Quantile regressions as a tool to evaluate how an exposure shifts and reshapes the outcome distribution: A primer for epidemiologists.

Quantifying how an exposure affects the entire outcome distribution is often important, e.g., for outcomes such as blood pressure which have non-linear effects on long-term morbidity and mortality. Quantile regressions offer a powerful way of estimating an exposure's relationship with the outcome distribution but remain underused in epidemiology. We introduce quantile regressions with a focus on distinguishing estimators for quantiles of the conditional and unconditional outcome distributions. We also present an empirical example in which we fit mean and quantile regressions to investigate educational attainment's association with later-life systolic blood pressure (SBP). We use data on 8,875 US-born respondents aged 50+ years from the US Health and Retirement Study. More education was negatively associated with mean SBP. Conditional and unconditional quantile regressions both suggested a negative association between education and SBP at all levels of SBP, but the absolute magnitudes of these associations were higher at higher SBP quantiles relative to lower quantiles. In addition to showing that educational attainment shifted the SBP distribution left-wards, quantile regression results revealed that education may have reshaped the SBP distribution through larger protective associations in the right tail, thus benefiting those at highest risk of cardiovascular diseases.

The Association between Education and Cognitive Performance Varies at Different Levels of Cognitive Performance: A Quantile Regression Approach.

INTRODUCTION: Educational differences in cognitive performance among older adults are well documented. Studies that explore this association typically estimate a single average effect of education on cognitive performance. We argue that the processes that contribute to the association between education and cognitive performance are unlikely to have equal effects at all levels of cognitive performance. In this study, we employ an analytical approach that enables us to go beyond averages to examine the association between education and five measures of global and domain-specific cognitive performance across the outcome distributions. METHODS: This cross-sectional study included 1,780 older adults aged 58-68 years from the Longitudinal Aging Study Amsterdam. Conditional quantile regression was used to examine variation across the outcome distribution. Cognitive outcomes included Mini-Mental State Examination (MMSE) score, crystallized intelligence, information processing speed, episodic memory, and a composite score of global cognitive performance. RESULTS: The results showed that the associations between education and different cognitive measures varied across the outcome distributions. Specifically, we found that education had a stronger association with crystallized intelligence, MMSE, and a composite cognitive performance measure in the lower tail of performance distributions. The associations between education and information processing speed and episodic memory were uniform across the outcome distributions. CONCLUSION: Larger associations between education and some domains of cognitive performance in the lower tail of the performance distributions imply that inequalities are primarily generated among individuals with lower performance rather than among average and high performers. Additionally, the varying associations across some of the outcome distributions indicate that estimating a single average effect through standard regression methods may overlook variations in cognitive performance between educational groups. Future studies should consider heterogeneity across the outcome distribution.

Penetrance of Polygenic Obesity Susceptibility Loci across the Body Mass Index Distribution.

A growing number of single-nucleotide polymorphisms (SNPs) have been associated with body mass index (BMI) and obesity, but whether the effects of these obesity-susceptibility loci are uniform across the BMI distribution remains unclear. We studied the effects of 37 BMI-associated SNPs in 75,230 adults of European ancestry across BMI percentiles by using conditional quantile regression (CQR) and meta-regression (MR) models. The effects of nine SNPs (24%)-rs1421085 (FTO; p = 8.69 × 10-15), rs6235 (PCSK1; p = 7.11 × 10-6), rs7903146 (TCF7L2; p = 9.60 × 10-6), rs11873305 (MC4R; p = 5.08 × 10-5), rs12617233 (FANCL; p = 5.30 × 10-5), rs11672660 (GIPR; p = 1.64 × 10-4), rs997295 (MAP2K5; p = 3.25 × 10-4), rs6499653 (FTO; p = 6.23 × 10-4), and rs3824755 (NT5C2; p = 7.90 × 10-4)-increased significantly across the sample BMI distribution. We showed that such increases stemmed from unadjusted gene interactions that enhanced the effects of SNPs in persons with a high BMI. When 125 height-associated SNPs were analyzed for comparison, only one (<1%), rs6219 (IGF1, p = 1.80 × 10-4), showed effects that varied significantly across height percentiles. Cumulative gene scores of these SNPs (GS-BMI and GS-height) showed that only GS-BMI had effects that increased significantly across the sample distribution (BMI: p = 7.03 × 10-37; height: p = 0.499). Overall, these findings underscore the importance of gene-gene and gene-environment interactions in shaping the genetic architecture of BMI and advance a method for detecting such interactions by using only the sample outcome distribution.

Highlighting differences between conditional and unconditional quantile regression approaches through an application to assess medication adherence.

The quantile regression (QR) framework provides a pragmatic approach in understanding the differential impacts of covariates along the distribution of an outcome. However, the QR framework that has pervaded the applied economics literature is based on the conditional quantile regression method. It is used to assess the impact of a covariate on a quantile of the outcome conditional on specific values of other covariates. In most cases, conditional quantile regression may generate results that are often not generalizable or interpretable in a policy or population context. In contrast, the unconditional quantile regression method provides more interpretable results as it marginalizes the effect over the distributions of other covariates in the model. In this paper, the differences between these two regression frameworks are highlighted, both conceptually and econometrically. Additionally, using real-world claims data from a large US health insurer, alternative QR frameworks are implemented to assess the differential impacts of covariates along the distribution of medication adherence among elderly patients with Alzheimer's disease.

Explaining Obesity- and Smoking-related Healthcare Costs through Unconditional Quantile Regression.

Background: This paper assesses obesity- and smoking-related incremental healthcare costs for the employees and dependents of a large U.S. employer. Objectives: Unlike previous studies, this study evaluates the distributional effects of obesity and smoking on healthcare cost distribution using a recently developed econometric framework: the unconditional quantile regression (UQR). Methods: Results were compared with the traditional conditional quantile regression (CQR), and the generalized linear modeling (GLM) framework that is commonly used for modeling healthcare cost. Results: The study found strong evidence of association of healthcare costs with obesity and smoking. More importantly, the study found that these effects are substantially higher in the upper quantiles of the healthcare cost distribution than in the lower quantiles. The insights on the heterogeneity of impacts of obesity and smoking on healthcare costs would not have been captured by traditional mean-based approaches. The study also found that UQR impact estimates were substantially different from CQR impact estimates in the upper quantiles of the cost distribution. Conclusions: These results suggest the potential role that smoking cessation and weight management programs can play in arresting the growth in healthcare costs. Specifically, given the finding that obesity and smoking have markedly higher impacts on high-cost patients, such programs appear to have significant cost saving potential if targeted toward high-cost patients.