We investigate conditions sufficient for identification of average treatment effects using instrumental variables. First we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect. We then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument. Finally we derive the probability limit of the standard IV estimator under these conditions. It is seen to be a weighted average of local average treatment effects.

Evolution and Rationality Some Recent Game-Theoretic Results. Identification and Estimation of Local Average Treatment Effects

Developments in genome-wide association studies and the increasing availability of summary genetic association data have made application of Mendelian randomization relatively straightforward. However, obtaining reliable results from a Mendelian randomization investigation remains problematic, as the conventional inverse-variance weighted method only gives consistent estimates if all of the genetic variants in the analysis are valid instrumental variables. We present a novel weighted median estimator for combining data on multiple genetic variants into a single causal estimate. This estimator is consistent even when up to 50% of the information comes from invalid instrumental variables. In a simulation analysis, it is shown to have better finite-sample Type 1 error rates than the inverse-variance weighted method, and is complementary to the recently proposed MR-Egger (Mendelian randomization-Egger) regression method. In analyses of the causal effects of low-density lipoprotein cholesterol and high-density lipoprotein cholesterol on coronary artery disease risk, the inverse-variance weighted method suggests a causal effect of both lipid fractions, whereas the weighted median and MR-Egger regression methods suggest a null effect of high-density lipoprotein cholesterol that corresponds with the experimental evidence. Both median-based and MR-Egger regression methods should be considered as sensitivity analyses for Mendelian randomization investigations with multiple genetic variants.

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Consistent Estimation in Mendelian Randomization with Some Invalid Instruments Using a Weighted Median Estimator.

Features of neighborhoods or residential environments may affect health and contribute to social and race/ethnic inequalities in health. The study of neighborhood health effects has grown exponentially over the past 15 years. This chapter summarizes key work in this area with a particular focus on chronic disease outcomes (specifically obesity and related risk factors) and mental health (specifically depression and depressive symptoms). Empirical work is classified into two main eras: studies that use census proxies and studies that directly measure neighborhood attributes using a variety of approaches. Key conceptual and methodological challenges in studying neighborhood health effects are reviewed. Existing gaps in knowledge and promising new directions in the field are highlighted.

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Neighborhoods and health.

Noncausal associations between exposures and outcomes are a threat to validity of causal inference in observational studies. Many techniques have been developed for study design and analysis to identify and eliminate such errors. Such problems are not expected to compromise experimental studies, where careful standardization of conditions (for laboratory work) and randomization (for population studies) should, if applied properly, eliminate most such noncausal associations. We argue, however, that a routine precaution taken in the design of biologic laboratory experiments--the use of "negative controls"--is designed to detect both suspected and unsuspected sources of spurious causal inference. In epidemiology, analogous negative controls help to identify and resolve confounding as well as other sources of error, including recall bias or analytic flaws. We distinguish 2 types of negative controls (exposure controls and outcome controls), describe examples of each type from the epidemiologic literature, and identify the conditions for the use of such negative controls to detect confounding. We conclude that negative controls should be more commonly employed in observational studies, and that additional work is needed to specify the conditions under which negative controls will be sensitive detectors of other sources of error in observational studies.

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Negative controls: a tool for detecting confounding and bias in observational studies.

The use of instrumental variable (IV) methods is attrac- tive because, even in the presence of unmeasured confounding, such methods may consistently estimate the average causal effect of an exposure on an outcome. However, for this consistent estimation to be achieved, several strong conditions must hold. We review the definition of an instrumental variable, describe the conditions re- quired to obtain consistent estimates of causal effects, and explore their implications in the context of a recent application of the instrumental variables approach. We also present (1) a description of the connection between 4 causal models—counterfactuals, causal directed acyclic graphs, nonparametric structural equation models, and linear structural equation models—that have been used to describe instrumental variables methods; (2) a unified presentation of IV methods for the average causal effect in the study population through structural mean models; and (3) a discussion and new extensions of instrumental variables methods based on assumptions of monotonicity.

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Instruments for causal inference: an epidemiologist's dream?

To correct for confounding, the method of instrumental variables (IV) has been proposed. Its use in medical literature is still rather limited because of unfamiliarity or inapplicability. By introducing the method in a nontechnical way, we show that IV in a linear model is quite easy to understand and easy to apply once an appropriate instrumental variable has been identified. We also point out some limitations of the IV estimator when the instrumental variable is only weakly correlated with the exposure. The IV estimator will be imprecise (large standard error), biased when sample size is small, and biased in large samples when one of the assumptions is only slightly violated. For these reasons, it is advised to use an IV that is strongly correlated with exposure. However, we further show that under the assumptions required for the validity of the method, this correlation between IV and exposure is limited. Its maximum is low when confounding is strong, such as in case of confounding by indication. Finally, we show that in a study in which strong confounding is to be expected and an IV has been used that is moderately or strongly related to exposure, it is likely that the assumptions of IV are violated, resulting in a biased effect estimate. We conclude that instrumental variables can be useful in case of moderate confounding but are less useful when strong confounding exists, because strong instruments cannot be found and assumptions will be easily violated.

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Instrumental variables: application and limitations.

