An extension of the mixed-effects growth model that considers between-person differences in the within-subject variance and the autocorrelation

Does hospital competition improve the quality of outpatient care? - empirical evidence from a quasi-experiment in a Chinese city

BACKGROUND

Although countries worldwide have launched a series of pro-competition reforms, the literature on the impacts of hospital competition has produced a complex and contradictory picture. This study examined whether hospital competition contributed to an increase in the quality of outpatient care.

METHODS

The dataset comprises encounter data on 406,664 outpatients with influenza between 2015 and 2019 in China. Competition was measured using the Herfindahl-Hirschman index (HHI). Whether patients had 14-day follow-up encounter for influenza at any healthcare facility, outpatient facility, and hospital outpatient department were the three quality outcomes assessed. Binary regression models with crossed random intercepts were constructed to estimate the impacts of the HHI on the quality of outpatient care. The intensity of nighttime lights was employed as an instrumental variable to address the endogenous relationship between the HHI and the quality of outpatient care.

RESULTS

We demonstrated that an increase in the degree of hospital competition was associated with improved quality of outpatient care. For each 1% increase in the degree of hospital competition, an individual's risk of having a 14-day follow-up encounter for influenza at any healthcare facility, outpatient facility, and hospital outpatient department fell by 34.9%, 18.3%, and 20.8%, respectively. The impacts of hospital competition on improving the quality of outpatient care were more substantial among females, individuals who used the Urban and Rural Residents Basic Medical Insurance to pay for their medical costs, individuals who visited accredited hospitals, and adults aged 25 to 64 years when compared with their counterparts.

CONCLUSION

This study demonstrated that hospital competition contributed to better quality of outpatient care under a regime with a regulated ceiling price. Competition is suggested to be promoted in the outpatient care market where hospitals have control over quality and government sets a limit on the prices that hospitals may charge.

Alternative covariance structures in mixed-effects models: Addressing intra- and inter-individual heterogeneity

Mixed-effects models for repeated measures and longitudinal data include random coefficients that are unique to the individual, and thus permit subject-specific growth trajectories, as well as direct study of how the coefficients of a growth function vary as a function of covariates. Although applications of these models often assume homogeneity of the within-subject residual variance that characterizes within-person variation after accounting for systematic change and the variances of the random coefficients of a growth model that quantify individual differences in aspects of change, alternative covariance structures can be considered. These include allowing for serial correlations between the within-subject residuals to account for dependencies in data that remain after fitting a particular growth model or specifying the within-subject residual variance to be a function of covariates or a random subject effect to address between-subject heterogeneity due to unmeasured influences. Further, the variances of the random coefficients can be functions of covariates to relax the assumption that these variances are constant across subjects and to allow for the study of determinants of these sources of variation. In this paper, we consider combinations of these structures that permit flexibility in how mixed-effects models are specified to understand within- and between-subject variation in repeated measures and longitudinal data. Data from three learning studies are analyzed using these different specifications of mixed-effects models.

A latent variable mixed-effects location scale model that also considers between-person differences in the autocorrelation

In public health research an increasing number of studies is conducted in which intensive longitudinal data is collected in an experience sampling or a daily diary design. Typically, the resulting data is analyzed with a mixed-effects model or mixed-effects location scale model because they allow one to examine a host of interesting longitudinal research questions. Here, we introduce an extension of the mixed-effects location scale model in which measurement error of the observed variables is considered by a latent factor model and in which-in addition to the mean-or location-related effects-the residual variance of the latent factor and the parameters of the autoregressive process of this latent factor can differ between persons. We show how to estimate the parameters of the model with a maximum likelihood approach, whose performance is also compared with a Bayesian approach in a small simulation study. We illustrate the models using a real data example and end with a discussion in which we suggest questions for future research.

A Mixed-Effects Model in Which the Parameters of the Autocorrelated Error Structure Can Differ between Individuals

Research in psychology has seen a rapid increase in the usage of experience sampling methods and daily diary methods. The data that result from using these methods are typically analyzed with a mixed-effects or a multilevel model because it allows testing hypotheses about the time course of the longitudinally assessed variable or the influence of time-varying predictors in a simple way. Here, we describe an extension of this model that does not only allow to include random effects for the mean structure but also for the residual variance, for the parameter of an autoregressive process of order 1 and/or the parameter of a moving average process of order 1. After we have introduced this extension, we show how to estimate the parameters with maximum likelihood. Because the likelihood function contains complex integrals, we suggest using adaptive Gauss-Hermite quadrature and Quasi-Monte Carlo integration to approximate it. We illustrate the models using a real data example and also report the results of a small simulation study in which the two integral approximation methods are compared.

Defining R-squared measures for mixed-effects location scale models

Ecological momentary assessment and other modern data collection technologies facilitate research on both within‐subject and between‐subject variability of health outcomes and behaviors. For such intensively measured longitudinal data, Hedeker et al extended the usual two‐level mixed‐effects model to a two‐level mixed‐effects location scale (MELS) model to accommodate covariates' influence as well as random subject effects on both mean (location) and variability (scale) of the outcome. However, there is a lack of existing standardized effect size measures for the MELS model. To fill this gap, our study extends Rights and Sterba's framework of R2 measures for multilevel models, which is based on model‐implied variances, to MELS models. Our proposed framework applies to two different specifications of the random location effects, namely, through covariate‐influenced random intercepts and through random intercepts combined with random slopes of observation‐level covariates. We also provide an R function, R2MELS, that outputs summary tables and visualization for values of our R2 measures. This framework is validated through a simulation study, and data from a health behaviors study and a depression study are used as examples to demonstrate this framework. These R2 measures can help researchers provide greater interpretation of their findings using MELS models.

Rethinking Autism Intervention Science: A Dynamic Perspective

Recent advances in longitudinal methodologies for observational studies have contributed to a better understanding of Autism as a neurodevelopmental condition characterized by within-person and between-person variability over time across behavioral domains. However, this finer-grained approach to the study of developmental variability has yet to be applied to Autism intervention science. The widely adopted experimental designs in the field-randomized control trials and quasi-experimental designs-hold value for inferring treatment effects; at the same time, they are limited in elucidating what works for whom, why, and when, given the idiosyncrasies of neurodevelopmental disorders where predictors and outcomes are often dynamic in nature. This perspective paper aims to serve as a primer for Autism intervention scientists to rethink the way we approach predictors of treatment response and treatment-related change using a dynamic lens. We discuss several empirical gaps, and potential methodological challenges and opportunities pertaining to: (1) capturing finer-grained treatment effects in specific behavioral domains as indexed by micro-level within-person changes during and beyond intervention; and (2) examining and modeling dynamic prediction of treatment response. Addressing these issues can contribute to enhanced study designs and methodologies that generate evidence to inform the development of more personalized interventions and stepped care approaches for individuals on the heterogeneous spectrum of Autism with changing needs across development.