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Confounding occurs when the estimate of measure of association is distorted by the presence of another risk factor. For a variable to be a confounder, it must be associated with both the exposure and the outcome, without being in the causal pathway.

6.2.1. Confounding by indication

Confounding by indication refers to a determinant of the outcome parameter that is present in people at perceived high risk or poor prognosis and is an indication for intervention. This means that differences in care between the exposed and non-exposed, for example, may partly originate from differences in indication for medical intervention such as the presence of specific risk factors for health problems. Another name for this type of confounding is ‘channeling’. Confounding by severity is a type of confounding by indication, where not only the disease but its severity acts as confounder (see Confounding by Indication: An Example of Variation in the Use of Epidemiologic Terminology, Am J Epidemiol. 1999;149(11):981-3).

This type of confounding has frequently been reported in studies evaluating the efficacy of pharmaceutical interventions and is almost always encountered in various extents in pharmacoepidemiological studies. A good example can be found in Confounding and indication for treatment in evaluation of drug treatment for hypertension (BMJ. 1997;315:1151-4).

With the more recent application of pharmacoepidemiological methods to assess effectiveness, confounding by indication is a greater challenge and the article Approaches to combat with confounding by indication in observational studies of intended drug effects (Pharmacoepidemiol Drug Saf. 2003;12(7):551-8) focusses on its possible reduction in studies of intended effects. An extensive review of these and other methodological approaches discussing their strengths and limitations is discussed in Methods to assess intended effects of drug treatment in observational studies are reviewed (J Clin Epidemiol. 2004;57(12):1223-31).

Complete adjustment for confounders would require detailed information on clinical parameters, lifestyle or over-the-counter medications, which are often not measured in electronic healthcare records, causing residual confounding bias. Using directed acyclic graphs to detect limitations of traditional regression in longitudinal studies (Int J Public Health 2010;55(6):701-3) reviews confounding and intermediate effects in longitudinal data and introduces causal graphs to understand the relationships between the variables in an epidemiological study.

Unmeasured confounding can be adjusted for only through randomisation. When this is not possible, as most often in pharmacoepidemiological studies, the potential impact of residual confounding on the results should be estimated and considered in the discussion.

Sensitivity analysis and external adjustment for unmeasured confounders in epidemiologic database studies of therapeutics (Pharmacoepidemiol Drug Saf. 2006;15(5):291-303) provides a systematic approach to sensitivity analyses to investigate the impact of residual confounding in pharmacoepidemiological studies that use healthcare utilisation databases. In this article, four basic approaches to sensitivity analysis were identified: (1) sensitivity analyses based on an array of informed assumptions; (2) analyses to identify the strength of residual confounding that would be necessary to explain an observed drug-outcome association; (3) external adjustment of a drug-outcome association given additional information on single binary confounders from survey data using algebraic solutions; (4) external adjustment considering the joint distribution of multiple confounders of any distribution from external sources of information using propensity score calibration. The paper concludes that sensitivity analyses and external adjustments can improve our understanding of the effects of drugs in epidemiological database studies. With the availability of easy-to-apply spreadsheets (e.g. at https://www.drugepi.org/dope/software#Sensitivity), sensitivity analyses should be used more frequently, substituting qualitative discussions of residual confounding.

The impact of residual and unmeasured confounding in epidemiologic studies: a simulation study (Am J Epidemiol. 2007;166(6):646–55) considers the extent and patterns of bias in estimates of exposure-outcome associations that can result from residual or unmeasured confounding, when there is no true association between the exposure and the outcome. Another important finding of this study was that when confounding factors (measured or unmeasured) are interrelated (e.g. in situations of confounding by indication), adjustment for a few factors can almost completely eliminate confounding.

6.2.3. Methods to address confounding

Methods to address confounding include case-only designs (see Chapters 5.2.3 and 5.4.3) and use of an active comparator (see Chapter 5.4.5). Other methods are detailed hereafter.

