Smooth quantile ratio estimation with regression: estimating medical expenditures for smoking-attributable diseases

A flexible quantile regression model for medical costs with application to Medical Expenditure Panel Survey Study

Medical costs are often skewed to the right and heteroscedastic, having a sophisticated relation with covariates. Mean function regression models with low-dimensional covariates have been extensively considered in the literature. However, it is important to develop a robust alternative to find the underlying relationship between medical costs and high-dimensional covariates. In this paper, we propose a new quantile regression model to analyze medical costs. We also consider variable selection, using an adaptive lasso penalized variable selection method to identify significant factors of the covariates. Simulation studies are conducted to illustrate the performance of the estimation method. We apply our method to the analysis of the Medical Expenditure Panel Survey dataset.

Bayesian Tobit quantile regression model for medical expenditure panel survey data

High expenditure on healthcare is an important segment of the U.S. economy, making healthcare cost modelling valuable in decision-making processes over a wide array of domains. In this paper, we analyze medical expenditure panel survey (MEPS) data. Tobit regression model has been popularly used for the medical expenditures. However, it is no longer sufficient for the MEPS data because: (i) the distribution of the expenditures shows skewness, heavy tails and heterogeneity; (ii) most predictors are categorical, including binary, nominal and ordinal variables; (iii) there are a few predictors which may be nonlinearly related to the response. We therefore propose a Bayesian Tobit quantile regression model to describe a complete distributional view on how the medical expenditures depend on the various predictors. Specifically, we assume an asymmetric Laplace error distribution to adapt the quantile regression to a Bayesian setting. Then, we propose a modified group Lasso for categorical factor selection, and a smoothing Gaussian prior for modelling the nonlinear effects. The estimates and their uncertainties are obtained using an efficient Monte Carlo Markov Chain sampling method. The effectiveness of our approach is demonstrated by modelling 2007 MEPS data.

Review of statistical methods for analysing healthcare resources and costs

We review statistical methods for analysing healthcare resource use and costs, their ability to address skewness, excess zeros, multimodality and heavy right tails, and their ease for general use. We aim to provide guidance on analysing resource use and costs focusing on randomised trials, although methods often have wider applicability. Twelve broad categories of methods were identified: (I) methods based on the normal distribution, (II) methods following transformation of data, (III) single-distribution generalized linear models (GLMs), (IV) parametric models based on skewed distributions outside the GLM family, (V) models based on mixtures of parametric distributions, (VI) two (or multi)-part and Tobit models, (VII) survival methods, (VIII) non-parametric methods, (IX) methods based on truncation or trimming of data, (X) data components models, (XI) methods based on averaging across models, and (XII) Markov chain methods. Based on this review, our recommendations are that, first, simple methods are preferred in large samples where the near-normality of sample means is assured. Second, in somewhat smaller samples, relatively simple methods, able to deal with one or two of above data characteristics, may be preferable but checking sensitivity to assumptions is necessary. Finally, some more complex methods hold promise, but are relatively untried; their implementation requires substantial expertise and they are not currently recommended for wider applied work.

Interval estimation of quantile ratios applied to anti-cancer drug screening by xenograft experiments

The current practice in analyzing data from anti-cancer drug screening by xenograft experiments lacks statistical consideration to account for experimental noise, and a sound inference procedure is necessary. A novel confidence bound and interval procedure for estimating quantile ratios developed in this paper fills the void. Justified by rigorous large-sample theory and a simulation study of small-sample performance, the proposed method performs well in a wide range of scenarios involving right-skewed distributions. By providing rigorous inference and much more interpretable statistics that account for experimental noise, the proposed method improves the current practice of analyzing drug activity data in xenograft experiments. The proposed method is fully nonparametric, simple to compute, performs equally well or better than known nonparametric methods, and is applicable to any statistical inference of a 'fold change' that can be formulated as a quantile ratio.

Testing for differences in distribution tails to test for differences in 'maximum' lifespan

BACKGROUND

Investigators are actively testing interventions intended to increase lifespan and wish to test whether the interventions increase maximum lifespan. Based on the fact that one cannot be assured of observing population maximum lifespans in finite samples, in previous work, we constructed and validated several tests of difference in the upper parts of lifespan distributions between a treatment group and a control group by testing whether the probabilities that observations are above some threshold defining 'old' or being in the tail of the survival distribution are equal in the two groups. However, a limitation of these tests is that they do not consider how much above the threshold any particular observation is.

METHODS

In this article we propose new methods which improve upon our previous tests by considering not only whether an observation is above some threshold, but also the magnitudes by which observations exceed the threshold.

RESULTS

Simulations show that the new methods control type I error rates quite well and that the power of the new methods is usually higher than that of the tests we previously proposed. In illustrative analyses of two real datasets involving rodents, when setting the threshold equal to 110 (100) weeks for the first (second) datasets, the new methods detected differences in 'maximum lifespan' between groups at nominal alpha levels of 0.01 (0.05) for the first (second) datasets and provided more significant results than competitor tests.

CONCLUSION

The new methods not only have good performance in controlling the type I error rates but also improve the power compared with the tests we previously proposed.

Treatment effects of maternal micronutrient supplementation vary by percentiles of the birth weight distribution in rural Nepal

Certain antenatal micronutrient supplements increased birth weight by 40-70 g in rural Nepal. The effect was estimated by calculating the mean difference in birth weight between control and treatment groups, which assumes a constant treatment effect across the birth weight distribution. By estimating differences (and CI) in birth weight between treatment and control groups as a nonlinear, smooth function of the percentiles of the birth weight distribution, we can examine whether the shape of the birth weight distribution for a treatment group is different from that of the control group. Supplementation groups were folic acid, folic acid and iron, folic acid and iron and zinc, and a multiple micronutrient supplement all with vitamin A, compared with the control group of vitamin A alone. The shape of the birth weight distribution in the multiple micronutrient group was the same as that of the control group; however, the location of the distribution had shifted. The folic acid and iron group had fewer infants in the lower tail of its distribution but a similar proportion in the upper tail compared with the control group. The biologic pathways affecting intrauterine growth may vary by micronutrients such that some may confer a benefit among the most vulnerable infants, whereas others may have a more constant effect across the birth weight distribution. Future analytic approaches to estimating benefits of maternal supplementation on birth weight should examine whether there is a constant or variable treatment effect across the distribution of birth weight.