Joseph Kang

Demystifying Double Robustness: A Comparison of Alternative Strategies for Estimating a Population Mean from Incomplete Data

When outcomes are missing for reasons beyond an investigators control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to missingness. One approach is to model the relationships between the covariates and the outcome and use those relationships to predict the missing values. Another is to model the probabilities of missingness given the covariates and incorporate them into a weighted or stratified estimate. Doubly robust (DR) procedures apply both types of model simultaneously and produce a consistent estimate of the parameter if either of the two models has been correctly specified. In this article, we show that DR estimates can be constructed in many ways. We compare the performance of various DR and non-DR estimates of a population mean in a simulated example where both models are incorrect but neither is grossly misspecified. Methods that use inverse-probabilities as weights, whether they are DR or not, are sensitive to misspecification of the propensity model when some estimated propensities are small. Many DR methods perform better than simple inverse-probability weighting. None of the DR methods we tried, however, improved upon the performance of simple regression-based prediction of the missing values. This study does not represent every missing-data problem that will arise in practice. But it does demonstrate that, in at least some settings, two wrong models are not better than one.We congratulate Drs. Kang and Schafer (KS henceforth) for a careful and thought-provoking contribution to the literature regarding the so-called “double robustness” property, a topic that still engenders some confusion and disagreement. The authors’ approach of focusing on the simplest situation of estimation of the population mean μ of a response y when y is not observed on all subjects according to a missing at random (MAR) mechanism (equivalently, estimation of the mean of a potential outcome in a causal model under the assumption of no unmeasured confounders) is commendable, as the fundamental issues can be explored without the distractions of the messier notation and considerations required in more complicated settings. Indeed, as the article demonstrates, this simple setting is sufficient to highlight a number of key points. As noted eloquently by Molenberghs (2005), in regard to how such missing data/causal inference problems are best addressed, two “schools” may be identified: the “likelihood-oriented” school and the “weighting-based” school. As we have emphasized previously (Davidian, Tsiatis and Leon, 2005), we prefer to view inference from the vantage point of semi-parametric theory, focusing on the assumptions embedded in the statistical models leading to different “types” of estimators (i.e., “likelihood-oriented” or “weighting-based”) rather than on the forms of the estimators themselves. In this discussion, we hope to complement the presentation of the authors by elaborating on this point of view. Throughout, we use the same notation as in the paper.

Average Causal Effects from Nonrandomized Studies: A Practical Guide and Simulated Example.

In a well-designed experiment, random assignment of participants to treatments makes causal inference straightforward. However, if participants are not randomized (as in observational study, quasi-experiment, or nonequivalent control-group designs), group comparisons may be biased by confounders that influence both the outcome and the alleged cause. Traditional analysis of covariance, which includes confounders as predictors in a regression model, often fails to eliminate this bias. In this article, the authors review Rubins definition of an average causal effect (ACE) as the average difference between potential outcomes under different treatments. The authors distinguish an ACE and a regression coefficient. The authors review 9 strategies for estimating ACEs on the basis of regression, propensity scores, and doubly robust methods, providing formulas for standard errors not given elsewhere. To illustrate the methods, the authors simulate an observational study to assess the effects of dieting on emotional distress. Drawing repeated samples from a simulated population of adolescent girls, the authors assess each method in terms of bias, efficiency, and interval coverage. Throughout the article, the authors offer insights and practical guidance for researchers who attempt causal inference with observational data.

Systematic evaluation of Axis-I DSM diagnoses in delayed sleep phase disorder and evening-type circadian preference.

BACKGROUND Alterations in circadian rhythms can have profound effects on mental health. High co-morbidity for psychiatric disorders has been observed in patients with circadian rhythm disorders, such as delayed sleep phase disorder (DSPD), and in those with an evening-type circadian preference. The aim of this study was to systematically determine the prevalence and type of Diagnostic and Statistical Manual of Mental Disorders fourth edition (DSM IV) Axis-I disorders in those with DSPD compared to evening-type controls. METHODS Forty-eight DSPD and 25 evening-type participants took part in this study. Sleep and wake parameters were assessed with actigraphy, diary and questionnaires (Pittsburgh Sleep Quality Index (PSQI) and Functional Outcomes of Sleep Questionnaire (FOSQ). Evening-type preference was defined by the Horne-Ostberg questionnaire. DSPD was determined by an interview according to International Classification of Sleep Disorders criteria. Current and past diagnoses of psychiatric disorders were assessed with a Structured Clinical Interview for DSM-IV disorders. RESULTS DSPD was associated with a later wake time, longer sleep time, higher PSQI score and lower Horne-Ostberg and FOSQ scores compared to evening-types. There were no significant differences in the prevalence or type of Axis-I disorders between those with DSPD or evening-type preference. Over 70% of participants met criteria for at least one past Axis-I disorder. Approximately 40% of both the DSPD and evening-types met criteria for a past diagnosis of mood, anxiety (most frequently phobia) or substance-use disorders. Evening types were more likely to have a past diagnosis of more than one Axis-I disorder. CONCLUSIONS These results highlight the important link between circadian rhythms and mental disorders. Specifically, an evening circadian chronotype regardless of DSPD status is associated with a risk for anxiety, depressive or substance-use disorders.

