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Issues in the Reporting and Conduct of Instrumental Variable Studies

A Systematic Review

Davies, Neil M.a; Smith, George Daveya; Windmeijer, Frankb; Martin, Richard M.a

Author Information
doi: 10.1097/EDE.0b013e31828abafb


Observational data are used to estimate associations of exposures with outcomes, but if exposures are not allocated randomly these associations may be confounded by associated characteristics.1–3 An approach to estimate causal effects in the presence of unmeasured confounding is instrumental variable analysis.4–7 Instrumental variables are defined by three assumptions: (1) relevance, that is, that the variable is associated with exposure; (2) exclusion restriction, that is, that the variable affects only the outcome through the likelihood of exposure; and (3) the instrument is independent of confounders.4,5 Without further assumptions, instrumental variables can generally estimate only the maximum and minimum values of the causal treatment effect consistent with the observed data. To estimate specific parameters (also referred to as point identification), such as the average treatment effect, stronger assumptions are required.5,8 Detailed reviews of instrumental variable methodology are available elsewhere,5,7–9 including use of Mendelian randomization10–12 and data from randomized controlled trials.13

For instrumental variables to provide meaningful evidence, authors must report sufficient information for readers and reviewers to assess, where possible, whether the instrumental variable assumptions are likely to hold. However, despite their increasing use in epidemiology14,15—and concerns that reporting is inadequate15—there are no specific recommendations for reporting of studies using instrumental variables.3 We build on previous findings15 by investigating the information provided in a broad range of clinical epidemiology studies using instrumental variables, including whether the point-identifying assumptions were specified. We propose a checklist of information to be reported by studies using instrumental variables.

We searched Embase and Medline for studies containing the term “instrumental variable$” published at any time up to October 2012. We included all articles with a clinical intervention and a clinical outcome. We excluded articles that (1) did not use instrumental variables; (2) had a nonclinical outcome or exposure, such as economic exposures or outcomes; (3) were analyses of randomized controlled trials; (4) were reviews or theoretical articles; or (5) were related publications from a single study. We extracted the following information from eligible studies: type of study, methods used to estimate the models, number of observations, whether the study discussed the identifying assumptions (ie, the relevance and exclusion restriction assumptions), and whether the authors tested the association of the instruments and observed confounders.

Our search returned 756 articles, of which 90 studies published since 1994 were eligible (eFigure, The number of studies using instrumental variables has increased markedly between 2003 and 2012 (Figure). Studies were published in general medical journals,16–24 economics and health services research journals,25–39 epidemiology journals,40–46 and a range of specialist journals (eTable 1,–105 The most commonly studied exposures were surgical and pharmacological (eTable 2, Several sources of variation were used as instruments (Table 1). A minority (n = 25, 28%) reported partial F-statistics or partial r2 of the association of the instruments with the exposures, with partial F-test statistics ranging from 4.21 to 32,266.* Others (n = 39, 43%) reported other measures, such as the C-statistic or the risk difference of exposure by level of the instrument. To quantify the association between instrument and exposure, six reported both partial F-statistics and risk differences.44,83,86,91,92,103 The remaining studies (n = 20, 22%) reported neither the magnitude of the association nor a partial F-test. The methods used to estimate the causal parameters and the target parameters estimated are shown in Tables 2 and 3, respectively.

Cumulative number of studies listed in Medline and Embase that used non-genetic instrumental variable analysis for medical research over time.
Type of Instrumental Variable in 90 Studies
Estimation Methods Used in 90 Instrumental Variable Studies
Target Parameter in 90 Studies Using Instrumental Variables

Some studies reported calculating standard errors that were valid under homoskedasticy (Table 4). Of these, a minority used two-stage least squares. Methods used to allow for heteroscedasticity included nonparametric bootstraps, clustered robust standard errors, sandwich estimators, generalized estimated equations, or generalized method of moments. A minority (n = 15, 17%) of studies reported the selection model equation (also known as the first-stage regression). The association of observed covariates with the instruments was reported by 44 (49%) studies and a minority (n = 20, 22%) of studies used multiple instruments in a single model.

Methods Used to Estimate Standard Errors and Reported Information in 90 Studies Using Instrumental Variables

Overall, we found that although the number of studies using instrumental variables is increasing, many did not report enough information to determine whether the inferences the authors drew were supported by their evidence. We propose a checklist of information to guide instrumental variable studies (Table 5).

