Relative Risk Regression in Medical Research: Models, Contrasts, Estimators, and Algorithms

The relative risk or prevalence ratio is a natural and familiar summary of association between a binary outcome and an exposure or intervention. For rare events, the relative risk can be approximately estimated by logistic regression. For common events estimation is more difficult. We review proposed estimation algorithms for relative risk regression. Some of these give inconsistent estimates or invalid standard errors. We show that the methods that give correct inference can be viewed as arising from a family of quasilikelihood estimating functions for the same generalized linear model, differing in their efficiency and in their robustness to outlying values of the predictors. We give recommendations for fitting relative risk regression models in various popular statistical systems

Racial/ethnic heterogeneity in associations of blood pressure and incident cardiovascular disease by functional status in a prospective cohort: the Multi-Ethnic Study of Atherosclerosis.

OBJECTIVES:Research has demonstrated that the association between high blood pressure and outcomes is attenuated among older adults with functional limitations, compared with healthier elders. However, it is not known whether these patterns vary by racial/ethnic group. We evaluated race/ethnicity-specific patterns of effect modification in the association between blood pressure and incident cardiovascular disease (CVD) by functional status. SETTING:We used data from the Multi-Ethnic Study of Atherosclerosis (2002-2004, with an average of 8.8 years of follow-up for incident CVD). We assessed effect modification of systolic blood pressure and cardiovascular outcomes by self-reported physical limitations and by age. PARTICIPANTS:The study included 6117 participants (aged 46 to 87; 40% white, 27% black, 22% Hispanic and 12% Chinese) who did not have CVD at the second study examination (when self-reported physical limitations were assessed). OUTCOME MEASURES:Incident CVD was defined as an incident myocardial infarction, coronary revascularisation, resuscitated cardiac arrest, angina, stroke (fatal or non-fatal) or death from CVD. RESULTS:We observed weaker associations between systolic blood pressure (SBP) and CVD among white adults with physical limitations (incident rate ratio (IRR) per 10 mm Hg higher SBP: 1.09 (95% CI 0.99 to 1.20)) than those without physical limitations (IRR 1.29 (1.19, 1.40); P value for interaction <0.01). We found a similar pattern among black adults. Poor precision among the estimates for Hispanic or Chinese participants limited the findings in these groups. The attenuated associations were consistent across both multiplicative and additive scales, though physical limitations showed clearer patterns than age on an additive scale. CONCLUSION:Attenuated associations between high blood pressure and incident CVD were observed for blacks and whites with poor function, though small sample sizes remain a limitation for identifying differences among Hispanic or Chinese participants. Identifying the characteristics that distinguish those in whom higher SBP is associated with less risk of morbidity or mortality may inform our understanding of the consequences of hypertension among older adults

Semiparametric Two-Part Models with Proportionality Constraints: Analysis of the Multi-Ethnic Study of Atherosclerosis (MESA)

SUMMARY. In this article, we analyze the coronary artery calcium (CAC) score in the Multi-Ethnic Study of Atherosclerosis (MESA), where about half of the CAC scores are zero and the rest are continuously distributed. When the observed data has a mixture distribution, two-part models can be the natural choice. With a two-part model, there are two covariate effects, with one in each part of the model. Determination of whether the two covariate effects are proportional can provide more insights into the process underlying development and progression of CAC. In this study, we model the CAC score using a semiparametric two-part model, and investigate the determination of proportionality of the covariate effects. We propose penalized maximum likelihood estimation and using thin plate splines in practical data analysis, and establish asymptotic estimation properties. We propose a step-wise hypothesis testing based approach to determine proportionality. Simulation studies suggest satisfactory finite-sample performance of the proposed approach. Analysis of the MESA data suggests that proportionality holds for all covariates except the LDL and HDL

Risk Factors for Long-Term Coronary Artery Calcium Progression in the Multi-Ethnic Study of Atherosclerosis.