*6.2.3.1. Disease risk
scores*

An approach to controlling for a large number of confounding variables is to summarise them in a single multivariable confounder score. Stratification by a multivariate confounder score (Am J Epidemiol. 1976;104(6):609-20) shows how control for confounding may be based on stratification by the score. An example is a disease risk score (DRS) that estimates the probability or rate of disease occurrence conditional on being unexposed. The association between exposure and disease is then estimated with adjustment for the disease risk score in place of the individual covariates.

DRSs are however difficult to estimate if outcomes are rare. Use of disease risk scores in pharmacoepidemiologic studies (Stat Methods Med Res. 2009;18(1):67-80) includes a detailed description of their construction and use, a summary of simulation studies comparing their performance to traditional models, a comparison of their utility with that of propensity scores, and some further topics for future research. Disease risk score as a confounder summary method: systematic review and recommendations (Pharmacoepidemiol Drug Saf. 2013;22(2);122-29), examines trends in the use and application of DRS as a confounder summary method and shows that large variation exists with differences in terminology and methods used.

In Role of disease risk scores in comparative effectiveness research with emerging therapies (Pharmacoepidemiol Drug Saf. 2012;21 Suppl 2:138–47), it is argued that DRS may have a place when studying drugs that are recently introduced to the market. In such situations, as characteristics of users change rapidly, exposure propensity scores may prove highly unstable. DRSs based mostly on biological associations would be more stable. However, DRS models are still sensitive to misspecification as discussed in Adjusting for Confounding in Early Postlaunch Settings: Going Beyond Logistic Regression Models (Epidemiology 2016;27(1):133-42).

*6.2.3.2. Propensity
scores*

Databases used in pharmacoepidemiological studies often include records of prescribed medications and encounters with medical care providers, from which one can construct surrogate measures for both drug exposure and covariates that are potential confounders. It is often possible to track day-by-day changes in these variables. However, while this information can be critical for study success, its volume can pose challenges for statistical analysis.

A propensity score (PS) is analogous to the disease risk score in that it combines a large number of possible confounders into a single variable (the score). The exposure propensity score (EPS) is the conditional probability of exposure to a treatment given observed covariates. In a cohort study, matching or stratifying treated and comparison subjects on EPS tends to balance all of the observed covariates. However, unlike random assignment of treatments, the propensity score may not balance unobserved covariates. Invited Commentary: Propensity Scores (Am J Epidemiol. 1999;150(4):327–33) reviews the uses and limitations of propensity scores and provide a brief outline of the associated statistical theory. The authors present results of adjustment by matching or stratification on the propensity score.

The estimated EPS summarises all measured confounders in a single variable and thus can be used in the analysis, as any other confounder, for matching, stratification, weighting or as a covariate in a regression model to adjust for the measured confounding. A description of these methods can be found in the following articles: An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies (Multivariate Behav Res. 2011;46(3):399-424), Tutorial and Case Study in Propensity Score Analysis: An Application to Estimating the Effect of In-Hospital Smoking Cessation Counseling on Mortality (Multivariate Behav Res. 2011;46(1):119-51) and Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effects in observational studies (Stat Med. 2015;34(28):3661-79).

Propensity score matching in cohort studies is frequently done 1:1, which, while allowing for selection of the best match for each member of the exposed cohort, may lead to severe depletion of the study population and the associated lower precision, especially when coupled with trimming. Increasing the matching ratio may increase precision but also negatively affect confounding control. One-to-many propensity score matching in cohort studies (Pharmacoepidemiol Drug Saf. 2012;21(S2):69-80) tests several methods for 1:n propensity score matching in simulation and empirical studies and recommends using a variable ratio that increases precision at a small cost of bias. Matching by propensity score in cohort studies with three treatment groups (Epidemiology 2013;24(3):401-9) develops and tests a 1:1:1 propensity score matching approach offering a way to compare three treatment options.

Use of EPS for stratification or weighing overcomes the precision-related limitation of matching-based methods, allowing use of a larger proportion of the study population in the analysis. Fine stratification approach is based on defining large number (50 or 100) number of EPS strata, as described in A Propensity-score-based Fine Stratification Approach for Confounding Adjustment When Exposure Is Infrequent (Epidemiology 2017;28(2):249-57).

