Reporting of treatment effects from randomized trials: A plea for multivariable risk ratios

Who benefits from indirect prevention and treatment of depression using an online intervention for insomnia? Results from an individual-participant data meta-analysis

BACKGROUND

Major depressive disorder (MDD) is highly prevalent and burdensome for individuals and society. While there are psychological interventions able to prevent and treat MDD, uptake remains low. To overcome structural and attitudinal barriers, an indirect approach of using online insomnia interventions seems promising because insomnia is less stigmatized, predicts MDD onset, is often comorbid and can outlast MDD treatment. This individual-participant-data meta-analysis evaluated the potential of the online insomnia intervention GET.ON Recovery as an indirect treatment to reduce depressive symptom severity (DSS) and potential MDD onset across a range of participant characteristics.

METHODS

Efficacy on depressive symptom outcomes was evaluated using multilevel regression models controlling for baseline severity. To identify potential effect moderators, clinical, sociodemographic, and work-related variables were investigated using univariable moderation and random-forest methodology before developing a multivariable decision tree.

RESULTS

IPD were obtained from four of seven eligible studies (N = 561); concentrating on workers with high work-stress. DSS was significantly lower in the intervention group both at post-assessment (d = -0.71 [95% CI-0.92 to -0.51]) and at follow-up (d = -0.84 [95% CI -1.11 to -0.57]). In the subsample (n = 121) without potential MDD at baseline, there were no significant group differences in onset of potential MDD. Moderation analyses revealed that effects on DSS differed significantly across baseline severity groups with effect sizes between d = -0.48 and -0.87 (post) and d = - 0.66 to -0.99 (follow-up), while no other sociodemographic, clinical, or work-related characteristics were significant moderators.

CONCLUSIONS

An online insomnia intervention is a promising approach to effectively reduce DSS in a preventive and treatment setting.

Adjustment for baseline characteristics in randomized trials using logistic regression: sample-based model versus true model

BACKGROUND

Adjustment for baseline prognostic factors in randomized clinical trials is usually performed by means of sample-based regression models. Sample-based models may be incorrect due to overfitting. To assess whether overfitting is a problem in practice, we used simulated data to examine the performance of the sample-based model in comparison to a "true" adjustment model, in terms of estimation of the treatment effect.

METHODS

We conducted a simulation study using samples drawn from a "population" in which both the treatment effect and the effect of the potential confounder were specified. The outcome variable was binary. Using logistic regression, we compared three estimates of the treatment effect in each situation: unadjusted, adjusted for the confounder using the sample, adjusted for the confounder using the true effect. Experimental factors were sample size (from 2 × 50 to 2 × 1000), treatment effect (logit of 0, 0.5, or 1.0), confounder type (continuous or binary), and confounder effect (logit of 0, - 0.5, or - 1.0). The assessment criteria for the estimated treatment effect were bias, variance, precision (proportion of estimates within 0.1 logit units), type 1 error, and power.

RESULTS

Sample-based adjustment models yielded more biased estimates of the treatment effect than adjustment models that used the true confounder effect but had similar variance, accuracy, power, and type 1 error rates. The simulation also confirmed the conservative bias of unadjusted analyses due to the non-collapsibility of the odds ratio, the smaller variance of unadjusted estimates, and the bias of the odds ratio away from the null hypothesis in small datasets.

CONCLUSIONS

Sample-based adjustment yields similar results to exact adjustment in estimating the treatment effect. Sample-based adjustment is preferable to no adjustment.

Valproic acid as adjuvant treatment for convulsive status epilepticus: a randomised clinical trial

BACKGROUND

Generalised convulsive status epilepticus (GCSE) is a medical emergency. Guidelines recommend a stepwise strategy of benzodiazepines followed by a second-line anti-seizure medicine (ASM). However, GCSE is uncontrolled in 20-40% patients and is associated with protracted hospitalisation, disability, and mortality. The objective was to determine whether valproic acid (VPA) as complementary treatment to the stepwise strategy improves the outcomes of patients with de novo established GCSE.

METHODS

This was a multicentre, double-blind, randomised controlled trial in 244 adults admitted to intensive care units for GCSE in 16 French hospitals between 2013 and 2018. Patients received standard care of benzodiazepine and a second-line ASM (except VPA). Intervention patients received a 30 mg/kg VPA loading dose, then a 1 mg/kg/h 12 h infusion, whilst the placebo group received an identical intravenous administration of 0.9% saline as a bolus and continuous infusion. Primary outcome was proportion of patients discharged from hospital by day 15. The secondary outcomes were seizure control, adverse events, and cognition at day 90.

