcome-blind simulations to inform nuisance parameter estimation and variance estimation for longitudinal targeted minimum loss-based estimation. Second, in a cluster randomized trial with missing outcomes, we use treatment-blind simulations to examine type-I error control in two-stage targeted minimum loss-based estimation. In both examples, realistic simulations empower us to prespecify an estimation approach that is expected to have strong finite sample performance and also yield quality-controlled computing code for the actual analysis. Together, this process helps to improve the rigor and reproducibility of our research.

Comments on "sensitivity of estimands in clinical trials with imperfect compliance" by Chen and Heitjan

Chen and Heitjan (Sensitivity of estimands in clinical trials with imperfect compliance. Int J Biostat. 2023) used linear extrapolation to estimate the population average causal effect (PACE) from the complier average causal effect (CACE) in multiple randomized trials with all-or-none compliance. For extrapolating from CACE to PACE in this setting and in the paired availability design involving different availabilities of treatment among before-and-after studies, we recommend the sensitivity analysis in Baker and Lindeman (J Causal Inference, 2013) because it is not restricted to a linear model, as it involves various random effect and trend models.

Sensitivity of estimands in clinical trials with imperfect compliance

In clinical trials that are subject to noncompliance, the commonly used intention-to-treat estimand is valid as a causal effect of treatment assignment but is sensitive to the level of compliance. An alternative estimand, the complier average causal effect (CACE), measures the average effect of treatment received in the latent subset of subjects who would comply with either assigned treatment. Because the principal stratum of compliers can vary with the circumstances of the trial, CACE too depends on the compliance fraction. We propose a model in which an underlying latent proto-compliance interacts with trial characteristics to determine a subject's compliance behavior. When the latent compliance is independent of the individual treatment effect, the average causal effect is constant across compliance classes, and CACE is robust across trials and equal to the population average causal effect. We demonstrate the potential degree of sensitivity of CACE in a simulation study, an analysis of data from a trial of vitamin A supplementation in children, and a meta-analysis of trials of epidural analgesia in labor.

Use of the instrumental inequalities in simulated mendelian randomization analyses with coarsened exposures

Mendelian randomization (MR) requires strong unverifiable assumptions to estimate causal effects. However, for categorical exposures, the MR assumptions can be falsified using a method known as the instrumental inequalities. To apply the instrumental inequalities to a continuous exposure, investigators must coarsen the exposure, a process which can itself violate the MR conditions. Violations of the instrumental inequalities for an MR model with a coarsened exposure might therefore reflect the effect of coarsening rather than other sources of bias. We aim to evaluate how exposure coarsening affects the ability of the instrumental inequalities to detect bias in MR models with multiple proposed instruments under various causal structures. To do so, we simulated data mirroring existing studies of the effect of alcohol consumption on cardiovascular disease under a variety of exposure-outcome effects in which the MR assumptions were met for a continuous exposure. We categorized the exposure based on subject matter knowledge or the observed data distribution and applied the instrumental inequalities to MR models for the effects of the coarsened exposure. In simulations of multiple binary instruments, the instrumental inequalities did not detect bias under any magnitude of exposure outcome effect when the exposure was coarsened into more than 2 categories. However, in simulations of both single and multiple proposed instruments, the instrumental inequalities were violated in some scenarios when the exposure was dichotomized. The results of these simulations suggest that the instrumental inequalities are largely insensitive to bias due to exposure coarsening with greater than 2 categories, and could be used with coarsened exposures to evaluate the required assumptions in applied MR studies, even when the underlying exposure is truly continuous.

Partial Identification of the Effects of Sustained Treatment Strategies

Although many epidemiologic studies focus on point identification, it is also possible to partially identify causal effects under consistency and the data alone. However, the literature on the so-called "assumption-free" bounds has focused on settings with time-fixed exposures. We describe assumption-free bounds for the effects of both static and dynamic sustained interventions. To provide intuition for the width of the bounds, we also discuss a mathematical connection between assumption-free bounds and clone-censor-weight approaches to causal effect estimation. The bounds, which are often wide in practice, can provide important information about the degree to which causal analyses depend on unverifiable assumptions made by investigators.

Comparative Analysis of Instrumental Variables on the Assignment of Buprenorphine/Naloxone or Methadone for the Treatment of Opioid Use Disorder

BACKGROUND

Instrumental variable (IV) analysis provides an alternative set of identification assumptions in the presence of uncontrolled confounding when attempting to estimate causal effects. Our objective was to evaluate the suitability of measures of prescriber preference and calendar time as potential IVs to evaluate the comparative effectiveness of buprenorphine/naloxone versus methadone for treatment of opioid use disorder (OUD).