High-dimensional Propensity Score Adjustment in Studies of Treatment Effects Using Healthcare Claims Data (Epidemiology 2009;20(4):512-22) discusses the high dimensional propensity score (hd-PS) model approach. It attempts to empirically identify large numbers of potential confounders in healthcare databases and, by doing so, to extract more information on confounders and proxies. Covariate selection in high-dimensional propensity score analyses of treatment effects in small samples (Am J Epidemiol. 2011;173(12):1404-13) evaluates the relative performance of hd-PS in smaller samples. Confounding adjustment via a semi-automated high-dimensional propensity score algorithm: an application to electronic medical records (Pharmacoepidemiol Drug Saf. 2012;20(8):849-57) evaluates the use of hd-PS in a primary care electronic medical record database. In addition, the article Using high-dimensional propensity scores to automate confounding control in a distributed medical product safety surveillance system (Pharmacoepidemiol Drug Saf. 2012;21(S1):41-9) summarises the application of this method for automating confounding control in sequential cohort studies as applied to safety monitoring systems using healthcare databases and also discusses the strengths and limitations of hd-PS.

The use of several measures of balance for developing an optimal propensity score model is described in Measuring balance and model selection in propensity score methods (Pharmacoepidemiol Drug Saf. 2011;20(11):1115-29) and further evaluated in Propensity score balance measures in pharmacoepidemiology: a simulation study (Pharmacoepidemiol Drug Saf. 2014;23(8):802-11). In most situations, the standardised difference performs best and is easy to calculate (see Balance measures for propensity score methods: a clinical example on beta-agonist use and the risk of myocardial infarction (Pharmacoepidemiol Drug Saf. 2011;20(11):1130-7) and Reporting of covariate selection and balance assessment in propensity score analysis is suboptimal: a systematic review (J Clin Epidemiol 2015;68(2):112-21)). Metrics for covariate balance in cohort studies of causal effects (Stat Med 2013;33:1685-99) shows in a simulation study that the c-statistics of the PS model after matching and the general weighted difference perform as well as the standardized difference and are preferred when an overall summary measure of balance is requested. Treatment effects in the presence of unmeasured confounding: dealing with observations in the tails of the propensity score distribution--a simulation study (Am J Epidemiol. 2010;172(7):843-54) demonstrates how ‘trimming’ of the propensity score eliminates subjects who are treated contrary to prediction and their exposed/unexposed counterparts, thereby reducing bias by unmeasured confounders.

Performance of propensity score calibration-–a simulation study (Am J Epidemiol. 2007;165(10):1110-8) introduces ‘propensity score calibration’ (PSC). This technique combines propensity score matching methods with measurement error regression models to address confounding by variables unobserved in the main study. This is done by using additional covariate measurements observed in a validation study, which is often a subset of the main study.

Principles of variable selection for inclusion in EPS are described, for example, in Variable selection for propensity score models (Am J Epidemiol. 2006;163(12):1149-56) and in Variable selection for propensity score models when estimating treatment effects on multiple outcomes: a simulation study (Pharmacoepidemiol Drug Saf. 2013;22(1):77-85).

Although in most situations, propensity score models, with the possible exception of hd-PS, do not have any advantages over conventional multivariate modelling in terms of adjustment for identified confounders, several other benefits may be derived. Propensity score methods may help to gain insight into determinants of treatment including age, frailty and comorbidity and to identify individuals treated against expectation. A statistical advantage of PS analyses is that if exposure is not infrequent it is possible to adjust for a large number of covariates even if outcomes are rare, a situation often encountered in drug safety research.

An important limitation of PS is that it is not directly amenable for case-control studies. A critical assessment of propensity scores is provided in Propensity scores: from naive enthusiasm to intuitive understanding (Stat Methods Med Res. 2012;21(3):273-93). Semiautomated and machine-learning based approaches to propensity score methods are currently being developed (Automated data-adaptive analytics for electronic healthcare data to study causal treatment effects (Clin Epidemiol 2018;10:771-88).