RESULTS

A total of 126 (52%) and 118 (48%) patients were included in the VPA and placebo groups. 224 (93%) and 227 (93%) received a first-line and a second-line ASM before VPA or placebo infusion. There was no between-group difference for patients hospital-discharged at day 15 [VPA, 77 (61%) versus placebo, 72 (61%), adjusted relative risk 1.04; 95% confidence interval (0.89-1.19); p = 0.58]. There were no between-group differences for secondary outcomes.

CONCLUSIONS

VPA added to the recommended strategy for adult GCSE is well tolerated but did not increase the proportion of patients hospital-discharged by day 15.

TRIAL REGISTRATION NO

NCT01791868 (ClinicalTrials.gov registry), registered: 15 February 2012.

Distribution-Free Approach to the Design and Analysis of Randomized Stroke Trials With the Modified Rankin Scale

BACKGROUND

Many methods have been suggested for analyzing the modified Rankin Scale (mRS). However, there lacks a unified approach to analysis and sample size determination that properly uses the ordinal nature of the data. We propose a simple method for CI estimation and corresponding sample size determination.

METHODS

We quantify treatment effect by the win probability (WinP) that a randomly selected patient in the treatment group has an equal or a better mRS score than a patient in the control group. Thus, a win probability of 0.5 means no effect, likened to a draw in competitive sports. We estimate the win probability and its SE based on the ranks of mRS scores, where tied scores are handled by average ranks. Corresponding methods for hypothesis testing, CI estimation, and sample size determination are derived. The methods are evaluated with a simulation study based on real data from 10 randomized stroke trials that used mRS as the outcome measure.

RESULTS

Simulation results demonstrated that the methods performed very well in terms of CI coverage, tail errors, and assurance to achieving the prespecified precision. Because the methods are very simple, we implemented them in an Excel spreadsheet, requiring only user inputs on frequencies of mRS scores in 2 comparison groups.

CONCLUSIONS

Sound statistical methods are important for the success of randomized stroke trials. The proposed methods and associated spreadsheet should prove useful for stroke researchers in the planning and analysis of randomized trials. Meta-analysis has also been made easy for trials with ordinal scores.

The benefits of covariate adjustment for adaptive multi-arm designs

Covariate adjustment via a regression approach is known to increase the precision of statistical inference when fixed trial designs are employed in randomized controlled studies. When an adaptive multi-arm design is employed with the ability to select treatments, it is unclear how covariate adjustment affects various aspects of the study. Consider the design framework that relies on pre-specified treatment selection rule(s) and a combination test approach for hypothesis testing. It is our primary goal to evaluate the impact of covariate adjustment on adaptive multi-arm designs with treatment selection. Our secondary goal is to show how the Uniformly Minimum Variance Conditionally Unbiased Estimator can be extended to account for covariate adjustment analytically. We find that adjustment with different sets of covariates can lead to different treatment selection outcomes and hence probabilities of rejecting hypotheses. Nevertheless, we do not see any negative impact on the control of the familywise error rate when covariates are included in the analysis model. When adjusting for covariates that are moderately or highly correlated with the outcome, we see various benefits to the analysis of the design. Conversely, there is negligible impact when including covariates that are uncorrelated with the outcome. Overall, pre-specification of covariate adjustment is recommended for the analysis of adaptive multi-arm design with treatment selection. Having the statistical analysis plan in place prior to the interim and final analyses is crucial, especially when a non-collapsible measure of treatment effect is considered in the trial.

Clinical research study implementation of case-finding strategies for heart failure and chronic obstructive pulmonary disease in the elderly with reduced exercise tolerance or dyspnea: A cluster randomized trial

BACKGROUND

Heart failure (HF) and chronic obstructive pulmonary disease (COPD) often remain undiagnosed in older individuals, although both disorders inhibit functionality and impair health. The aim of the study was to assess the effectiveness of a case-finding strategy of these disorders.

METHODS

This is a clustered randomized trial; 18 general practices from the vicinity of Utrecht, the Netherlands, were randomly allocated to a case-finding strategy or usual care. Multimorbid community subjects (≥65 years) with dyspnea or reduced exercise tolerance were eligible for inclusion. The case-finding strategy consisted of history taking, physical examination, blood tests, electrocardiography, spirometry, and echocardiography. Subsequent treatment decisions were at the discretion of the general practitioner. Questionnaires regarding health status and functionality were filled out at baseline and after 6 months of follow-up. Information regarding changes in medication and health care use during the 6 months follow-up was extracted.