METHODS

Using linked population-level health administrative data, we constructed five IVs: prescribing preference at the individual, facility, and region levels (continuous and categorical variables), calendar time, and a binary prescriber's preference IV in analyzing the treatment assignment-treatment discontinuation association using both incident-user and prevalent-new-user designs. Using published guidelines, we assessed and compared each IV according to the four assumptions for IVs, employing both empirical assessment and content expertise. We evaluated the robustness of results using sensitivity analyses.

RESULTS

The study sample included 35,904 incident users (43.3% on buprenorphine/naloxone) initiated on opioid agonist treatment by 1585 prescribers during the study period. While all candidate IVs were strong (A1) according to conventional criteria, by expert opinion, we found no evidence against assumptions of exclusion (A2), independence (A3), monotonicity (A4a), and homogeneity (A4b) for prescribing preference-based IV. Some criteria were violated for the calendar time-based IV. We determined that preference in provider-level prescribing, measured on a continuous scale, was the most suitable IV for comparative effectiveness of buprenorphine/naloxone and methadone for the treatment of OUD.

CONCLUSIONS

Our results suggest that prescriber's preference measures are suitable IVs in comparative effectiveness studies of treatment for OUD.

Using instrumental variables to address unmeasured confounding in causal mediation analysis

Mediation analysis is a strategy for understanding the mechanisms by which interventions affect later outcomes. However, unobserved confounding concerns may be compounded in mediation analyses, as there may be unobserved exposure-outcome, exposure-mediator, and mediator-outcome confounders. Instrumental variables (IVs) are a popular identification strategy in the presence of unobserved confounding. However, in contrast to the rich literature on the use of IV methods to identify and estimate a total effect of a non-randomized exposure, there has been almost no research into using IV as an identification strategy to identify mediational indirect effects. In response, we define and nonparametrically identify novel estimands-double complier interventional direct and indirect effects-when 2, possibly related, IVs are available, one for the exposure and another for the mediator. We propose nonparametric, robust, efficient estimators for these effects and apply them to a housing voucher experiment.

A nonparametric instrumental approach to confounding in competing risks models

This paper discusses nonparametric identification and estimation of the causal effect of a treatment in the presence of confounding, competing risks and random right-censoring. Our identification strategy is based on an instrumental variable. We show that the competing risks model generates a nonparametric quantile instrumental regression problem. Quantile treatment effects on the subdistribution function can be recovered from the regression function. A distinguishing feature of the model is that censoring and competing risks prevent identification at some quantiles. We characterize the set of quantiles for which exact identification is possible and give partial identification results for other quantiles. We outline an estimation procedure and discuss its properties. The finite sample performance of the estimator is evaluated through simulations. We apply the proposed method to the Health Insurance Plan of Greater New York experiment.

Mendelian randomization mixed-scale treatment effect robust identification and estimation for causal inference

Standard Mendelian randomization (MR) analysis can produce biased results if the genetic variant defining an instrumental variable (IV) is confounded and/or has a horizontal pleiotropic effect on the outcome of interest not mediated by the treatment variable. We provide novel identification conditions for the causal effect of a treatment in the presence of unmeasured confounding by leveraging a possibly invalid IV for which both the IV independence and exclusion restriction assumptions may be violated. The proposed Mendelian randomization mixed-scale treatment effect robust identification (MR MiSTERI) approach relies on (i) an assumption that the treatment effect does not vary with the possibly invalid IV on the additive scale; (ii) that the confounding bias does not vary with the possibly invalid IV on the odds ratio scale; and (iii) that the residual variance for the outcome is heteroskedastic with respect to the possibly invalid IV. Although assumptions (i) and (ii) have, respectively, appeared in the IV literature, assumption (iii) has not; we formally establish that their conjunction can identify a causal effect even with an invalid IV. MR MiSTERI is shown to be particularly advantageous in the presence of pervasive heterogeneity of pleiotropic effects on the additive scale. We propose a simple and consistent three-stage estimator that can be used as a preliminary estimator to a carefully constructed efficient one-step-update estimator. In order to incorporate multiple, possibly correlated, and weak invalid IVs, a common challenge in MR studies, we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach for strengthened identification and improved estimation accuracy. Both simulation studies and UK Biobank data analysis results demonstrate the robustness of the proposed methods.