*6.2.3.3. Instrumental
variables*

An instrumental variable (IV) is defined in Instrumental variable methods in comparative safety and effectiveness research (Pharmacoepidemiol Drug Saf. 2010; 19(6):537-54) as a factor that is assumed to be related to treatment but is neither directly nor indirectly related to the study outcome. An IV should fulfil three assumptions: (1) it should affect treatment or be associated with treatment by sharing a common cause; (2) it should be a factor that is as good as randomly assigned so that it is unrelated to patient characteristics, and (3) it should be related to the outcome only through its association with treatment. This article also presents a practical guidance on IV analyses in pharmacoepidemiology. The article Instrumental variable methods for causal inference (Stat Med. 2014;33(13):2297-340) is a tutorial, including statistical code for performing IV analysis.

IV analysis is an approach to address uncontrolled confounding in comparative studies. An introduction to instrumental variables for epidemiologists (Int J Epidemiol. 2000;29(4):722-9) presents those developments, illustrated by an application of IV methods to non-parametric adjustment for non-compliance in randomised trials. The author mentions a number of caveats but concludes that IV corrections can be valuable in many situations. A review of IV analysis for observational comparative effectiveness studies suggested that in the large majority of studies, in which IV analysis was applied, one of the assumptions could be violated (Potential bias of instrumental variable analyses for observational comparative effectiveness research, Ann Intern Med. 2014;161(2):131-8).

The complexity of the issues associated with confounding by indication, channeling and selective prescribing is explored in Evaluating short-term drug effects using a physician-specific prescribing preference as an instrumental variable (Epidemiology 2006;17(3):268-75). A conventional, adjusted multivariable analysis showed a higher risk of gastrointestinal toxicity for selective COX-2-inhibitors than for traditional NSAIDs, which was at odds with results from clinical trials. However, a physician-level instrumental variable approach (a time-varying estimate of a physician’s relative preference for a given drug, where at least two therapeutic alternatives exist) yielded evidence of a protective effect due to COX-2 exposure, particularly for shorter term drug exposures. Despite the potential benefits of physician-level IVs their performance can vary across databases and strongly depends on the definition of IV used as discussed in Evaluating different physician's prescribing preference based instrumental variables in two primary care databases: a study of inhaled long-acting beta2-agonist use and the risk of myocardial infarction (Pharmacoepidemiol Drug Saf. 2016;25 Suppl 1:132-41).

An important limitation of IV analysis is that weak instruments (small association between IV and exposure) lead to decreased statistical efficiency and biased IV estimates as detailed in Instrumental variables: application and limitations (Epidemiology 2006;17:260-7). For example, in the above mentioned study on non-selective NSAIDs and COX-2-inhibitors, the confidence intervals for IV estimates were in the order of five times wider than with conventional analysis. Performance of instrumental variable methods in cohort and nested case-control studies: a simulation study (Pharmacoepidemiol Drug Saf. 2014;23(2):165-77) demonstrates that a stronger IV-exposure association is needed in nested case-control studies compared to cohort studies in order to achieve the same bias reduction. Increasing the number of controls reduces this bias from IV analysis with relatively weak instruments.

Selecting on treatment: a pervasive form of bias in instrumental variable analyses (Am J Epidemiol. 2015;181(3):191-7) warns against bias in IV analysis by including only a subset of possible treatment options.