RESULTS

A total of 829 participants were randomized: 389 in the case-finding strategy group and 440 in the usual care group. More patients in the case-finding group received a new diagnosis of HF or COPD than the usual care group (cumulative incidence 34% vs 2% and 17% vs. 2%, respectively). Scores for health status, functionality, and health care use were similar between the 2 strategies after 6 months of follow-up.

CONCLUSIONS

A case-finding strategy applied in primary care to multimorbid older people with dyspnea or reduced exercise tolerance resulted in a number of new diagnoses of HF and COPD but did not result in short-term improvement of health status compared to usual care.

Impact of Modified Transesophageal Echocardiography on Mortality and Stroke after Cardiac Surgery: A Large Cohort Study

The aim of this study was to investigate the impact of perioperative screening with modified transesophageal echocardiography (A-View method). We compared, in consecutive patients who underwent cardiac surgery between 2006 and 2014, 30-day mortality and in-hospital stroke incidence, operated either with perioperative modified TEE screening (intervention group) or only with conventional TEE screening (control group). Of the 8,605 study patients, modified TEE was applied in 1,391 patients (16.2%). Patients in the intervention group were on average older (71 versus 68 years, p < 0.001) and more often females (31.0% versus 28.0%, p < 0.001) and had a higher predicted mortality (EuroSCORE I: 5.9% versus 4.0%, p < 0.001). The observed 30-day mortality was 2.2% and 2.5% in both groups, respectively, with multivariable and propensity-score adjusted relative risks (RRs) of 0.70 (95% CI: 0.50–1.00, p = 0.05) and 0.67 (95% CI: 0.45–0.98, p = 0.04). In-hospital stroke was 2.9% and 2.1% in both groups, respectively, with adjusted RRs of 1.03 (95% CI: 0.73–1.45) and 1.01 (95% CI: 0.71–1.43). In patients undergoing cardiac surgery, use of perioperative screening for aortic atherosclerosis with modified TEE was associated with lower postoperative mortality, but not stroke, as compared to patients operated on without such screening.

Impact of Selection Bias on Estimation of Subsequent Event Risk

BACKGROUND

Studies of recurrent or subsequent disease events may be susceptible to bias caused by selection of subjects who both experience and survive the primary indexing event. Currently, the magnitude of any selection bias, particularly for subsequent time-to-event analysis in genetic association studies, is unknown.

METHODS AND RESULTS

We used empirically inspired simulation studies to explore the impact of selection bias on the marginal hazard ratio for risk of subsequent events among those with established coronary heart disease. The extent of selection bias was determined by the magnitudes of genetic and nongenetic effects on the indexing (first) coronary heart disease event. Unless the genetic hazard ratio was unrealistically large (>1.6 per allele) and assuming the sum of all nongenetic hazard ratios was <10, bias was usually <10% (downward toward the null). Despite the low bias, the probability that a confidence interval included the true effect decreased (undercoverage) with increasing sample size because of increasing precision. Importantly, false-positive rates were not affected by selection bias.

CONCLUSIONS

In most empirical settings, selection bias is expected to have a limited impact on genetic effect estimates of subsequent event risk. Nevertheless, because of undercoverage increasing with sample size, most confidence intervals will be over precise (not wide enough). When there is no effect modification by history of coronary heart disease, the false-positive rates of association tests will be close to nominal.

Does integrated training in evidence-based medicine (EBM) in the general practice (GP) specialty training improve EBM behaviour in daily clinical practice? A cluster randomised controlled trial

OBJECTIVES

Evidence-based medicine (EBM) is an important element in the general practice (GP) specialty training. Studies show that integrating EBM training into clinical practice brings larger benefits than stand-alone modules. However, these studies have neither been performed in GP nor assessed EBM behaviour of former trainees in daily clinical practice.

SETTING

GP specialty training in the Netherlands.

PARTICIPANTS

All 82 third year GP trainees who started their final third year in 2011 were approached for inclusion, of whom 79 (96%) participated: 39 in the intervention group and 40 in the control group.

