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Statistics Medical education 19 June 2017 Free

Deconfounding confounding part 2: using directed acyclic graphs (DAGs)

In the previous article on confounding in this series,1 we presented the traditional explanation of a confounder. Over the past few decades, it has become clear that this definition has many limitations. For example, confounding can be induced by a network of variables rather than just a single variable, and adjusting for potential confounders can paradoxically increase confounding. What are directed acyclic graphs? One of the few true innovations in epidemiological methods has been the emergence of directed acyclic graphs (DAGs) to identify confounding. This development began in the early 1990s with work by Pearl and Robins based on formal logic and machine learning.2-4 DAGs are a formal system of mapping variables and the direction of causal relationships among them. “Directed” refers to arrows indicating the direction of causality between variables, and “acyclic” means that it should not be possible to start from any one variable and follow a series of arrows back to the original variable. Entire books are devoted to this method,2-4 but just a few highlights are sufficient to help clinicians understand confounding.5 In the example of smoking (exposure) and dementia (outcome) that we used in the previous article, we postulated that alcohol might be a confounder.1 These relationships are illustrated using a simple DAG in Box 1. Drinking alcohol may increase the risk of smoking — hence the arrow pointing from alcohol to smoking — and may also increase the risk of developing dementia — hence the arrow pointing from alcohol to dementia — but alcohol is not an intermediate between smoking and dementia. Smoking leads to cardiovascular disease (CVD), which also increases the risk of dementia; in this case, CVD is an intermediate between smoking and dementia. Alcohol is likewise causally related to CVD. If we observe a relationship between smoking and dementia, it is therefore not clear whether this is valid or whether it is spurious because of the effect of the other variables. How to read a DAG The steps to take in interpreting a DAG are as follows: Remove all arrows emanating from the exposure of interest. Look for any remaining path, called a “backdoor path”, that links the outcome to the exposure. A path is defined by successive arrows regardless of the direction of the arrowheads. A backdoor path is “closed” if any variable on that path is a “collider”, which is a variable with two arrowheads pointing into it from other variables on the same path. If a backdoor path can be traced and is “open” (ie, it does not include a collider), then adjusting for any variable on that path will close the backdoor path and remove confounding. Adjusting for a collider will reopen the backdoor path and increase confounding. In our example (Box 1), when we remove the arrows pointing from the exposure (smoking), we can no longer trace a path from dementia through CVD to smoking. This means that CVD is not a confounder but a mediator. Adjusting for CVD could therefore remove part of the effect of smoking that we are trying to detect; this is called over-adjustment bias.6 However, we can still trace a path from dementia through alcohol to smoking. This path does not include a collider and is thus open. By adjusting for alcohol, we can close this backdoor path and remove confounding due to alcohol. Note that another backdoor path exists from dementia through CVD to alcohol and then smoking. Adjusting for alcohol has therefore closed two backdoor paths at once. Using DAGs may seem like a convoluted process, with little benefit, compared with the old definition of confounding we presented in the previous article.1 This is certainly true when models are as simple as this one. But what happens when we want to tackle more complicated models? Let us assume we add the variables of socio-economic status (SES), diet, sex and age to the model, as shown in Box 2. How does the old definition of confounding apply here? Should we just adjust for everything? The DAG helps us sort out these relationships and decide on covariates to include in regression models. Open backdoor paths in this model include: Dementia – CVD – diet – SES – smoking Dementia – alcohol – SES – smoking Dementia – CVD – age – sex – smoking We should therefore adjust for a variable on these paths to remove confounding (eg, adjusting for SES closes the first two backdoor paths and adjusting for age closes the third backdoor path). Note that CVD remains a mediator. Another backdoor path that can be traced is: Dementia – CVD – age – sex – alcohol – SES – smoking This is already a closed path because alcohol is a collider on this path (ie, two arrows point into alcohol along this path, from sex and SES). Note that alcohol is a collider on this path but not necessarily on other paths. As this path is already closed, we do not need to adjust for any variables on it; indeed, if we were to adjust for alcohol (the collider), we would reopen a route for confounding! It takes reading and practice to become familiar with these rules, but they are extremely powerful in teasing out complex causal pathways. The astute reader will realise that trying to reduce confounding by adjusting for one variable along an open backdoor path could increase confounding if that variable is also a collider on another backdoor path. For example, as we saw above, adjusting for alcohol could close the backdoor path of dementia – alcohol – smoking, but it could also reopen the closed path of dementia – CVD – diet – SES – alcohol – sex – smoking, because alcohol is a collider on this pathway (Box 2). A tool to help readers learn to draw and interpret DAGs is a free software program called DAGitty (http://www.dagitty.net/dags.html).7 This program is reasonably intuitive, flexible and fast to learn. It allows the user to easily draw DAGs and, as a bonus, “reads” the DAG to provide the minimum set of variables for which it is essential to adjust to remove confounding. Other similar programs are also available, such as TETRAD (http://www.phil.cmu.edu/projects/tetrad), DAG (https://epi.dife.de/dag), and dagR, a set of functions for the statistical software R. The power of DAGs DAGs are powerful in that they lead us to several observations: Identifying confounders depends on the underlying causal model that is assumed. Confounding can be due to a network of variables, not just a single variable. Assumptions (model) must be drawn before conclusions (analysis) are drawn. The relationship between variables can be specified in many different ways (ie, the direction of the arrows can influence decisions made for analysis). All backdoor paths must ultimately have one variable with an arrowhead leading into the exposure; this means that confounding in complex webs of causation can be analysed by looking for the few variables that have arrows pointing to the exposure. Many routes of confounding can potentially be closed by adjusting for just one or two variables. Adjusting for confounding It could be argued that one should just adjust for all potential variables — the so-called kitchen sink approach — rather than taking any chances on specifying a potentially incorrect model. Although often appealing because of its simplicity, there are two main reasons why this approach is not recommended. The first is inefficiency: every variable that is added to the model uses degrees of freedom, which are the currency of power. This is particularly a problem for small studies, where problems such as over-fitting due to data sparsity and collinearity may arise.8 Adjusting for variables that are not confounders wastes power and may reduce the ability to detect an association. (There is a separate argument for including variables on the basis that they help explain the outcome and hence increase power; this can be thought of as “mopping up” some of the variance in the outcome so that there is more power to detect the contribution of the exposure, but this consideration is separate from confounding.) The second reason is bias: as we have seen, adjusting for a variable that is a collider reopens a backdoor path and increases the potential for confounding. Ideally, every study should make explicit the causal model behind the analysis. Residual confounding Unfortunately, even accurate specification of the causal model and expert use of DAGs do not completely remove confounding. This situation is called residual confounding, which occurs for three reasons. First, longitudinal data may not be available. With cross-sectional data, we can never be sure about the direction of causality (ie, the “chicken and egg” problem). Second, as we are not able to measure most variables perfectly, even adjusting for a variable cannot fully remove its effect. If we think of confounding as a flow of water that travels along the backdoor path, our inability to accurately measure SES, for example, means that we are unable to fully turn off the tap at that point. This is an argument for possibly adjusting for multiple variables along a backdoor path, so that the flow of confounding is reduced at multiple points instead of one point only. Third, in any observational study, we can never be sure that we have included and measured all the relevant potential confounders. What other variables have we not thought of, and not included on the diagram, that could create a backdoor path between our outcome and our exposure? As we saw in the previous article,1 the ultimate solution to confounding is a randomised controlled trial. When this is possible, it means that all known and unknown confounders are evenly balanced across the arms of the trial, thus removing their ability to affect the outcome. Box 1 – Simple causal diagram of smoking and dementia, with effect of alcohol (potential confounder) and cardiovascular disease (mediator)* People who drink alcohol are also more likely to smoke; alcohol may affect risk of dementia and CVD; and CVD may influence risk of dementia (eg, through subclinical infarcts). Green arrows radiating from the exposure are ignored when reading the pathways for potential confounding. CVD = cardiovascular disease. *Figure originally drawn with DAGitty (http://www.dagitty.net/dags.html). Box 2 – Causal diagram of smoking and dementia, with effect of alcohol (potential confounder) and cardiovascular disease (mediator), plus sex, age, socio-economic status and diet* Sex influences alcohol consumption, smoking and age (men are more likely than women to drink alcohol and smoke, and women live longer than men); SES influences alcohol consumption, smoking and diet; diet influences CVD; and age influences risk of CVD and dementia. As in the simple model in , we have to adjust for alcohol to close the dementia – alcohol – smoking path. However, doing this reopens the dementia – CVD – diet – SES – alcohol – sex – smoking path, because alcohol is a collider on this path. So we have to also adjust for sex or SES, or both, to reclose this path. Adjusting for sex, alcohol and SES would therefore be sufficient to remove confounding in this analysis of smoking and dementia. CVD = cardiovascular disease. SES = socio-economic status. *Figure originally drawn with DAGitty (http://www.dagitty.net/dags.html).

