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Causal diagrams
, 2008
"... Abstract: From their inception, causal systems models (more commonly known as structuralequations models) have been accompanied by graphical representations or path diagrams that provide compact summaries of qualitative assumptions made by the models. These diagrams can be reinterpreted as probabil ..."
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Cited by 23 (2 self)
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Abstract: From their inception, causal systems models (more commonly known as structuralequations models) have been accompanied by graphical representations or path diagrams that provide compact summaries of qualitative assumptions made by the models. These diagrams can be reinterpreted as probability models, enabling use of graph theory in probabilistic inference, and allowing easy deduction of independence conditions implied by the assumptions. They can also be used as a formal tool for causal inference, such as predicting the effects of external interventions. Given that the diagram is correct, one can see whether the causal effects of interest (target effects, or causal estimands) can be estimated from available data, or what additional observations are needed to validly estimate those effects. One can also see how to represent the effects as familiar standardized effect measures. The present article gives an overview of: (1) components of causal graph theory; (2) probability interpretations of graphical models; and (3) methodologic implications of the causal and probability structures encoded in the graph, such as sources of bias and the data needed for their control.
Instruments for Causal Inference  An Epidemiologist’s Dream?
, 2006
"... The use of instrumental variable (IV) methods is attractive 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 h ..."
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Cited by 18 (0 self)
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The use of instrumental variable (IV) methods is attractive 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 required 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
Mendelian Randomisation: Why Epidemiology needs a Formal Language for Causality
"... abstract. For ethical or practical reasons, randomised cotrolled trials are not always an option to test epidemiological hypotheses. Epidemiologists are consequently faced with the problem of how to make causal inferences from observational data, particularly when confounding is present and not full ..."
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Cited by 6 (4 self)
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abstract. For ethical or practical reasons, randomised cotrolled trials are not always an option to test epidemiological hypotheses. Epidemiologists are consequently faced with the problem of how to make causal inferences from observational data, particularly when confounding is present and not fully understood. The method of instrumental variables can be exploited for this purpose in a process known as Mendelian randomisation. However, the approach has not been developed to deal satisfactorily with a binary outcome variable in the presence of confounding. This has not been properly understood in the medical literature. We show that by defining the problem using a formal causal language, the difficulties can be identified and misinterpretations avoided. 1
Instrumental Variable Estimators for Binary Outcomes
, 2009
"... The Centre for Market and Public Organisation (CMPO) is a leading research centre, combining expertise in economics, geography and law. Our objective is to study the intersection between the public and private sectors of the economy, and in particular to understand the right way to organise and deli ..."
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Cited by 5 (1 self)
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The Centre for Market and Public Organisation (CMPO) is a leading research centre, combining expertise in economics, geography and law. Our objective is to study the intersection between the public and private sectors of the economy, and in particular to understand the right way to organise and deliver public services. The Centre aims to develop research, contribute to the public debate and inform policymaking. CMPO, now an ESRC Research Centre was established in 1998 with two large
Twostage instrumental variable methods for estimating the causal odds ratio: analysis of bias
 Statistics in Medicine 2011
"... We present closed form expressions of asymptotic bias for the causal odds ratio from two estimation approaches of instrumental variable logistic regression: 1) the twostage predictor substitution (2SPS) method; and 2) the twostage residual inclusion (2SRI) approach. Under the 2SPS approach, the fi ..."
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Cited by 2 (0 self)
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We present closed form expressions of asymptotic bias for the causal odds ratio from two estimation approaches of instrumental variable logistic regression: 1) the twostage predictor substitution (2SPS) method; and 2) the twostage residual inclusion (2SRI) approach. Under the 2SPS approach, the first stage model yields the predicted value of treatment as a function of an instrument and covariates, and in the second stage model for the outcome, this predicted value replaces the observed value of treatment as a covariate. Under the 2SRI approach, the first stage is the same, but the residual term of the first stage regression is included in the second stage regression, retaining the observed treatment as a covariate. Our bias assessment is for a different context than that of Terza[1] who focused on the causal odds ratio conditional on the unmeasured confounder, whereas we focus on the causal odds ratio among compliers under the principal stratification framework. Our closed form bias results show that the 2SPS logistic regression generates asymptotically biased estimates of this causal odds ratio when there is no unmeasured confounding and that this bias increases with increasing unmeasured confounding. The 2SRI logistic regression is asymptotically unbiased when there is no unmeasured confounding, but when there is unmeasured confounding, there is bias and it increases with increasing unmeasured confounding. The closed form bias results provide guidance for using these IV logistic regression methods. Our simulation results are consistent with our closed form analytic results under different combinations of parameter settings. Copyright c ○ 2000 John Wiley & Sons, Ltd. 1.
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"... Mendelian randomization as an instrumental variable approach to causal inference ..."
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Mendelian randomization as an instrumental variable approach to causal inference
www.mrc.ac.uk/complexinterventionsguidance Developing and evaluating complex interventions: new guidance Contents
"... Developing and evaluating complex interventions: new guidance Prepared on behalf of the Medical Research Council by: ..."
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Developing and evaluating complex interventions: new guidance Prepared on behalf of the Medical Research Council by:
DOI: 10.1111/j.15410420.2008.01066.x A Comparison of Methods for Estimating the Causal Effect of a Treatment in Randomized Clinical Trials Subject to Noncompliance
, 2009
"... Summary. We consider the analysis of clinical trials that involve randomization to an active treatment (T =1)oracontrol treatment (T = 0), when the active treatment is subject to allornothing compliance. We compare three approaches to estimating treatment efficacy in this situation: astreated ana ..."
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Summary. We consider the analysis of clinical trials that involve randomization to an active treatment (T =1)oracontrol treatment (T = 0), when the active treatment is subject to allornothing compliance. We compare three approaches to estimating treatment efficacy in this situation: astreated analysis, perprotocol analysis, and instrumental variable (IV) estimation, where the treatment effect is estimated using the randomization indicator as an IV. Both model and methodofmoment based IV estimators are considered. The assumptions underlying these estimators are assessed, standard errors and mean squared errors of the estimates are compared, and design implications of the three methods are examined. Extensions of the methods to include observed covariates are then discussed, emphasizing the role of compliance propensity methods and the contrasting role of covariates in these extensions. Methods are illustrated on data from the Women Take Pride study, an assessment of behavioral treatments for women with heart disease.