Falsification of the instrumental variable conditions in Mendelian randomization studies in the UK Biobank

Mendelian randomization (MR) is an increasingly popular approach to estimating causal effects. Although the assumptions underlying MR cannot be verified, they imply certain constraints, the instrumental inequalities, which can be used to falsify the MR conditions. However, the instrumental inequalities are rarely applied in MR. We aimed to explore whether the instrumental inequalities could detect violations of the MR conditions in case studies analyzing the effect of commonly studied exposures on coronary artery disease risk.Using 1077 single nucleotide polymorphisms (SNPs), we applied the instrumental inequalities to MR models for the effects of vitamin D concentration, alcohol consumption, C-reactive protein (CRP), triglycerides, high-density lipoprotein (HDL) cholesterol, and low-density lipoprotein (LDL) cholesterol on coronary artery disease in the UK Biobank. For their relevant exposure, we applied the instrumental inequalities to MR models proposing each SNP as an instrument individually, and to MR models proposing unweighted allele scores as an instrument. We did not identify any violations of the MR assumptions when proposing each SNP as an instrument individually. When proposing allele scores as instruments, we detected violations of the MR assumptions for 5 of 6 exposures.Within our setting, this suggests the instrumental inequalities can be useful for identifying violations of the MR conditions when proposing multiple SNPs as instruments, but may be less useful in determining which SNPs are not instruments. This work demonstrates how incorporating the instrumental inequalities into MR analyses can help researchers to identify and mitigate potential bias.

Bounding the average causal effect in Mendelian randomisation studies with multiple proposed instruments: An application to prenatal alcohol exposure and attention deficit hyperactivity disorder

BACKGROUND

As large-scale observational data become more available, caution regarding causal assumptions remains critically important. This may be especially true for Mendelian randomisation (MR), an increasingly popular approach. Point estimation in MR usually requires strong, often implausible homogeneity assumptions beyond the core instrumental conditions. Bounding, which does not require homogeneity assumptions, is infrequently applied in MR.

OBJECTIVES

We aimed to demonstrate computing nonparametric bounds for the causal risk difference derived from multiple proposed instruments in an MR study where effect heterogeneity is expected.

METHODS

Using data from the Norwegian Mother, Father and Child Cohort Study (n = 2056) and Avon Longitudinal Study of Parents and Children (n = 6216) to study the average causal effect of maternal pregnancy alcohol use on offspring attention deficit hyperactivity disorder symptoms, we proposed 11 maternal SNPs as instruments. We computed bounds assuming subsets of SNPs were jointly valid instruments, for all combinations of SNPs where the MR model was not falsified.

RESULTS

The MR assumptions were violated for all sets with more than 4 SNPs in one cohort and for all sets with more than 2 SNPs in the other. Bounds assuming one SNP was an individually valid instrument barely improved on assumption-free bounds. Bounds tightened as more SNPs were assumed to be jointly valid instruments, and occasionally identified directions of effect, though bounds from different sets varied.

CONCLUSIONS

Our results suggest that, when proposing multiple instruments, bounds can contextualise plausible magnitudes and directions of effects. Computing bounds over multiple assumption sets, particularly in large, high-dimensional data, offers a means of triangulating results across different potential sources of bias within a study and may help researchers to better evaluate and emphasise which estimates are compatible with the most plausible assumptions for their specific setting.

Instrumental variable estimation of the marginal structural Cox model for time-varying treatments

Robins (1998) introduced marginal structural models, a general class of counterfactual models for the joint effects of time-varying treatments in complex longitudinal studies subject to time-varying confounding. Robins (1998) established the identification of marginal structural model parameters under a sequential randomization assumption, which rules out unmeasured confounding of treatment assignment over time. The marginal structural Cox model is one of the most popular marginal structural models for evaluating the causal effect of time-varying treatments on a censored failure time outcome. In this paper, we establish sufficient conditions for identification of marginal structural Cox model parameters with the aid of a time-varying instrumental variable, in the case where sequential randomization fails to hold due to unmeasured confounding. Our instrumental variable identification condition rules out any interaction between an unmeasured confounder and the instrumental variable in its additive effects on the treatment process, the longitudinal generalization of the identifying condition of Wang & Tchetgen Tchetgen (2018). We describe a large class of weighted estimating equations that give rise to consistent and asymptotically normal estimators of the marginal structural Cox model, thereby extending the standard inverse probability of treatment weighted estimation of marginal structural models to the instrumental variable setting. Our approach is illustrated via extensive simulation studies and an application to estimating the effect of community antiretroviral therapy coverage on HIV incidence.

Partial Identification of the Average Causal Effect in Multiple Study Populations: The Challenge of Combining Mendelian Randomization Studies

BACKGROUND

Researchers often use random-effects or fixed-effects meta-analysis to combine findings from multiple study populations. However, the causal interpretation of these models is not always clear, and they do not easily translate to settings where bounds, rather than point estimates, are computed.