John R Attia · Christopher Oldmeadow · Elizabeth G Holliday · Michael P Jones

16 01167
Cardiovascular diseases Medical education 5 June 2017 Free

Expectorate the unexpected

A 43-year-old man underwent a computed tomography pulmonary angiography for suspected pulmonary embolism after he presented with an episode of orthopnoea associated with blood-stained expectorate. The only finding was a left atrial mass (Figure, A, arrow). Further history revealed 6 months of progressive postural presyncope, malaise and weight loss of 3 kg. Echocardiography showed a circumscribed 7.0 × 4.5 cm heterogeneous mass, with areas of cystic degeneration (Figure, B, yellow arrows) and frond-like extensions (∼ 3 mm; Figure, B, red arrow), consistent with a myxoma. The mass was attached to the interatrial septum via a small stalk and prolapsed through the mitral valve, causing significant mitral inlet obstruction; the mean gradient was approximately 12 mmHg (Figure, C). The mass was successfully removed (Figure, D). Figure LA = left atrium. LV = left ventricle. RA = right atrium. RV = right ventricle.

David J Russell · Francis A Ponnuthurai

16 00877
Research design Medical education 3 April 2017 Free

Deconfounding confounding part 1: traditional explanations

The first article of this series1 presented a framework to assist in judging the presence of bias: selection bias, or systematic error in how participants are identified or selected; measurement bias, or systematic error in how variables are measured; and analytical bias — also known as confounding — or systematic error in the measure of association or conclusion about causation, due to improper or incomplete analysis. Selection and measurement bias should be managed pre-emptively by good design before the start of the study, but can be detected post hoc by critical appraisal. No statistical method removes the effect of selection or measurement bias post hoc, although there are methods that allow us to model different degrees of bias and evaluate the effect on the measure of association.1 Confounding is slightly different in that it can be adjusted for in the analysis, as long as its sources are understood and measured without too much error. What is confounding? A confounder has been traditionally defined as a variable associated with both the exposure and outcome of interest without being an intermediate on the causal pathway between them, which causes a spurious or distorted estimate of the exposure–outcome association. This may be conceptually difficult to understand in the abstract, so a concrete example is useful. At the beginning of this series,1 we used the example of smoking (exposure) and dementia (outcome), and we postulated that alcohol may be a confounder. In this sense, alcohol is associated with smoking, that is, people who drink also tend to smoke, and alcohol may independently contribute to the risk of dementia. We may decide to study 100 people who smoke and 100 people who do not smoke and follow them over many years for the development of dementia (Box 1). In our study, 30% of people who smoke and 18% of those who do not smoke develop dementia. The relative risk (RR) of developing dementia is therefore 30%/18% = 1.7. However, based on our clinical knowledge, we have identified alcohol as a potential confounder and we want to adjust for this variable in estimating the effect of smoking on dementia. We may perform this adjustment either by including alcohol as a covariate in a regression model or by stratifying on this variable. In this article, we will do the latter because it makes the relationship between the variables more obvious. Stratifying the sample into drinking and non-drinking groups means that we remove the effect of drinking from our analysis. One way to understand this is to consider that within the strata of drinking status, everyone has the same level of drinking; thus, there is no variation in this variable and no potential to influence the outcome. This is a simplification, but it is useful for demonstration purposes. The relationship between smoking and dementia stratified by drinking status is shown in Box 2. The RR of dementia with smoking is one in each stratum of drinking status. How is it that combining two groups that individually show no association between smoking and dementia yields an overall group that shows an association? Summing the frequencies of the respective cells across the two 2 × 2 tables in the strata (Box 2) yields the same numbers as the overall 2 × 2 table (Box 1). To understand how confounding works in this example, we need to see two relationships: Drinking is associated with smoking: in Box 2, (25 + 25)/(25 + 25 + 10 + 10) = 50/70 ∼ 70% of people who drink also smoke, and (5 + 45)/(5 + 45 + 8 + 72) = 50/130 ∼ 40% of people who do not drink smoke. Drinking is associated with dementia: the risk of dementia in people who do not drink (Box 2) is 10%, compared with 50% in people who drink (Box 2). Drinking status is, therefore, a confounder of the relationship between smoking and drinking. Another way of understanding this is to recognise that in the overall table, what is labelled as the smoking group is actually a drinking group, and it is the drinking that is responsible for the development of dementia. We may see this by rearranging the 2 × 2 tables (Box 2) by strata of smoking, and looking at the relationship between drinking and dementia (Box 3). These tables show that the RR of dementia with drinking is 50%/10% = 5, regardless of whether smoking is present or absent, that is, RR = 5 in both strata (Box 3). In this case, the effect of smoking was completely confounded by alcohol, and adjusting for alcohol reduced the effect of smoking to zero. In reality, many associations are only partially confounded, and the effect of smoking may have been reduced after adjustment for alcohol rather than removed. In other cases, confounding may be so extreme that the effect size is reversed after adjustment for the confounding variable — this is called Simpson’s paradox. Why should a confounder not be an intermediate? The last part of the definition of a confounder is that it should not be an intermediate between the exposure and the outcome, that is, the confounder should not be caused by the exposure. In the example, we could postulate that smoking led to drinking and that drinking is what caused the increased risk of dementia. In this case, adjusting for drinking would remove precisely the effect we were trying to see. The effect of smoking on dementia may be entirely mediated through drinking, in which case, adjusting for drinking would remove the effect we are trying to measure. On the other hand, the effect of smoking on dementia may be mediated partially through drinking and partially through other mechanisms, and therefore, adjusting for drinking would remove part of the effect of smoking. We may then speak about the total effect of smoking on dementia, which includes all pathways, and then tease out the direct effect (effect of smoking directly on dementia) or multiple indirect effects (effect of smoking on dementia via drinking or other intermediates). The ultimate solution to confounding In an observational study, we cannot ensure that all potential confounders are identified and accurately measured, and hence there is always the possibility of residual confounding. Some authors have suggested that the choice of a control exposure (which should have no association with the outcome) or a control outcome (which should have no association with the exposure) may be used to shed light on the possibility of residual confounding.2 However, using a randomised controlled trial (RCT) is the only way we can ensure that confounding is handled definitively. This is exemplified by the debate over hormone replacement therapy, where results from over 30 years of data from hundreds of observational studies — collected in different settings and analysed with adjustment for different potential confounders — were overturned by one large RCT.3 Why is the RCT so powerful? By randomly assigning a sufficiently large number of people to two (or more) groups, we achieve an even distribution of all known — and more importantly, unknown — confounders across the trial arms. Any difference in outcome between the two groups is due to the only difference between them: the intervention assigned. Nevertheless, this does not mean that results from all RCTs can be believed; between the time of randomisation (when all potential confounders are evenly balanced) and the time of analysis (when outcomes are measured), there are many opportunities for that even balance of confounders to be upset and we must use our critical appraisal skills to evaluate the validity of the trial.4 Box 1 – Association of smoking and dementia Dementia Risk of outcome Present Absent Smoking 30 70 30% Non-smoking 18 82 18% Box 2 – Association of smoking and dementia stratified by non-drinking and drinking Dementia Risk of outcome Present Absent Non-drinking Smoking 5 45 10% Non-smoking 8 72 10% Drinking Smoking 25 25 50% Non-smoking 10 10 50% Box 3 – Association between drinking and dementia stratified by non-smoking and smoking Dementia Risk of outcome Present Absent Non-smoking Drinking 10 10 50% Non-drinking 8 72 10% Smoking Drinking 25 25 50% Non-drinking 5 45 10%