BackgroundCoronary artery calcium (CAC) detected by noncontrast cardiac computed tomography scanning is a measure of coronary atherosclerosis burden. Increasing CAC levels have been strongly associated with increased coronary events. Prior studies of cardiovascular disease risk factors and CAC progression have been limited by short follow-up or restricted to patients with advanced disease.Methods and resultsWe examined cardiovascular disease risk factors and CAC progression in a prospective multiethnic cohort study. CAC was measured 1 to 4 times (mean 2.5 scans) over 10 years in 6810 adults without preexisting cardiovascular disease. Mean CAC progression was 23.9 Agatston units/year. An innovative application of mixed-effects models investigated associations between cardiovascular disease risk factors and CAC progression. This approach adjusted for time-varying factors, was flexible with respect to follow-up time and number of observations per participant, and allowed simultaneous control of factors associated with both baseline CAC and CAC progression. Models included age, sex, study site, scanner type, and race/ethnicity. Associations were observed between CAC progression and age (14.2 Agatston units/year per 10 years [95% CI 13.0 to 15.5]), male sex (17.8 Agatston units/year [95% CI 15.3 to 20.3]), hypertension (13.8 Agatston units/year [95% CI 11.2 to 16.5]), diabetes (31.3 Agatston units/year [95% CI 27.4 to 35.3]), and other factors.ConclusionsCAC progression analyzed over 10 years of follow-up, with a novel analytical approach, demonstrated strong relationships with risk factors for incident cardiovascular events. Longitudinal CAC progression analyzed in this framework can be used to evaluate novel cardiovascular risk factors

Late systolic central hypertension as a predictor of incident heart failure : the Multi-Ethnic Study of Atherosclerosis

Background: Experimental studies demonstrate that high aortic pressure in late systole relative to early systole causes greater myocardial remodeling and dysfunction, for any given absolute peak systolic pressure. Methods and Results: We tested the hypothesis that late systolic hypertension, defined as the ratio of late (last one third of systole) to early (first two thirds of systole) pressure-time integrals (PTI) of the aortic pressure waveform, independently predicts incident heart failure (HF) in the general population. Aortic pressure waveforms were derived from a generalized transfer function applied to the radial pressure waveform recorded noninvasively from 6124 adults. The late/early systolic PTI ratio (L/ESPTI) was assessed as a predictor of incident HF during median 8.5 years of follow-up. The L/ESPTI was predictive of incident HF (hazard ratio per 1% increase= 1.22; 95% CI= 1.15 to 1.29; P58.38%) was more predictive of HF than the presence of hypertension. After adjustment for each other and various predictors of HF, the HR associated with hypertension was 1.39 (95% CI= 0.86 to 2.23; P=0.18), whereas the HR associated with a high L/E was 2.31 (95% CI=1.52 to 3.49; P<0.0001). Conclusions: Independently of the absolute level of peak pressure, late systolic hypertension is strongly associated with incident HF in the general population

How Important Is Diabetes as a Risk Factor for Cardiovascular and Other Diseases in Older Adults?

Patel and Kengne discuss a new study inPLoS Medicine which found a 2-fold increased risk of cardiovascular death associated with diabetes in people over 65 years old

Assessing the sensitivity of regression results to unmeasured confounders in observational studies

This paper presents a general approach for assessing the sensitivity of the point and interval estimates of the primary exposure effect in an observational study to the residual confounding effects of unmeasured variables after adjusting for measured covariates. The proposed method assumes that the true exposure effect can be represented in a regression model that includes the exposure indicator as well as the measured and unmeasured confounders. One can use the corresponding reduced model that omits the unmeasured confounder to make statistical inferences about the true exposure effect by specifying the distributions of the unmeasured confounder in the exposed and unexposed groups along with the effects of the unmeasured confounder on the outcome variable. Under certain conditions, there exists a simple algebraic relationship between the true exposure effect in the full model and the apparent exposure effect in the reduced model. One can then estimate the true exposure effect by making a simple adjustment to the point and interval estimates of the apparent exposure effect obtained from standard software or published reports. The proposed method handles both binary response and censored survival time data, accommodates any study design, and allows the unmeasured confounder to be discrete or normally distributed. We describe applications to two major medical studies