METHODS

If bounds on an average causal effect of interest in a well-defined population are computed in multiple study populations under specified identifiability assumptions, then under those assumptions the average causal effect would lie within all study-specific bounds and thus the intersection of the study-specific bounds. We demonstrate this by pooling bounds on the average causal effect of prenatal alcohol exposure on attention deficit-hyperactivity disorder symptoms, computed in two European cohorts and under multiple sets of assumptions in Mendelian randomization (MR) analyses.

RESULTS

For all assumption sets considered, pooled bounds were wide and did not identify the direction of effect. The narrowest pooled bound computed implied the risk difference was between -4 and 34 percentage points.

CONCLUSIONS

All pooled bounds computed in our application covered the null, illustrating how strongly point estimates from prior MR studies of this effect rely on within-study homogeneity assumptions. We discuss how the interpretation of both pooled bounds and point estimation in MR is complicated by possible heterogeneity of effects across populations.

Negative Control Exposures: Causal Effect Identifiability and Use in Probabilistic-bias and Bayesian Analyses With Unmeasured Confounders

BACKGROUND

Probabilistic bias and Bayesian analyses are important tools for bias correction, particularly when required parameters are nonidentifiable. Negative controls are another tool; they can be used to detect and correct for confounding. Our goals are to present conditions that assure identifiability of certain causal effects and to describe and illustrate a probabilistic bias analysis and related Bayesian analysis that use a negative control exposure.

METHODS

Using potential-outcome models, we characterized assumptions needed for identification of causal effects using a dichotomous, negative control exposure when residual confounding exists. We defined bias parameters, characterized their relationships with the negative control and with specified causal effects, and described the corresponding probabilistic-bias and Bayesian analyses. We present analytic examples using data on hormone therapy and suicide attempts among transgender people. To address possible confounding by healthcare utilization, we used prior tetanus-diphtheria-pertussis (TdaP) vaccination as a negative control exposure.

RESULTS

Hormone therapy was weakly associated with risk (risk ratio [RR] = 0.9). The negative control exposure was associated with risk (RR = 1.7), suggesting confounding. Based on an assumed prior distribution for the bias parameter, the 95% simulation interval for the distribution of confounding-adjusted RR was (0.17, 1.6), with median 0.5; the 95% credibility interval was similar.

CONCLUSIONS

We used dichotomous negative control exposure to identify causal effects when a confounder was unmeasured under strong assumptions. It may be possible to relax assumptions and the negative control exposure could prove helpful for probabilistic bias analyses and Bayesian analyses.

Assessing the causal relationships between gout and hypertension: a bidirectional Mendelian randomisation study with coarsened exposures

Objectives

Observational studies have demonstrated associations between gout and hypertension, but whether they are causal remains unclear. Our work aims to assess the causal relationship between gout and hypertension.

Methods

We obtained genetic information from the Taiwan Biobank, including 88,347 participants and 686,439 single-nucleotide polymorphisms (SNPs). A novel model of Mendelian randomisation (MR) with coarsened exposures was used to examine the causality between the liability of gout on hypertension and vice versa, using 4 SNPs associated with gout and 10 SNPs associated with hypertension after removal of SNPs associated with measured confounders. The binary exposure (gout/hypertension) can be considered a coarsened approximation of a latent continuous trait. The inverse-variance weighted (IVW) and polygenic risk score (PRS) methods were used to estimate effect size. The MR analysis with coarsened exposures was performed with and without adjustments for covariates.

Results

Of the 88,347 participants, 3253 (3.68%) had gout and 11,948 (13.52%) had hypertension (men, 31.9%; mean age 51.1 [SD, 11.1] years). After adjusting to measured confounders, MR analysis with coarsened exposures showed a significant positive causal effect of the liability of gout on hypertension in both the IVW method (relative risk [RR], 1.10; 95% confidence interval [CI], 1.03–1.19; p = 0.0077) and the PRS method (RR, 1.10; 95% CI, 1.02–1.19; p = 0.0092). The result of causality was the same before and after involving measured confounders. However, there was no causal effect of the liability of hypertension on gout.

Conclusions

In this study, we showed that the liability of gout has a causal effect on hypertension, but the liability of hypertension does not have a causal effect on gout. Adequate management of gout may reduce the risk of developing hypertension.

Supplementary Information

The online version contains supplementary material available at 10.1186/s13075-022-02933-4.

