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A Weight of Evidence Approach to Causal Inference

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A Weight of Evidence Approach to Causal Inference Journal of Clinical Epidemiology 62 (2009) 270e277 A weight of evidence approach to causal inference Gerard Swaena,*, Ludovic van Amelsvoortb aEpidemiology Department, the Dow Chemical Company, The Netherlands bEpidemiology Department, School for Public health and Primary Care (CAPHRI), Maastricht University, The Netherlands Accepted 24 June 2008 Abstract Objective: The Bradford Hill criteria are the best available criteria for causal inference. However, there is no information on how the criteria should be weighed and they cannot be combined into one probability estimate for causality. Our objective is to provide an empirical basis for weighing the Bradford Hill criteria and to develop a transparent method to estimate the probability for causality. Study Design and Setting: All 159 agents classified by International Agency for Research of Cancer as category 1 or 2A carcinogens were evaluated by applying the nine Bradford Hill criteria. Discriminant analysis was used to estimate the weights for each of the nine Bradford Hill criteria. Results: The discriminant analysis yielded weights for the nine causality criteria. These weights were used to combine the nine criteria into one overall assessment of the probability that an association is causal. The criteria strength, consistency of the association and exper- imental evidence were the three criteria with the largest impact. The model correctly predicted 130 of the 159 (81.8%) agents. Conclusion: The proposed approach enables using the Bradford Hill criteria in a quantitative manner resulting in a probability estimate of the probability that an association is causal. Ó 2008 Published by Elsevier Inc. Keywords: Causal inference; Bradford Hill criteria; Epidemiology; Risk assessment; Methodology; Epistemology 1. Introduction criteria formulated in a landmark surgeon general’s report on smoking and health. These causality criteria are widely One of the main objectives of epidemiological research accepted and only marginal changes have been proposed is to identify causes of disease. A cause of a disease can be since they were first published. They are not only used in defined as a factor that affects its incidence. Elimination of epidemiology. Guzelian et al. proposed a framework for ev- the causal factor would result in a change in disease inci- idence-based toxicology which heavily relies on the Brad- dence. There is no universal consensus on the definition ford Hill criteria for causal inference [5]. of a cause and several types of definitions have been The rigid use of strict causality criteria has been chal- described [1,2]. lenged. Kundi for instance pointed out that causality crite- Causal inference from epidemiological studies is com- ria can be used to falsely postpone public health action plex and has been the subject of extensive debate. For many under the pretext that the available evidence does not fulfill associations between risk factors and health effects there is the criteria [1]. Kundi proposed to use a pragmatic ap- still some room for doubt about their causality. Perhaps the proach for assessing causal inference based on prior knowl- most realistic conclusion on causal inference was drawn by edge, epidemiology, animal studies, and in vitro studies. Weed who stated that the purpose of epidemiology is not to Kundi proposed that temporal relation, association, and en- prove causeeeffect relationships but to acquire knowledge vironmental and population equivalence would suffice for about the determinants and distribution of disease and to a verdict of potential causation. apply that knowledge to improve public health [3]. From the papers published on this topic, it is clear that Bradford Hill has formulated a set of criteria to assess the Bradford Hill criteria still remain key components to causality [4]. Hill’s criteria were an expansion of a set of causal inference. However, there is no agreement on what weight should be given to each individual criterion and per- haps trying to draw absolute conclusions on causality is too far fetched. A more fruitful and practical approach would * Corresponding author. Tel.: 31 (0)433626042; Fax: 31 (0)115674164. Epidemiology Department, The Dow Chemical Company, P.O. Box 444, be to use the Bradford Hill criteria to estimate the likeli- Terneuzen, Zeeland, The Netherlands. hood that an association is causal. The outcome of such E-mail address: [email protected] (G. Swaen). a probabilistic approach could be an estimate of the 0895-4356/09/$ e see front matter Ó 2008 Published by Elsevier Inc. doi: 10.1016/j.jclinepi.2008.06.013 G. Swaen, L. van Amelsvoort / Journal of Clinical Epidemiology 62 (2009) 270e277 271 the overall causality assessment. It is obvious that not all What is new? criteria equally contribute to the overall evidence for cau- The Bradford Hill criteria offer the best guidance sality and some may argue that the strength of evidence