INTERVENTION

Integrated EBM training, in which EBM is embedded closely within the clinical context by joint assignments for the trainee and supervisor in daily practice, and teaching sessions based on dilemmas from actual patient consultations.

COMPARISON

Stand-alone EBM training at the institute only.

PRIMARY AND SECONDARY OUTCOMES

Our primary outcome was EBM behaviour, assessed by measuring guideline adherence (incorporating rational, motivated deviation) and information-seeking behaviour. Our secondary outcomes were EBM attitude and EBM knowledge. Data were acquired using logbooks and questionnaires, respectively. Analyses were performed using mixed models.

RESULTS

Logbook data were available from 76 (96%) of the participating trainees at baseline (7614 consultations), 60 (76%) at the end of the third year (T1, 4973 consultations) and 53 (67%) 1 year after graduation (T2, 3307 consultations). We found no significant differences in outcomes between the 2 groups, with relative risks for guideline adherence varying between 0.96 and 0.99 (95% CI 0.86 to 1.11) at T1, and 0.99 and 1.10 (95% CI 0.92 to 1.25) at T2, and for information-seeking behaviour between 0.97 and 1.16 (95% CI 0.70 to 1.91) and 0.90 and 1.10 (95% CI 0.70 to 1.32), respectively.

CONCLUSIONS

Integrated EBM training compared with stand-alone EBM training does not improve EBM behaviour, attitude or knowledge of (future) GPs.

Studying noncollapsibility of the odds ratio with marginal structural and logistic regression models

One approach to quantifying the magnitude of confounding in observational studies is to compare estimates with and without adjustment for a covariate, but this strategy is known to be defective for noncollapsible measures such as the odds ratio. Comparing estimates from marginal structural and standard logistic regression models, the total difference between crude and conditional effects can be decomposed into the sum of a noncollapsibility effect and confounding bias. We provide an analytic approach to assess the noncollapsibility effect in a point-exposure study and provide a general formula for expressing the noncollapsibility effect. Next, we provide a graphical approach that illustrates the relationship between the noncollapsibility effect and the baseline risk, and reveals the behavior of the noncollapsibility effect for a range of different exposure and covariate effects. Various observations about noncollapsibility can be made from the different scenarios with or without confounding; for example, the magnitude of effect of the covariate plays a more important role in the noncollapsibility effect than does that of the effect of the exposure. In order to explore the noncollapsibility effect of the odds ratio in the presence of time-varying confounding, we simulated an observational cohort study. The magnitude of noncollapsibility was generally comparable to the effect in the point-exposure study in our simulation settings. Finally, in an applied example we demonstrate that collapsibility can have an important impact on estimation in practice.

False Appearance of Gene-Environment Interactions in Genetic Association Studies

Under the assumption of gene-environment independence, unknown/unmeasured environmental factors, irrespective of what they may be, cannot confound the genetic effects. This may lead many people to believe that genetic heterogeneity across different levels of the studied environmental exposure should only mean gene-environment interaction--even though other environmental factors are not adjusted for. However, this is not true if the odds ratio is the effect measure used for quantifying genetic effects. This is because the odds ratio is a "noncollapsible" measure--a marginal odds ratio is not a weighted average of the conditional odds ratios, but instead has a tendency toward the null. In this study, the authors derive formulae for gene-environment interaction bias due to noncollapsibility. They use computer simulation and real data example to show that the bias can be substantial for common diseases. For genetic association study of nonrare diseases, researchers are advised to use collapsible measures, such as risk ratio or peril ratio.

Odds ratio vs risk ratio in randomized controlled trials

OBJECTIVE

Use of odds ratio (OR) in randomized controlled trials (RCTs) has been criticized because it overestimates the effect size, if incorrectly interpreted as risk ratio (RR). To what extent does this make a difference in the context of clinical research is unclear. We, therefore, aimed to address this issue considering its importance in evidence-based practice of medicine.

METHODS

We reviewed 580 RCTs published in the New England Journal of Medicine between January 2004 and June 2014 and identified 107 RCTs that reported unadjusted RR (n = 76) or OR (n = 31) for the primary outcome. For studies reporting ORs, we calculated RRs, and vice versa, using Stata software. The percentage of divergence between the reported and calculated effect size estimates was analyzed.

RESULTS

None of the RCTs showed a statistically significant result becoming insignificant or vice versa depending on the effect size estimate. OR exaggerated the RR in 62% of the RCTs. The percentage of overestimation was > 50% in 28 RCTs and > 100% in 13 RCTs. The degree of overestimation was positively correlated with the prevalence of outcomes (spearman's rho = 0.84 and 0.66, p < 0.001).