Reporting of covariate selection and balance assessment in propensity score analysis is suboptimal: a systematic review

Studying the temporal dynamics of bistable perception can be useful for understanding neural mechanisms underlying the phenomenon. We take a closer look at those temporal dynamics, using data from four different ambiguous stimuli. We focus our analyses on two recurrent themes in bistable perception literature. First, we address the question whether percept durations follow a gamma distribution, as is commonly assumed. We conclude that this assumption is not justified by the gamma distribution’s approximate resemblance to distributions of percept durations. We instead present two straightforward distributions of reciprocal percept durations (i.e., rates) that both easily surpass the classic gamma distribution in terms of resemblance to empirical data. Second, we compare the distributions arising from binocular rivalry with those from other forms of bistable perception. Parallels in temporal dynamics between those classes of stimuli are often mentioned as an indication of a similar neural basis, but have never been studied in detail. Our results demonstrate that the distributions arising from binocular rivalry and other forms of bistable perception are indeed similar up to a high level of detail.

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Distributions of alternation rates in various forms of bistable perception.

In randomized controlled trials as well as in observational studies, researchers are often interested in effects of treatment or exposure in different subgroups, i.e. effect modification [1, 2]. There are several methods to assess effect modification and the debate on which method is best is still ongoing [2–5]. In this article we focus on an invalid method to assess effect modification, which is often used in articles in health sciences journals [6], namely concluding that there is no effect modification if the confidence intervals of the subgroups are overlapping [7–9].

When assessing effect modification by looking at overlap of the 95% confidence intervals in subgroups, a type 1 error probability of 0.05 is often mistakenly assumed. In other words, if the confidence intervals are overlapping, the difference in effect estimates between the two subgroups is judged to be statistically insignificant. By using mathematical derivation, we calculated that the chance of finding non-overlapping 95% confidence intervals under the null hypothesis is 0.0056 if the variance of both effect estimates is equal and the effect estimates are independent (see Supplemental material for derivation of this probability). If the variance of the effect estimates is not equal, the chance of finding non-overlapping 95% confidence intervals can be calculated by taking into account ρ, i.e. the ratio between the standard deviations in the subgroups, σ2/σ1 (Supplementary material, formula (3)). Figure. 1 shows the relation between ρ and the type 1 error probability if the effect estimates are independent. If the effect estimates are not independent, the correlation coefficient between the effect estimates can also be accounted for (Supplementary material, formula (3)).



Fig. 1

Relation between ρ, which is the ratio of σ2 and σ1, and the probability of non-overlapping confidence intervals under the null hypothesis (type 1 error)



To arrive at a type 1 error probability of 0.05, 83.4% confidence intervals should be calculated around the effect estimates in subgroups if the variance is equal and the effect estimates are independent (see Supplementary material for derivation of this percentage). If the variance is not equal, ρ should be taken into account (Supplementary material, formula (11)). Figure. 2 shows the relation between ρ and the level of the confidence interval. If the effect estimates are not independent, the correlation coefficient should be taken into account (Supplementary material, formula (11)). Adapting the level of the confidence interval can be especially useful for graphical presentations, for example in meta-analyses [10]. However, it is necessary to explicitly and clearly state which percentage confidence interval is calculated and its meaning should be thoroughly explained to the reader. Many readers will still interpret this ‘new’ confidence interval as if it were a 95% confidence interval, because this percentage is so commonly used. To prevent such confusion, other methods to assess effect modification could be used, such as calculating a 95% confidence interval around the difference in effect estimates [8].



Fig. 2

Relation between ρ, which is the ratio of σ2 and σ1, and the percentage confidence intervals to be calculated to arrive at a type 1 error probability of 0.05



The assumption used in the formulas presented in the appendices is that the effect estimators in the subgroups are normally distributed. Assuming that epidemiologic effect measures, such as the odds ratio, risk ratio, hazard ratio and risk difference, follow a normal distribution, the methods presented can also be used for these epidemiologic measures. Note that the assumption for normality is generally unreasonable in small samples, but a satisfactory approximation in large samples.

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The (mis)use of overlap of confidence intervals to assess effect modification

*Accepted 1 April 2008Background In medical research both propensity score methods and logisticregression analysis are used to estimate treatment effects in obser-vational studies. From literature reviews it has been concluded thattreatment effect estimates from both methods are quite similar.With this study we will show that there are systematic differenceswhich can be substantial.Methods We used a simulated population with a known marginal treatmenteffect and applied a propensity score method and logistic regressionanalysis to adjust for confounding.Results The adjusted treatment effect in logistic regression is in generalfurther away from the true marginal treatment effect than theadjusted effect in propensity score methods. The difference issystematic and dependent on the incidence proportion, the numberof prognostic factors and the magnitude of the treatment effect. Forinstance, a substantial difference of 20% is found when the treat-ment effect is 2.0, the incidence proportion is 0.20 and there aremore than 11 prognostic factors.Conclusions Propensity score methods give in general treatment effect estimatesthat are closer to the true marginal treatment effect than a logisticregression model in which all confounders are modelled.Keywords Propensity scores, confounding, adjusted treatment effect, logisticregression, conditional treatment effect, marginal treatment effect,observational studies

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Wiebe R. Pestman

Papers

Instrumental variables: application and limitations.

Reporting of covariate selection and balance assessment in propensity score analysis is suboptimal: a systematic review

Distributions of alternation rates in various forms of bistable perception.

The (mis)use of overlap of confidence intervals to assess effect modification

Systematic differences in treatment effect estimates between propensity score methods and logistic regression