Causal inference on neuroimaging data with Mendelian randomisation

While population-scale neuroimaging studies offer the promise of discovery and characterisation of subtle risk factors, massive sample sizes increase the power for both meaningful associations and those attributable to confounds. This motivates the need for causal modelling of observational data that goes beyond statements of association and towards deeper understanding of complex relationships between individual traits and phenotypes, clinical biomarkers, genetic variation, and brain-related measures of health. Mendelian randomisation (MR) presents a way to obtain causal inference on the basis of genetic data and explicit assumptions about the relationship between genetic variables, exposure and outcome. In this work, we provide an introduction to and overview of causal inference methods based on Mendelian randomisation, with examples involving imaging-derived phenotypes from UK Biobank to make these methods accessible to neuroimaging researchers. We motivate the use of MR techniques, lay out the underlying assumptions, introduce common MR methods and focus on several scenarios in which modelling assumptions are potentially violated, resulting in biased effect estimates. Importantly, we give a detailed account of necessary steps to increase the reliability of MR results with rigorous sensitivity analyses.

Comparative Safety and Effectiveness of Ticagrelor versus Clopidogrel in Patients With Acute Coronary Syndrome: An On-Treatment Analysis From a Multicenter Registry

Background:

The net clinical benefit of ticagrelor over clopidogrel in acute coronary syndrome (ACS) has recently been questioned by observational studies which did not account for time-dependent confounders. We aimed to assess the comparative safety and effectiveness of ticagrelor vs. clopidogrel accounting for non-adherence in a real-life setting.

Methods

This is a prospective, multicenter cohort study of patients with ACS discharged on ticagrelor or clopidogrel between 2015 and 2019. Major exclusions were previous intracranial bleeding, and the use of prasugrel or oral anticoagulation. Association of P2Y₁₂ inhibitor therapy with 1-year risk of Bleeding Academic Research Consortium Type 3 or 5 bleeding; major adverse cardiac events (MACEs), a composite endpoint of all-cause death, nonfatal myocardial infarction (MI), nonfatal stroke, or urgent target lesion revascularization; definite/probable stent thrombosis; vascular death; and net adverse clinical event (a composite endpoint of major bleeding and MACE) were analyzed according to the “on-treatment” principle, using fully adjusted Cox and Fine-Gray regression models with doubly robust inverse probability of censoring weighted estimators.

Results

Among 2,070 patients (mean age 63 years, 27% women, 62.5% ST-elevation MI), 1,035 were discharged on ticagrelor and clopidogrel, respectively. Ticagrelor-treated patients were younger and had few comorbidities, but high rates of medication non-compliance, compared with clopidogrel users. After comprehensive multivariate adjustments, ticagrelor did not increase the risk of major bleeding compared with clopidogrel [subhazard ratio, 1.40; 95% confidence interval (CI), 0.96–2.05], while proved superior in reducing MACE (hazard ratio 0.62; 95% CI, 0.43–0.90), vascular death (subhazard ratio, 0.71; 95% CI, 0.52–0.97) and definite/probable stent thrombosis (subhazard ratio, 0.54; 95% CI, 0.30-0.79); thereby resulting in a favorable net clinical benefit (hazard ratio 0.78; 95% CI, 0.60–0.98) compared with clopidogrel. Results from sensitivity analyses were consistent with those from the primary analysis, whereas those from the intention-to-treat (ITT) analysis went in the opposite direction.

Conclusion

Among all-comers with ACS, ticagrelor did not significantly increase the risk of major bleeding, while resulting in a net clinical benefit compared with clopidogrel. Further research is warranted to confirm these findings in high bleeding risk populations.

CREA-ARIAM Andalucía

(ClinicalTrials.gov Identifier: NCT02500290); Current pre-specified analysis (ClinicalTrials.gov Identifier: NCT04630288).

Invited Commentary: Conducting and Emulating Trials to Study Effects of Social Interventions

All else being equal, if we had 1 causal effect we wished to estimate, we would conduct a randomized trial with a protocol that mapped onto that causal question, or we would attempt to emulate that target trial with observational data. However, studying the social determinants of health often means there are not just 1 but several causal contrasts of simultaneous interest and importance, and each of these related but distinct causal questions may have varying degrees of feasibility in conducting trials. With this in mind, we discuss challenges and opportunities that arise when conducting and emulating such trials. We describe designing trials with the simultaneous goals of estimating the intention-to-treat effect, the per-protocol effect, effects of alternative protocols or joint interventions, effects within subgroups, and effects under interference, and we describe ways to make the most of all feasible randomized trials and emulated trials using observational data. Our comments are grounded in the study results of Courtin et al. (Am J Epidemiol. 2022;191(8):1444-1452).