Racial Differences in Risks for First Cardiovascular Events and Noncardiovascular Death The Atherosclerosis Risk in Communities Study, the Cardiovascular Health Study, and the Multi-Ethnic Study of Atherosclerosis

Background— No studies have compared first cardiovascular disease (CVD) events and non-CVD death between races in a competing risks framework, which examines risks for numerous events simultaneously. Methods and Results— We used competing Cox models to estimate hazards for first CVD events and non-CVD death within and between races in 3 multicenter, National Heart, Lung, and Blood Institute–sponsored cohorts. Of 14 569 Atherosclerosis Risk in Communities (ARIC) study participants aged 45 to 64 years with mean follow-up of 10.5 years, 11.6% had CVD and 5.0% had non-CVD death as first events; among 4237 Cardiovascular Health Study (CHS) study participants aged 65 to 84 years and followed for 8.5 years, these figures were 43.2% and 15.7%, respectively. Middle-aged blacks were significantly more likely than whites to experience any CVD as a first event; this disparity disappeared by older adulthood and after adjustment for CVD risk factors. The pattern of results was similar for Multi-Ethnic Study of Atherosclerosis (MESA) participants. Traditional Cox and competing risks models yielded different results for coronary heart disease risk. Black men appeared somewhat more likely than white men to experience coronary heart disease with use of a standard Cox model (hazard ratio 1.06; 95% CI 0.90, 1.26), whereas they appeared less likely than white men to have a first coronary heart disease event with use of a competing risks model (hazard ratio, 0.77; 95% CI, 0.60, 1.00). Conclusions— CVD affects blacks at an earlier age than whites; this may be attributable in part to elevated CVD risk factor levels among blacks. Racial disparities in first CVD incidence disappear by older adulthood. Competing risks analyses may yield somewhat different results than traditional Cox models and provide a complementary approach to examining risks for first CVD events. # CLINICAL PERSPECTIVE {#article-title-33}Background— No studies have compared first cardiovascular disease (CVD) events and non-CVD death between races in a competing risks framework, which examines risks for numerous events simultaneously. Methods and Results— We used competing Cox models to estimate hazards for first CVD events and non-CVD death within and between races in 3 multicenter, National Heart, Lung, and Blood Institute–sponsored cohorts. Of 14 569 Atherosclerosis Risk in Communities (ARIC) study participants aged 45 to 64 years with mean follow-up of 10.5 years, 11.6% had CVD and 5.0% had non-CVD death as first events; among 4237 Cardiovascular Health Study (CHS) study participants aged 65 to 84 years and followed for 8.5 years, these figures were 43.2% and 15.7%, respectively. Middle-aged blacks were significantly more likely than whites to experience any CVD as a first event; this disparity disappeared by older adulthood and after adjustment for CVD risk factors. The pattern of results was similar for Multi-Ethnic Study of Atherosclerosis (MESA) participants. Traditional Cox and competing risks models yielded different results for coronary heart disease risk. Black men appeared somewhat more likely than white men to experience coronary heart disease with use of a standard Cox model (hazard ratio 1.06; 95% CI 0.90, 1.26), whereas they appeared less likely than white men to have a first coronary heart disease event with use of a competing risks model (hazard ratio, 0.77; 95% CI, 0.60, 1.00). Conclusions— CVD affects blacks at an earlier age than whites; this may be attributable in part to elevated CVD risk factor levels among blacks. Racial disparities in first CVD incidence disappear by older adulthood. Competing risks analyses may yield somewhat different results than traditional Cox models and provide a complementary approach to examining risks for first CVD events.