CONCLUSION

Use of OR instead of RR in RCTs does not change the qualitative inference of results. However, the use of OR can markedly exaggerate the effect size in RCTs if misinterpreted as RR and, hence, has the potential to mislead clinicians.

Serum bilirubin and the risk of hypertension

BACKGROUND

Experimental studies suggest oxidative stress could lead to the development of hypertension. Serum bilirubin is a major contributor to the antioxidant capacity in blood plasma and has been identified as an independent cardiovascular risk factor in cohort studies. However, data on the relationship between bilirubin and blood pressure are scarce and inconclusive.

METHODS

We analysed data from the National Health and Nutrition Examination Surveys (NHANES) 1999-2012 (N=31069). Fifty multiple imputed data sets were generated and analysed to avoid selection/confounding bias due to excluding individuals/variables with missing values. A minimal sufficient adjustment set of variables (MSAS) needed to estimate the unconfounded effect of bilirubin on blood pressure and hypertension (systolic/diastolic blood pressure ≥ 140/90 mmHg or using antihypertensive medication) was identified using the back-door criterion and included in all regression models.

RESULTS

After adjustment for the MSAS variables, systolic blood pressure decreased progressively up to -2.5 mmHg (p<0.001) and the prevalence of hypertension was up to 25% lower (P<0.001) in those with bilirubin ≥ 1.0 mg/dl-the highest two deciles-compared with those with 0.1-0.4 mg/dl-the lowest decile. Sensitivity analyses showed these results were unlikely to be explained by residual confounding or selection bias.

CONCLUSIONS

High serum bilirubin may decrease the risk of hypertension by inactivating and inhibiting the synthesis of reactive oxygen species in vascular cells. Strategies to boost the bioavailability of circulating and tissue bilirubin or to mimic bilirubin's antioxidant properties could have a significant impact on prevention and control of hypertension as well as coronary heart disease.

Social relationship correlates of major depressive disorder and depressive symptoms in Switzerland: nationally representative cross sectional study

BACKGROUND

The quality and quantity of social relationships are associated with depression but there is less evidence regarding which aspects of social relationships are most predictive. We evaluated the relative magnitude and independence of the association of four social relationship domains with major depressive disorder and depressive symptoms.

METHODS

We analyzed a cross-sectional telephone interview and postal survey of a probability sample of adults living in Switzerland (N=12,286). Twelve-month major depressive disorder was assessed via structured interview over the telephone using the Composite International Diagnostic Interview (CIDI). The postal survey assessed depressive symptoms as well as variables representing emotional support, tangible support, social integration, and loneliness.

RESULTS

Each individual social relationship domain was associated with both outcome measures, but in multivariate models being lonely and perceiving unmet emotional support had the largest and most consistent associations across depression outcomes (incidence rate ratios ranging from 1.55-9.97 for loneliness and from 1.23-1.40 for unmet support, p's<0.05). All social relationship domains except marital status were independently associated with depressive symptoms whereas only loneliness and unmet support were associated with depressive disorder.

CONCLUSIONS

Perceived quality and frequency of social relationships are associated with clinical depression and depressive symptoms across a wide adult age spectrum. This study extends prior work linking loneliness to depression by showing that a broad range of social relationship domains are associated with psychological well-being.

Covariate adjustment increased power in randomized controlled trials: an example in traumatic brain injury

OBJECTIVE

We aimed to determine to what extent covariate adjustment could affect power in a randomized controlled trial (RCT) of a heterogeneous population with traumatic brain injury (TBI).

STUDY DESIGN AND SETTING

We analyzed 14-day mortality in 9,497 participants in the Corticosteroid Randomization After Significant Head Injury (CRASH) RCT of corticosteroid vs. placebo. Adjustment was made using logistic regression for baseline covariates of two validated risk models derived from external data (International Mission on Prognosis and Analysis of Clinical Trials in Traumatic Brain Injury [IMPACT]) and from the CRASH data. The relative sample size (RESS) measure, defined as the ratio of the sample size required by an adjusted analysis to attain the same power as the unadjusted reference analysis, was used to assess the impact of adjustment.