Nonparametric bounds in two-sample summary-data Mendelian randomization: Some cautionary tales for practice

Recently, in genetic epidemiology, Mendelian randomization (MR) has become a popular approach to estimate causal exposure effects by using single nucleotide polymorphisms from genome-wide association studies (GWAS) as instruments. The most popular type of MR study, a two-sample summary-data MR study, relies on having summary statistics from two independent GWAS and using parametric methods for estimation. However, little is understood about using a nonparametric bound-based analysis, a popular approach in traditional instrumental variables frameworks, to study causal effects in two-sample MR. In this article, we explore using a nonparametric, bound-based analysis in two-sample MR studies, focusing primarily on implications for practice. We also propose a framework to assess how likely one can obtain more informative bounds if we used a different MR design, notably a one-sample MR design. We conclude by demonstrating our findings through two real data analyses concerning the causal effect of smoking on lung cancer and the causal effect of high cholesterol on heart attacks. Overall, our results suggest that while a bound-based analysis may be appealing due to its nonparametric nature, it is far more conservative in two-sample settings than in one-sample settings to get informative bounds on the causal exposure effect.

Robust Mendelian randomization in the presence of residual population stratification, batch effects and horizontal pleiotropy

Mendelian Randomization (MR) studies are threatened by population stratification, batch effects, and horizontal pleiotropy. Although a variety of methods have been proposed to mitigate those problems, residual biases may still remain, leading to highly statistically significant false positives in large databases. Here we describe a suite of sensitivity analysis tools that enables investigators to quantify the robustness of their findings against such validity threats. Specifically, we propose the routine reporting of sensitivity statistics that reveal the minimal strength of violations necessary to explain away the MR results. We further provide intuitive displays of the robustness of the MR estimate to any degree of violation, and formal bounds on the worst-case bias caused by violations multiple times stronger than observed variables. We demonstrate how these tools can aid researchers in distinguishing robust from fragile findings by examining the effect of body mass index on diastolic blood pressure and Townsend deprivation index.

Robust Mendelian randomization in the presence of residual population stratification, batch effects and horizontal pleiotropy

Mendelian Randomization (MR) studies are threatened by population stratification, batch effects, and horizontal pleiotropy. Although a variety of methods have been proposed to mitigate those problems, residual biases may still remain, leading to highly statistically significant false positives in large databases. Here we describe a suite of sensitivity analysis tools that enables investigators to quantify the robustness of their findings against such validity threats. Specifically, we propose the routine reporting of sensitivity statistics that reveal the minimal strength of violations necessary to explain away the MR results. We further provide intuitive displays of the robustness of the MR estimate to any degree of violation, and formal bounds on the worst-case bias caused by violations multiple times stronger than observed variables. We demonstrate how these tools can aid researchers in distinguishing robust from fragile findings by examining the effect of body mass index on diastolic blood pressure and Townsend deprivation index.

Mendelian randomization

Mendelian randomization (MR) is a term that applies to the use of genetic variation to address causal questions about how modifiable exposures influence different outcomes. The principles of MR are based on Mendel's laws of inheritance and instrumental variable estimation methods, which enable the inference of causal effects in the presence of unobserved confounding. In this Primer, we outline the principles of MR, the instrumental variable conditions underlying MR estimation and some of the methods used for estimation. We go on to discuss how the assumptions underlying an MR study can be assessed and give methods of estimation that are robust to certain violations of these assumptions. We give examples of a range of studies in which MR has been applied, the limitations of current methods of analysis and the outlook for MR in the future. The difference between the assumptions required for MR analysis and other forms of non-interventional epidemiological studies means that MR can be used as part of a triangulation across multiple sources of evidence for causal inference.

Diemer and Swanson Reply to "Considerations Before Using Pandemic as Instrument"

Dimitris and Platt (Am J Epidemiol. 2021;190(11):2275-2279) take on the challenging topic of using "shocks" such as the severe acute respiratory system coronavirus 2 (SARS-CoV-2) pandemic as instrumental variables to study the effect of some exposure on some outcome. Evoking our recent lived experiences, they conclude that the assumptions necessary for an instrumental variable analysis will often be violated and therefore strongly caution against such analyses. Here, we build upon this warranted caution while acknowledging that such analyses will still be pursued and conducted. We discuss strategies for evaluating or reasoning about when such an analysis is clearly inappropriate for a given research question, as well as strategies for interpreting study findings with special attention to incorporating plausible sources of bias in any conclusions drawn from a given finding.