Longitudinal assessment of fibrinogen in relation to subclinical cardiovascular disease: the CARDIA study

Summary.  Objective: To examine the strength of the associations of fibrinogen with subclinical atherosclerosis in healthy persons. Methods: A population‐based, prospective, observational study of black and white men and women (Coronary Artery Risk Development in Young Adults [CARDIA]). Fibrinogen levels were measured at year 7 (ages 25–37, n = 2969), and again at year 20 (ages 38–50, n = 2832). Measures of subclinical atherosclerosis (coronary artery calcification [CAC] and carotid intimal‐medial thickness [CIMT]) were recorded at year 20. Results: Over the 13‐year study interval (1992–1993 to 2005–2006), fibrinogen rose from a mean of 3.32 to 4.05 g L−1. After adjusting for age, gender and race, fibrinogen was positively associated with greater incidence of CAC and increased CIMT cross‐sectionally as well as after 13 years of follow‐up (all P‐trend < 0.001). After further adjustment for field center, BMI, smoking, education, systolic blood pressure, diabetes, antihypertensive medication use, total and HDL cholesterol, and CRP, significant positive relationships between fibrinogen and incidence of CAC remained for the total cohort longitudinally (P‐trend = 0.037), but not cross‐sectionally (P‐trend = 0.147). Conclusion: This 13‐year study demonstrates that higher levels of fibrinogen during young adulthood are positively associated with incidence of CAC and increased CIMT in middle‐age, but the strength of the association declines with increasing age.

Timing and Intensity of Light Correlate with Body Weight in Adults

Light exposure can influence sleep and circadian timing, both of which have been shown to influence weight regulation. The goal of this study was to evaluate the relationship between ambient light, sleep and body mass index. Participants included 54 individuals (26 males, mean age 30.6, SD = 11.7 years). Light levels, sleep midpoint and duration were measured with wrist actigraphy (Actiwatch-L) for 7 days. BMI was derived from self-reported height and weight. Caloric intake was determined from 7 days of food logs. For each participant, light and activity data were output in 2 minute epochs, smoothed using a 5 point (10 minute) moving average and then aggregated over 24 hours. The mean light timing above 500 lux (MLiT500) was defined as the average clock time of all aggregated data points above 500 lux. MLiT500 was positively correlated with BMI (r = 0.51, p<0.001), and midpoint of sleep (r = 0.47, p<0.01). In a multivariable linear regression model including MLiT500 and midpoint of sleep, MLiT500 was a significant predictor of BMI (B = 1.26 SE = 0.34, β = 0.53 p = 0.001, r 2 Δ = 0.22). Adjusting for covariates, MLiT500 remained an independent predictor of BMI (B = 1.28 SE = 0.36, β = 0.54, p = 0.002, r 2 Δ = 0.20). The full model accounted for 34.7% of the variance in BMI (p = 0.01). Exposure to moderate levels of light at biologically appropriate times can influence weight, independent of sleep timing and duration.

Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data

When outcomes are missing for reasons beyond an investigators control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to missingness. One approach is to model the relationships between the covariates and the outcome and use those relationships to predict the missing values. Another is to model the probabilities of missingness given the covariates and incorporate them into a weighted or stratified estimate. Doubly robust (DR) procedures apply both types of model simultaneously and produce a consistent estimate of the parameter if either of the two models has been correctly specified. In this article, we show that DR estimates can be constructed in many ways. We compare the performance of various DR and non-DR estimates of a population mean in a simulated example where both models are incorrect but neither is grossly misspecified. Methods that use inverse-probabilities as weights, whether they are DR or not, are sensitive to misspecification of the propensity model when some estimated propensities are small. Many DR methods perform better than simple inverse-probability weighting. None of the DR methods we tried, however, improved upon the performance of simple regression-based prediction of the missing values. This study does not represent every missing-data problem that will arise in practice. But it does demonstrate that, in at least some settings, two wrong models are not better than one.We congratulate Drs. Kang and Schafer (KS henceforth) for a careful and thought-provoking contribution to the literature regarding the so-called “double robustness” property, a topic that still engenders some confusion and disagreement. The authors’ approach of focusing on the simplest situation of estimation of the population mean μ of a response y when y is not observed on all subjects according to a missing at random (MAR) mechanism (equivalently, estimation of the mean of a potential outcome in a causal model under the assumption of no unmeasured confounders) is commendable, as the fundamental issues can be explored without the distractions of the messier notation and considerations required in more complicated settings. Indeed, as the article demonstrates, this simple setting is sufficient to highlight a number of key points. As noted eloquently by Molenberghs (2005), in regard to how such missing data/causal inference problems are best addressed, two “schools” may be identified: the “likelihood-oriented” school and the “weighting-based” school. As we have emphasized previously (Davidian, Tsiatis and Leon, 2005), we prefer to view inference from the vantage point of semi-parametric theory, focusing on the assumptions embedded in the statistical models leading to different “types” of estimators (i.e., “likelihood-oriented” or “weighting-based”) rather than on the forms of the estimators themselves. In this discussion, we hope to complement the presentation of the authors by elaborating on this point of view. Throughout, we use the same notation as in the paper.

