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Treatment effects beyond the mean using distributional regression: Methods and guidance.

ABSTRACT: This paper introduces distributional regression also known as generalized additive models for location, scale and shape (GAMLSS) as a modeling framework for analyzing treatment effects beyond the mean. In contrast to mean regression models, GAMLSS relate each distributional parameter to covariates. Therefore, they can be used to model the treatment effect not only on the mean but on the whole conditional distribution. Since they encompass a wide range of different distributions, GAMLSS provide a flexible framework for modeling non-normal outcomes in which additionally nonlinear and spatial effects can easily be incorporated. We elaborate on the combination of GAMLSS with program evaluation methods including randomized controlled trials, panel data techniques, difference in differences, instrumental variables, and regression discontinuity design. We provide practical guidance on the usage of GAMLSS by reanalyzing data from the Mexican Progresa program. Contrary to expectations, no significant effects of a cash transfer on the conditional consumption inequality level between treatment and control group are found.

SUBMITTER: Hohberg M

PROVIDER: S-EPMC7021287 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Treatment effects beyond the mean using distributional regression: Methods and guidance.

Hohberg Maike M Pütz Peter P Kneib Thomas T

PloS one 20200214 2

This paper introduces distributional regression also known as generalized additive models for location, scale and shape (GAMLSS) as a modeling framework for analyzing treatment effects beyond the mean. In contrast to mean regression models, GAMLSS relate each distributional parameter to covariates. Therefore, they can be used to model the treatment effect not only on the mean but on the whole conditional distribution. Since they encompass a wide range of different distributions, GAMLSS provide a ...[more]

PMID: 32058999

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Project description:BackgroundThe classical linear model is widely used in the analysis of clinical trials with continuous outcomes. However, required model assumptions are frequently not met, resulting in estimates of treatment effect that can be inefficient and biased. In addition, traditional models assess treatment effect only on the mean response, and not on other aspects of the response, such as the variance. Distributional regression modelling overcomes these limitations. The purpose of this paper is to demonstrate its usefulness for the analysis of clinical trials, and superior performance to that of traditional models.MethodsDistributional regression models are demonstrated, and contrasted with normal linear models, on data from the LIPID randomized controlled trial, which compared the effects of pravastatin with placebo in patients with coronary heart disease. Systolic blood pressure (SBP) and the biomarker midregional pro-adrenomedullin (MR-proADM) were analysed. Treatment effect was estimated in models that used response distributions more appropriate than the normal (Box-Cox-t and Johnson's Su for MR-proADM and SBP, respectively), applied censoring below the detection limit of MR-proADM, estimated treatment effect on distributional parameters other than the mean, and included random effects for longitudinal observations. A simulation study was conducted to compare the performance of distributional regression models with normal linear regression, under conditions mimicking the LIPID study. The R package gamlss (Generalized Additive Models for Location, Scale and Shape), which implements maximum likelihood estimation for distributional regression modelling, was used throughout.ResultsIn all cases the distributional regression models fit the data well, in contrast to poor fits obtained for traditional models; for MR-proADM a small but significant treatment effect on the mean was detected by the distributional regression model and not the normal model; and for SBP a beneficial treatment effect on the variance was demonstrated. In the simulation study distributional models strongly outperformed normal models when the response variable was non-normal and heterogeneous; and there was no disadvantage introduced by the use of distributional regression modelling when the response satisfied the normal linear model assumptions.ConclusionsDistributional regression models are a rich framework, largely untapped in the clinical trials world. We have demonstrated a sample of the capabilities of these models for the analysis of trials. If interest lies in accurate estimation of treatment effect on the mean, or other distributional features such as variance, the use of distributional regression modelling will yield superior estimates to traditional normal models, and is strongly recommended.Trial registrationThe LIPID trial was retrospectively registered on ANZCTR on 27/04/2016, registration number ACTRN12616000535471 .

Project description:Radiomics involves the study of tumor images to identify quantitative markers explaining cancer heterogeneity. The predominant approach is to extract hundreds to thousands of image features, including histogram features comprised of summaries of the marginal distribution of pixel intensities, which leads to multiple testing problems and can miss out on insights not contained in the selected features. In this paper, we present methods to model the entire marginal distribution of pixel intensities via the quantile function as functional data, regressed on a set of demographic, clinical, and genetic predictors to investigate their effects of imaging-based cancer heterogeneity. We call this approach quantile functional regression, regressing subject-specific marginal distributions across repeated measurements on a set of covariates, allowing us to assess which covariates are associated with the distribution in a global sense, as well as to identify distributional features characterizing these differences, including mean, variance, skewness, heavy-tailedness, and various upper and lower quantiles. To account for smoothness in the quantile functions, account for intrafunctional correlation, and gain statistical power, we introduce custom basis functions we call quantlets that are sparse, regularized, near-lossless, and empirically defined, adapting to the features of a given data set and containing a Gaussian subspace so non-Gaussianness can be assessed. We fit this model using a Bayesian framework that uses nonlinear shrinkage of quantlet coefficients to regularize the functional regression coefficients and provides fully Bayesian inference after fitting a Markov chain Monte Carlo. We demonstrate the benefit of the basis space modeling through simulation studies, and apply the method to Magnetic resonance imaging (MRI) based radiomic dataset from Glioblastoma Multiforme to relate imaging-based quantile functions to various demographic, clinical, and genetic predictors, finding specific differences in tumor pixel intensity distribution between males and females and between tumors with and without DDIT3 mutations.

Project description:BackgroundThe burden of child under-nutrition still remains a global challenge, with greater severity being faced by low- and middle-income countries, despite the strategies in the Sustainable Development Goals (SDGs). Globally, malnutrition is the one of the most important risk factors associated with illness and death, affecting hundreds of millions of pregnant women and young children. Sub-Saharan Africa is one of the regions in the world struggling with the burden of chronic malnutrition. The 2018 Zambia Demographic and Health Survey (ZDHS) report estimated that 35% of the children under five years of age are stunted. The objective of this study was to analyse the distribution, and associated factors of stunting in Zambia.MethodsWe analysed the relationships between socio-economic, and remote sensed characteristics and anthropometric outcomes in under five children, using Bayesian distributional regression. Georeferenced data was available for 25,852 children from two waves of the ZDHS, 31% observation were from the 2007 and 69% were from the 2013/14. We assessed the linear, non-linear and spatial effects of covariates on the height-for-age z-score.ResultsStunting decreased between 2007 and 2013/14 from a mean z-score of 1.59 (credible interval (CI): -1.63; -1.55) to -1.47 (CI: -1.49; -1.44). We found a strong non-linear relationship for the education of the mother and the wealth of the household on the height-for-age z-score. Moreover, increasing levels of maternal education above the eighth grade were associated with a reduced variation of stunting. Our study finds that remote sensed covariates alone explain little of the variation of the height-for-age z-score, which highlights the importance to collect socio-economic characteristics, and to control for socio-economic characteristics of the individual and the household.ConclusionsWhile stunting still remains unacceptably high in Zambia with remarkable regional inequalities, the decline is lagging behind goal two of the SDGs. This emphasises the need for policies that help to reduce the share of chronic malnourished children within Zambia.

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Treatment effects beyond the mean using distributional regression: Methods and guidance.

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Treatment effects beyond the mean using distributional regression: Methods and guidance.

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