On the identification of individual level pleiotropic, pure direct, and principal stratum direct effects without cross world assumptions

The analysis of natural direct and principal stratum direct effects has a controversial history in statistics and causal inference as these effects are commonly identified with either untestable cross world independence or graphical assumptions. This article demonstrates that the presence of individual level natural direct and principal stratum direct effects can be identified without cross world independence assumptions. We also define a new type of causal effect, called pleiotropy, that is of interest in genomics, and provide empirical conditions to detect such an effect as well. Our results are applicable for all types of distributions concerning the mediator and outcome.

Machine intelligence for individualized decision making under a counterfactual world: A rejoinder

This JASA rejoinder concerns the problem of individualized decision making under point, sign, and partial identification. The paper unifies various classical decision making strategies through a lower bound perspective proposed in Cui and Tchetgen Tchetgen (2020b) in the context of optimal treatment regimes under uncertainty due to unmeasured confounding. Building on this unified framework, the paper also provides a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision making/policy assignment.

Non-adherence in non-inferiority trials: pitfalls and recommendations

Non-adherence in non-inferiority trials can affect treatment effect estimates and often increases the chance of claiming non-inferiority under the standard intention-to-treat analysis. This article discusses the implications of different patterns of non-adherence in non-inferiority trials and offers practical recommendations for trial design, alternative analysis strategies, and outcome reporting to reduce bias in treatment estimates and improve transparency in reporting.

Risk of Stillbirth for Fetuses With Specific Birth Defects

OBJECTIVE

To estimate the risk of stillbirth (fetal death at 20 weeks of gestation or more) associated with specific birth defects.

METHODS

We identified a population-based retrospective cohort of neonates and fetuses with selected major birth defects and without known or strongly suspected chromosomal or single-gene disorders from active birth defects surveillance programs in nine states. Abstracted medical records were reviewed by clinical geneticists to confirm and classify all birth defects and birth defect patterns. We estimated risks of stillbirth specific to birth defects among pregnancies overall and among those with isolated birth defects; potential bias owing to elective termination was quantified.

RESULTS

Of 19,170 eligible neonates and fetuses with birth defects, 17,224 were liveborn, 852 stillborn, and 672 electively terminated. Overall, stillbirth risks ranged from 11 per 1,000 fetuses with bladder exstrophy (95% CI 0-57) to 490 per 1,000 fetuses with limb-body-wall complex (95% CI 368-623). Among those with isolated birth defects not affecting major vital organs, elevated risks (per 1,000 fetuses) were observed for cleft lip with cleft palate (10; 95% CI 7-15), transverse limb deficiencies (26; 95% CI 16-39), longitudinal limb deficiencies (11; 95% CI 3-28), and limb defects due to amniotic bands (110; 95% CI 68-171). Quantified bias analysis suggests that failure to account for terminations may lead to up to fourfold underestimation of the observed risks of stillbirth for sacral agenesis (13/1,000; 95% CI 2-47), isolated spina bifida (24/1,000; 95% CI 17-34), and holoprosencephaly (30/1,000; 95% CI 10-68).

CONCLUSION

Birth defect-specific stillbirth risk was high compared with the U.S. stillbirth risk (6/1,000 fetuses), even for isolated cases of oral clefts and limb defects; elective termination may appreciably bias some estimates. These data can inform clinical care and counseling after prenatal diagnosis.

Generalized instrumental inequalities: testing the instrumental variable independence assumption

This paper proposes a new set of testable implications for the instrumental variable independence assumption for discrete treatment, but unrestricted outcome and instruments: generalized instrumental inequalities. When outcome and treatment are both binary, but instruments are unrestricted, we show that the generalized instrumental inequalities are necessary and sufficient to detect all observable violations of the instrumental variable independence assumption. To test the generalized instrumental inequalities, we propose an approach combining a sample splitting procedure and an inference method for intersection bounds. This idea allows one to easily implement the test using existing Stata packages. We apply our proposed strategy to assess the validity of the instrumental variable independence assumption for various instruments used in the returns to college literature.

Nonparametric Bounds for the Risk Function

Nonparametric bounds for the risk difference are straightforward to calculate and make no untestable assumptions about unmeasured confounding or selection bias due to missing data (e.g., dropout). These bounds are often wide and communicate uncertainty due to possible systemic errors. An illustrative example is provided.

Generalizing the per-protocol treatment effect: The case of ACTG A5095

BACKGROUND

Intention-to-treat comparisons of randomized trials provide asymptotically consistent estimators of the effect of treatment assignment, without regard to compliance. However, decision makers often wish to know the effect of a per-protocol comparison. Moreover, decision makers may also wish to know the effect of treatment assignment or treatment protocol in a user-specified target population other than the sample in which the trial was fielded. Here, we aimed to generalize results from the ACTG A5095 trial to the US recently HIV-diagnosed target population.