RESULTS

Corticosteroid was associated with higher mortality compared with placebo (odds ratio=1.25, 95% confidence interval=1.13-1.39). RESS of 0.79 and 0.73 were obtained by adjustment using the IMPACT and CRASH models, respectively, which, for example, implies an increase from 80% to 88% and 91% power, respectively.

CONCLUSION

Moderate gains in power may be obtained using covariate adjustment from logistic regression in heterogeneous conditions such as TBI. Although analyses of RCTs might consider covariate adjustment to improve power, we caution against this approach in the planning of RCTs.

Dealing with missing outcome data in randomized trials and observational studies

Although missing outcome data are an important problem in randomized trials and observational studies, methods to address this issue can be difficult to apply. Using simulated data, the authors compared 3 methods to handle missing outcome data: 1) complete case analysis; 2) single imputation; and 3) multiple imputation (all 3 with and without covariate adjustment). Simulated scenarios focused on continuous or dichotomous missing outcome data from randomized trials or observational studies. When outcomes were missing at random, single and multiple imputations yielded unbiased estimates after covariate adjustment. Estimates obtained by complete case analysis with covariate adjustment were unbiased as well, with coverage close to 95%. When outcome data were missing not at random, all methods gave biased estimates, but handling missing outcome data by means of 1 of the 3 methods reduced bias compared with a complete case analysis without covariate adjustment. Complete case analysis with covariate adjustment and multiple imputation yield similar estimates in the event of missing outcome data, as long as the same predictors of missingness are included. Hence, complete case analysis with covariate adjustment can and should be used as the analysis of choice more often. Multiple imputation, in addition, can accommodate the missing-not-at-random scenario more flexibly, making it especially suited for sensitivity analyses.

Balance measures for propensity score methods: a clinical example on beta-agonist use and the risk of myocardial infarction

PURPOSE

Propensity score (PS) methods aim to control for confounding by balancing confounders between exposed and unexposed subjects with the same PS. PS balance measures have been compared in simulated data but limited in empirical data. Our objective was to compare balance measures in clinical data and assessed the association between long-acting inhalation beta-agonist (LABA) use and myocardial infarction.

METHODS

We estimated the relationship between LABA use and myocardial infarction in a cohort of adults with a diagnosis of asthma or chronic obstructive pulmonary disorder from the Utrecht General Practitioner Research Network database. More than two thousand PS models, including information on the observed confounders age, sex, diabetes, cardiovascular disease and chronic obstructive pulmonary disorder status, were applied. The balance of these confounders was assessed using the standardised difference (SD), Kolmogorov-Smirnov (KS) distance and overlapping coefficient. Correlations between these balance measures were calculated. In addition, simulation studies were performed to assess the correlation between balance measures and bias.

RESULTS

LABA use was not related to myocardial infarction after conditioning on the PS (median heart rate = 1.14, 95%CI = 0.47-2.75). When using the different balance measures for selecting a PS model, similar associations were obtained. In our empirical data, SD and KS distance were highly correlated balance measures (r = 0.92). In simulations, SD, KS distance and overlapping coefficient were similarly correlated to bias (e.g. r = 0.55, r = 0.52 and r = -0.57, respectively, when conditioning on the PS).

CONCLUSIONS

We recommend using the SD or the KS distance to quantify the balance of confounder distributions when applying PS methods.

Selection of confounding variables should not be based on observed associations with exposure

In observational studies, selection of confounding variables for adjustment is often based on observed baseline incomparability. The aim of this study was to evaluate this selection strategy. We used clinical data on the effects of inhaled long-acting beta-agonist (LABA) use on the risk of mortality among patients with obstructive pulmonary disease to illustrate the impact of selection of confounding variables for adjustment based on baseline comparisons. Among 2,394 asthma and COPD patients included in the analyses, the LABA ever-users were considerably older than never-users, but cardiovascular co-morbidity was equally prevalent (19.9% vs. 19.9%). Adjustment for cardiovascular co-morbidity status did not affect the crude risk ratio (RR) for mortality: crude RR 1.19 (95% CI 0.93–1.51) versus RR 1.19 (95% CI 0.94–1.50) after adjustment for cardiovascular co-morbidity. However, after adjustment for age (RR 0.95, 95% CI 0.76–1.19), additional adjustment for cardiovascular co-morbidity status did affect the association between LABA use and mortality (RR 1.01, 95% CI 0.80–1.26). Confounding variables should not be discarded based on balanced distributions among exposure groups, because residual confounding due to the omission of confounding variables from the adjustment model can be relevant.