Wednesday, April 9, 2014

Quantile Regression and Healthcare Costs

I thought this was a nice statement that speaks to the utility of quantile regression (which holds to any distribution with these issues not just cost data):

The quantile regression framework allows us to obtain a more complete picture of the effects of the covariates on the health care cost, and is naturally adapted to the skewness and heterogeneity of the cost data.


Health care cost data are characterized by a high level of skewness and heteroscedastic variances…Most of the existing literature on health care cost data analysis have been focused on modeling the conditional mean (or average) of the health care cost given the covariates such as age, gender, race, marital status and disease status. The conditional mean framework has two important limitations. First, the application of the conditional mean regression model to health care cost data analysis is usually not straightforward. Due to the presence of skewness and nonconstant variances, transformation of the response variable is often required when constructing the mean regression model and retransformation is needed in order to obtain direct inference on the mean cost. Second, the conditional mean model focuses primarily on the marginal effects of the risk factors on the central tendency of the conditional distribution. When the marginal effects vary across the conditional distribution, focusing on the marginal effects at the central tendency may substantially distort the information of interest at the tails. For example, a weak relationship between a risk factor and the mean health care cost does not preclude a stronger relationship at the upper or lower quantiles of the conditional distribution….By considering different quantiles, we are able to obtain a more complete picture of the effects of the covariates on health care cost.


Weighted Quantile Regression for Analyzing Health Care Cost Data with Missing Covariates. Ben Sherwood, Lan Wang and Xiao-Hua Zhou Statistics in Medicine. 2012

 “heavy upper tails may influence the "robustness" with which some parameters are estimated. Indeed, in worlds described by heavy-tailed Pareto or Burr- Singh-Maddala distributions (Mandelbrot, 1963; Singh and Maddala, 1976) some traditionally interesting parameters (means, variances) may not even be finite, a situation never encountered in, e.g., a normal or log-normal world. Such concerns should translate into empirical strategies that target the high-end parameters of particular interest, e.g. models for Prob(y k | x) or quantile regression models.."
John Mullahy
Univ. of Wisconsin-Madison
January 2009
See also: Quantile Regression with Count Data

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