METHODS

We first replicated the published conventional intention-to-treat estimate (2-year risk difference and hazard ratio) comparing a four-drug antiretroviral regimen to a three-drug regimen in the A5095 trial. We then estimated the intention-to-treat effect that accounted for informative dropout and the per-protocol effect that additionally accounted for protocol deviations by constructing inverse probability weights. Furthermore, we employed inverse odds of sampling weights to generalize both intention-to-treat and per-protocol effects to a target population comprising US individuals with HIV diagnosed during 2008-2014.

RESULTS

Of 761 subjects in the analysis, 82 dropouts (36 in the three-drug arm and 46 in the four-drug arm) and 59 protocol deviations (25 in the three-drug arm and 34 in the four-drug arm) occurred during the first 2 years of follow-up. A total of 169 subjects incurred virologic failure or death. The 2-year risks were similar both in the trial and in the US HIV-diagnosed target population for estimates from the conventional intention-to-treat, dropout-weighted intention-to-treat, and per-protocol analyses. In the US target population, the 2-year conventional intention-to-treat risk difference (unit: %) for virologic failure or death comparing the four-drug arm to the three-drug arm was -0.4 (95% confidence interval: -6.2, 5.1), while the hazard ratio was 0.97 (95% confidence interval: 0.70, 1.34); the 2-year risk difference was -0.9 (95% confidence interval: -6.9, 5.3) for the dropout-weighted intention-to-treat comparison (hazard ratio = 0.95, 95% confidence interval: 0.68, 1.32) and -0.7 (95% confidence interval: -6.7, 5.5) for the per-protocol comparison (hazard ratio = 0.96, 95% confidence interval: 0.69, 1.34).

CONCLUSION

No benefit of four-drug antiretroviral regimen over three-drug regimen was found from the conventional intention-to-treat, dropout-weighted intention-to-treat or per-protocol estimates in the trial sample or target population.

Mendelian randomization with a binary exposure variable: interpretation and presentation of causal estimates

Mendelian randomization uses genetic variants to make causal inferences about a modifiable exposure. Subject to a genetic variant satisfying the instrumental variable assumptions, an association between the variant and outcome implies a causal effect of the exposure on the outcome. Complications arise with a binary exposure that is a dichotomization of a continuous risk factor (for example, hypertension is a dichotomization of blood pressure). This can lead to violation of the exclusion restriction assumption: the genetic variant can influence the outcome via the continuous risk factor even if the binary exposure does not change. Provided the instrumental variable assumptions are satisfied for the underlying continuous risk factor, causal inferences for the binary exposure are valid for the continuous risk factor. Causal estimates for the binary exposure assume the causal effect is a stepwise function at the point of dichotomization. Even then, estimation requires further parametric assumptions. Under monotonicity, the causal estimate represents the average causal effect in 'compliers', individuals for whom the binary exposure would be present if they have the genetic variant and absent otherwise. Unlike in randomized trials, genetic compliers are unlikely to be a large or representative subgroup of the population. Under homogeneity, the causal effect of the exposure on the outcome is assumed constant in all individuals; rarely a plausible assumption. We here provide methods for causal estimation with a binary exposure (although subject to all the above caveats). Mendelian randomization investigations with a dichotomized binary exposure should be conceptualized in terms of an underlying continuous variable.

Understanding the Assumptions Underlying Instrumental Variable Analyses: a Brief Review of Falsification Strategies and Related Tools

PURPOSE OF REVIEW

Instrumental variable (IV) methods continue to be applied to questions ranging from genetic to social epidemiology. In the epidemiologic literature, discussion of whether the assumptions underlying IV analyses hold is often limited to only certain assumptions and even then, arguments are mostly made using subject matter knowledge. To complement subject matter knowledge, there exist a variety of falsification strategies and other tools for weighing the plausibility of the assumptions underlying IV analyses.

RECENT FINDINGS

There are many tools that can refute the IV assumptions or help estimate the magnitude or direction of possible bias if the conditions do not hold perfectly. Many of these tools, including both recently developed strategies and strategies described decades ago, are underused or only used in specific applications of IV methods in epidemiology.

SUMMARY

Although estimating causal effects with IV analyses relies on unverifiable assumptions, the assumptions can sometimes be refuted. We suggest that the epidemiologists using IV analyses employ all the falsification strategies that apply to their research question in order to avoid settings that demonstrably violate a core condition for valid inference.