for causal inference. contributes more than plausibility for instance. Swaen et al. for instance reported that a doseeresponse relation- However, there is no empirical information on how ship or biological gradient decreased the chance of a false to weigh the criteria against each other. positive finding [8]. Again, this weight of evidence can be This paper provides an original and empirically regarded as being a matter of expert judgment, but prefer- based approach to causal inference. ably it would be based on empirical data. The Bradford Hill criteria usually are not applied in The outcome of the approach is a probability esti- a very systematic manner. On occasion the criteria that mate that the association is causal. are thought to be met are listed and a conclusion on causal- The approach is tested on examples and seems to ity is drawn. A more systematic and predetermined weight work well and should be further tested in future of evidence approach would have the advantage that the causal inference studies. overall assessment of causality becomes a more transparent and reproducible approach. A more systematic approach could also improve validity and reproducibility compared to the nonsystematic approach commonly used. The purpose of our analysis is to develop a weight of ev- probability that the association is causal. The estimate of idence approach to causal inference resulting in an estimate the likelihood that an association is causal should be based of the overall probability that an association is causal. We on all nine Bradford Hill criteria and some criteria might be have applied a weight of evidence approach to 159 chemi- more useful than others. However, the weight of evidence cals or agents evaluated by International Agency for that each single criterion contributes to the overall probabil- Research of Cancer (IARC) as category 1 or 2A carcino- ity is not specified and a matter of subjective interpretation, gens. Taking the IARC classification as the gold standard, or ‘‘expert judgment.’’ Hill did not believe that any hard- we estimated the optimal weights for each criterion. and-fast rules of evidence could be laid down and he em- phasized that his nine ‘‘viewpoints’’ were neither necessary nor sufficient for causation [6]. Weed evaluated two 2. The causality criteria accounts of the use of the Bradford Hill criteria and The best and most recent description of Hill’s causality concluded that the criteria of consistency, strength, dosee criteria is given by Rothman and Greenland [9]. In short, response, and biological plausibility but not often temporal- Rothman and Greenland list the following nine causality ity were used when judging weak associations [7]. criteria: In a weight of evidence approach to causal inference, two aspects need to be quantified. First, the probability that 1 Strength of the association, the stronger the associa- a certain criterion is met needs to be estimated based on the tion the more likely that the association is causal. available (epidemiological and other) evidence. In most 2 Consistency, if more studies find similar results, the cases, the available evidence in support of a particular cau- more likely it is that the association is causal. sality criterion will not be evaluated to be 100%. For in- 3 Specificity, a specific exposure should exert a specific stance, the available evidence for the consistency may be effect. There are causal associations that are not assessed to be 75% in a situation that three out of four stud- specific, for example, cigarette smoking, asbestos ies report an association and the fourth does not. Or the ev- exposure, which are associated with multiple carcino- idence for the plausibility criterion can be estimated to be genic effects. met by a probability of 60% if only one animal study has 4 Temporality, the causal exposure should precede the found similar results, which essentially is an arbitrary esti- caused disease in time. mate but must be seen in the perspective of a most com- 5 Biological gradient or doseeresponse. If a dosee plete data set of animal in vivo, in vitro experiments, and response is seen, it is more likely that the association mechanistic supportive information which would receive is causal. a 1,005 probability if all evidence were in support of the 6 Plausibility depends on the current knowledge of the association. The analogy criterion can be estimated to be etiology of the disease. For instance, is it known that met for 0% if well-designed studies on a similar compound the agent or metabolite reaches the target organ, are are negative. Such estimates of the probability of the crite- studies in animal models positive? rion being met need to be made for each of the nine 7 Coherence, refers to other observed biological effects criteria. possibly relevant in the etiologic pathway that make Second, a weight must be given to each of the nine cri- a causal association more likely, for example, histo- teria expressing the relative importance of each criterion for logical changes in the target organ. 272 G.
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