John R Attia · Michael P Jones · Alexis Hure

16 00491
Ophthalmology Medical education 3 April 2017 Free

Clozapine-induced maculopathy

A 57-year-old man was treated for schizophrenia with clozapine 900 mg daily over 22 years. His history included epilepsy, hypertension and hypercholesterolaemia, which was treated with clonazepam, clonidine and atorvastatin. Examination showed acuity 6/5 bilaterally, corneal and macular pigmentation (Figure, A, arrow, compared with B, which is normal macula), with subfoveal atrophy and disruption of the photoreceptor-retinal pigment epithelium junction on optical coherence tomography scan ([OCT]; Figure, C compared with D, which is a normal OCT, arrows), and left eye macular dysfunction on multifocal electroretinography ([ERG]; Figure, E compared with F, which is a normal ERG). These changes were similar to previously described clozapine-associated retinopathy.1 Clonazepam is associated with depigmentary retinopathy and normal ERG responses.2 Clonidine and atorvastatin have no documented retinopathy. The patient’s hyperpigmentation may be due to clozapine absorption via the choroid, binding to retinal pigment epithelium and interrupting photoreceptor phagocytosis.3 High dose clozapine warrants ophthalmic follow-up. Figure

Jessica Y Tong · Amy Pai · Peter Heydon · Stephanie H Young

16 00563
Pain management Medical education 20 March 2017 Free

Crowned dens syndrome: a rare cause of neck pain and fever

An 86-year-old man presented with acute severe neck pain, restricted neck movement and fever. The white cell count, erythrocyte sedimentation rate and C-reactive protein were all elevated. After excluding an infective aetiology, review of computed tomography images of the cervical spine (Figure) showed calcification of the transverse ligament of the atlas with crown-like density around the odontoid process. This was consistent with a diagnosis of crowned dens syndrome, an uncommon manifestation of calcium pyrophosphate dehydrate deposition disease.1,2 The patient’s symptoms were self-limiting over 1 week without the use of anti-inflammatories or corticosteroids. Figure

Matthew Jiang · Sukumar Navanathan

16 01077
Urology Medical education 6 March 2017 Free

Henoch–Schönlein purpura following Yersinia enterocolitica infection

We describe a case of Henoch–Schönlein purpura (HSP) in a 19-year-old woman triggered by a diarrhoeal illness from Yersinia enterocolitica. The patient subsequently developed a widespread purpuric rash on the upper and lower limbs (Box), spasmodic abdominal pain, polyarthralgia and macroscopic haematuria. A skin biopsy confirmed leukocytoclastic vasculitis. Immunofluorescence testing on a percutaneous renal biopsy revealed strong mesangial staining for IgA. While post-infectious proliferative glomerulonephritis with Y. enterocolitica is described in several case series, the syndrome of HSP after this infection has rarely been reported.1,2 This case reinforces that any immune stimulus in IgA-producing tissue, including gastrointestinal infection, can trigger HSP. Box –

Kylie Ngu · Kate J Robson · David J Goodman

16 00222

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