Association of elevated plasminogen activator inhibitor 1 levels with diminished lung function in patients with asthma

BACKGROUND We previously reported that plasminogen activator inhibitor 1 (PAI-1) was upregulated in human asthmatic airways and promotes airway fibrosis in an allergen-challenged murine model of asthma. OBJECTIVES To examine whether elevated plasma levels of PAI-1 are associated with poor lung function in asthmatic patients. METHODS Five hundred nineteen adults were eligible for the study, and ultimately 353 adults were enrolled and completed the baseline protocol between January 24, 2004, and July 30, 2005. Of these, 231 adults with asthma from the Chicago Initiative to Raise Asthma Health Equity study were randomly selected and the plasma levels of PAI-1 were measured by enzyme-linked immunosorbent assay. Asthma burden, medication, smoking status, and body mass index (BMI) were obtained by history and spirometry was performed. A multivariate regression analysis was performed to evaluate the association of PAI-1 levels and lung function and the potential determinant variables that were associated with PAI-1. RESULTS We found associations between PAI-1 and BMI (β = 0.606, P = .002), smoking (β = 7.526, P = .001), and African American race (β = -9.061, P = .01). Obese patients showed a significant increase in PAI-1, and current smokers demonstrated higher levels of PAI-1 compared with nonsmokers. When we evaluated the associations between lung function parameters and PAI-1, we found that PAI-1 was negatively associated with forced vital capacity (FVC) (β = -0.098, P = .011) but not with forced expiratory volume in 1 second (FEV(1)) or the FEV(1)/FVC ratio. There was a negative association between BMI and FVC, and PAI-1 may mediate some of this association. CONCLUSIONS This study suggests a significant association between PAI-1 and lung function in patients with asthma. The effect of obesity on FVC may in part be mediated by PAI-1.

Original articleAsthma, lower airway diseaseAssociation of elevated plasminogen activator inhibitor 1 levels with diminished lung function in patients with asthma

BACKGROUND We previously reported that plasminogen activator inhibitor 1 (PAI-1) was upregulated in human asthmatic airways and promotes airway fibrosis in an allergen-challenged murine model of asthma. OBJECTIVES To examine whether elevated plasma levels of PAI-1 are associated with poor lung function in asthmatic patients. METHODS Five hundred nineteen adults were eligible for the study, and ultimately 353 adults were enrolled and completed the baseline protocol between January 24, 2004, and July 30, 2005. Of these, 231 adults with asthma from the Chicago Initiative to Raise Asthma Health Equity study were randomly selected and the plasma levels of PAI-1 were measured by enzyme-linked immunosorbent assay. Asthma burden, medication, smoking status, and body mass index (BMI) were obtained by history and spirometry was performed. A multivariate regression analysis was performed to evaluate the association of PAI-1 levels and lung function and the potential determinant variables that were associated with PAI-1. RESULTS We found associations between PAI-1 and BMI (β = 0.606, P = .002), smoking (β = 7.526, P = .001), and African American race (β = -9.061, P = .01). Obese patients showed a significant increase in PAI-1, and current smokers demonstrated higher levels of PAI-1 compared with nonsmokers. When we evaluated the associations between lung function parameters and PAI-1, we found that PAI-1 was negatively associated with forced vital capacity (FVC) (β = -0.098, P = .011) but not with forced expiratory volume in 1 second (FEV(1)) or the FEV(1)/FVC ratio. There was a negative association between BMI and FVC, and PAI-1 may mediate some of this association. CONCLUSIONS This study suggests a significant association between PAI-1 and lung function in patients with asthma. The effect of obesity on FVC may in part be mediated by PAI-1.

Do statins reduce the risk of myocardial infarction in patients with heart failure? A pooled individual‐level reanalysis of CORONA and GISSI‐HF

Current guidelines do not explicitly recommend statin use in heart failure (HF). Relatively low numbers of atherothrombotic events among HF patients, in the context of their elevated competing risks for non‐atherothrombotic causes of death, may have prevented previous analyses of clinical trials from detecting a benefit for statins. We pooled data from two landmark trials of HF patients not on statin therapy randomized to rosuvastatin 10 mg daily vs. placebo, CORONA and GISSI‐HF, in order to improve our power to detect statistically significant differences in atherothrombotic events. We also accounted for competing risks from other causes of death.