*6.2.3.4. Prior event
rate ratios*

Another method proposed to control for unmeasured confounding is the Prior Event Rate Ratio (PERR) adjustment method, in which the effect of exposure is estimated using the ratio of rate ratios (RRs) between the exposed and unexposed from periods before and after initiation of a drug exposure, as discussed in Replicated studies of two randomized trials of angiotensin converting enzyme inhibitors: further empiric validation of the ‘prior event rate ratio’ to adjust for unmeasured confounding by indication (Pharmacoepidemiol Drug Saf. 2008;17(7):671-685). For example, when a new drug is launched, direct estimation of the drugs effect observed in the period after launch is potentially confounded. Differences in event rates in the period before the launch between future users and future non-users may provide a measure of the amount of confounding present. By dividing the effect estimate from the period after launch by the effect obtained in the period before launch, the confounding in the second period can be adjusted for. This method requires that confounding effects are constant over time, that there is no confounder-by-treatment interaction, and outcomes are non-lethal events.

Performance of prior event rate ratio adjustment method in pharmacoepidemiology: a simulation study (Pharmacoepidemiol Drug Saf. 2015(5);24:468-477) discusses that the PERR adjustment method can help to reduce bias as a result of unmeasured confounding in certain situations but that theoretical justification of assumptions should be provided.

*6.2.3.5. Handling
time-dependent confounding in the analysis*

In longitudinal studies, the value of covariates may change and be measured over time. These covariates are time-dependent confounders if they are affected by prior treatment and predict the future treatment decision and future outcome conditional on the past treatment exposure (see Comparison of Statistical Approaches Dealing with Time-dependent Confounding in Drug Effectiveness Studies, Stat Methods Med Res. 2016). Methods for dealing with time-dependent confounding (Stat Med. 2013;32(9):1584-618) provides an overview of how time-dependent confounding can be handled in the analysis of a study. It provides an in-depth discussion of marginal structural models and g-computation.

G-estimation is a method for estimating the joint effects of time-varying treatments using ideas from instrumental variables methods. G-estimation of Causal Effects: Isolated Systolic Hypertension and Cardiovascular Death in the Framingham Heart Study (Am J Epidemiol. 1998;148(4):390-401) demonstrates how the G-estimation procedure allows for appropriate adjustment of the effect of a time-varying exposure in the presence of time-dependent confounders that are themselves influenced by the exposure.

The use of Marginal Structural Models can be an alternative to G-estimation. Marginal Structural Models and Causal Inference in Epidemiology (Epidemiology 2000;11(5):550-60) introduces a class of causal models that allow for improved adjustment for confounding in situations of time-dependent confounding. MSMs have two major advantages over G-estimation. Even if it is useful for survival time outcomes, continuous measured outcomes and Poisson count outcomes, logistic G-estimation cannot be conveniently used to estimate the effect of treatment on dichotomous outcomes unless the outcome is rare. The second major advantage of MSMs is that they resemble standard models, whereas G-estimation does not (see Marginal Structural Models to Estimate the Causal Effect of Zidovudine on the Survival of HIV-Positive Men. Epidemiology 2000;11(5):561-70).

Effect of highly active antiretroviral therapy on time to acquired immunodeficiency syndrome or death using marginal structural models (Am J Epidemiol. 2003;158(7):687-94) provides a clear example in which standard Cox analysis failed to detect a clinically meaningful net benefit of treatment because it does not appropriately adjust for time-dependent covariates that are simultaneously confounders and intermediate variables. This net benefit was shown using a marginal structural survival model. In Time-dependent propensity score and collider-stratification bias: an example of beta2-agonist use and the risk of coronary heart disease (Eur J Epidemiol. 2013;28(4):291-9), various methods to control for time-dependent confounding are compared in an empirical study on the association between inhaled beta-2-agonists and the risk of coronary heart disease. MSMs resulted in slightly reduced associations compared to standard Cox-regression.

*6.2.3.6. The
trend-in-trend design*

The Trend-in-trend Research Design for Causal Inference (Epidemiology 2017;28(4):529-36) presents a semi-ecological design, whereby trends in exposure and in outcome rates are compared in subsets of the population that have different rates of uptake for the drug in question. These subsets are identified through PS modelling. There is a formal framework for transforming the observed trends into an effect estimate. Simulation and empirical studies showed the design to be less statistically efficient than a cohort study, but more resistant to confounding. The trend-in-trend method may be useful in settings where there is a strong time trend in exposure, such as a newly approved drug.