Proposed Reporting Checklist for Authors, Editors, and Reviewers of Instrumental Variable Studies

Although estimation methods for instrumental variables are asymptotically unbiased, studies using small samples or weak instruments that explain little of the variation in the exposure can produce biased estimates of the causal parameters.106,107 The sample size required for a sufficiently powered instrumental variable analysis depends on the distributions of the outcomes, exposures, and instruments. All else being equal, the weaker the association of the instrument with the exposure, the larger the sample size required to detect a given effect size. Studies with insufficient observations are unlikely to provide evidence of clinically meaningful treatment effects or differences between the instrumental variable and conventional observational results.15

Reporting of the strength of the association between instrumental variables and exposures was frequently insufficient because the partial F-statistic or partial r2 were not provided. If studies do not report the strength of the association of instruments with exposure, it is not possible to tell whether the instrument is valid or whether weak instruments could bias the results toward the conventional observational estimates.106–109 Many studies reported the magnitude of the association of the instrument with exposure using either the risk difference in exposure by value of the instrumental variable or the C-statistic. However, these parameters do not incorporate information about the number of observations included in the analysis.

Although the associations of an instrument and the unobserved confounders cannot be estimated, the associations with observed potential confounding factors can be quantified and tested and should be reported. Of the 90 eligible studies, 44 reported the association of observed covariates with the instrumental variables, and of these studies, 15 performed no formal statistical tests.§ Of the studies that tested these associations, all except three23,30,45 found some evidence of associations of covariates with the instruments. This suggests that the instrumental variable assumptions are violated to some extent in each of these studies, and it is not possible to prove which approach (the instrumental variable or conventional results) would be more prone to bias.5 Furthermore, some studies used characteristics of the patients as instruments for their treatment; such characteristics are unlikely to be independent of the confounding variables.27,29,51,62

Ideally, studies should identify their results using the weakest set of assumptions possible. The studies used many different methods to estimate their results, and hence targeted different parameters. Structural mean models can estimate causal risk differences, risk ratios, or odds ratios under relatively weak semiparametric assumptions,5,8,110 although this comes at a cost of precision. Estimators with stronger assumptions, such as a fully specified parametric bivariate probit, may be more precise and can also identify causal risk differences, risk ratios, or odds ratios.7 If the assumptions underlying the bivariate probit do not hold in the data, then the bivariate probit estimates may be biased.111

Standard output from techniques such as two-stage least squares report standard errors that are valid under conditional homoscedasticity. If the variance of the error terms is heteroskedastic (eg, if the outcome is binary in a linear effects model), then the estimates of the confidence intervals may be biased. Therefore, studies should use heteroscedasticity robust standard errors (sandwich estimators).112

In most epidemiologic studies, treatment effects are likely to be heterogeneous across the population. This is particularly true for studies with binary outcomes,5 which can be point-identified by assuming monotonicity or no effect modification.5,7 Under monotonicity, studies identify a weighted average of local average treatment effects. This causal parameter is the effect of treatment on those persons whose treatment decision was affected by the instrumental variable.113 The assumption of no effect modification by the instrument among the treated identifies the average effect of treatment on the treated subpopulation (see Hernán and Robins5 for sufficient conditions and a detailed exposition of these issues). Even given identical observational and experimental samples in which the average treatment effects were identical, the parameters estimated by instrumental variables will not necessarily equal the intention-to-treat parameter found in a randomized controlled trial. This is true for two reasons: first, the persons who choose to be treated or are caused to change treatment may not be representative of the whole population; second, the intention-to-treat parameter is the difference in outcomes across two arms of a trial. If there has been noncompliance or incomplete follow-up, then the intention-to-treat estimate will generally be smaller than the average treatment effect in the population.13

Instrumental variables can estimate the causal effects of exposures in the presence of unmeasured or residual confounding.4,5,114,115 At present, the reporting of studies using instrumental variables is often inadequate to determine whether the instrumental variables were valid or whether the authors’ inferences are supported by the empirical evidence presented. Strong assumptions must be satisfied for instrumental variable studies to be valid and are not always met. Therefore, it is essential for studies to report tests of these assumptions, as readers will need to determine whether the bias because of residual confounding is likely to be smaller or greater than the bias because of violations of the exclusion restriction assumption, magnified by the weakness of the instruments.5 Studies using instrumental variables must report sufficient information for reviewers, readers, and editors to evaluate the extent to which the results provide evidence about the hypotheses being asked.


We are grateful for comments and suggestions from Paul Clarke, Tom Palmer, Nic Timpson, and Vanessa Didelez.

* References 24–28, 30, 36, 37, 45, 46, 49, 51, 52, 57, 64, 72, 81, 82, 88, 89, 93, 94, 100, 101, 104.
Cited Here

† References 17–21, 23, 29, 31, 33, 40–42, 47, 48, 54–56, 59, 61–63, 65–68, 70, 71, 73–75, 77, 78, 80, 85, 87, 90, 96, 102.
Cited Here

‡ References 16, 22, 32, 34, 38, 39, 43, 50, 53, 58, 60, 69, 76, 79, 84, 95, 97–99.
Cited Here

§ References 18, 21, 33, 35, 41, 42, 44, 52, 74, 76, 85, 90–92, 101.
Cited Here


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