Mental Health Admissions to Paediatric Wards Study (MAPS): a protocol for the analysis of Hospital Episode Statistics (HES) data.

INTRODUCTION: Children and young people (CYP) presenting with a mental health (MH) crisis are frequently admitted to general acute paediatric wards as a place of safety. Prior to the pandemic, a survey in England showed that CYP occupied 6% of general paediatric inpatient beds due to an MH crisis, and there have been longstanding concerns about the quality of care to support these patients in this setting. Mental Health Admissions to Paediatric Wards Study aims to generate a theory of change (ToC) model to improve the quality of care for CYP admitted to acute paediatric services after presenting in a MH crisis. METHODS AND ANALYSIS: We will undertake a national (England), sequential, mixed methods study to inform a ToC framework alongside a stakeholder group consisting of patients, families/carers and healthcare professionals (HCPs). Our study consists of four work packages (WP) undertaken over 30 months. WP1 is limited to using national routine administrative data to identify and characterise trends in MH admissions in acute paediatric wards in England between 2015- 2022. ETHICS AND DISSEMINATION: WP1 received ethical approval (Ref 23/NW/0192). We will publish the overall synthesis of data and the final ToC to improve care of CYP with MH crisis admitted to general acute paediatric settings. As coproducers of the ToC, we will work with our stakeholder group to ensure wide dissemination of findings. Potential impacts will be on service development, new models of care, training and workforce planning.

Health impact assessment for air pollution in the presence of regional variation in effect sizes: The implications of using different meta-analytic approaches.

The estimated health effects of air pollution vary between studies, and this variation is caused by factors associated with the study location, hereafter termed regional heterogeneity. This heterogeneity raises a methodological question as to which studies should be used to estimate risks in a specific region in a health impact assessment. Should one use all studies across the world, or only those in the region of interest? The current study provides novel insight into this question in two ways. Firstly, it presents an up-to-date analysis examining the magnitude of continent-level regional heterogeneity in the short-term health effects of air pollution, using a database of studies collected by Orellano et al. (2020). Secondly, it provides in-depth simulation analyses examining whether existing meta-analyses are likely to be underpowered to identify statistically significant regional heterogeneity, as well as evaluating which meta-analytic technique is best for estimating region-specific estimates. The techniques considered include global and continent-specific (sub-group) random effects meta-analysis and meta-regression, with omnibus statistical tests used to quantify regional heterogeneity. We find statistically significant regional heterogeneity for 4 of the 8 pollutant-outcome pairs considered, comprising NO2, O3 and PM2.5 with all-cause mortality, and PM2.5 with cardiovascular mortality. From the simulation analysis statistically significant regional heterogeneity is more likely to be identified as the number of studies increases (between 3 and 30 in each region were considered), between region heterogeneity increases and within region heterogeneity decreases. Finally, while a sub-group analysis using Cochran's Q test has a higher median power (0.71) than a test based on the moderators' coefficients from meta-regression (0.59) to identify regional heterogeneity, it also has an inflated type-1 error leading to more false positives (median errors of 0.15 compared to 0.09).

A tutorial on spatio-temporal disease risk modelling in R using Markov chain Monte Carlo simulation and the CARBayesST package.

Population-level disease risk varies in space and time, and is typically estimated using aggregated disease count data relating to a set of non-overlapping areal units for multiple consecutive time periods. A large research base of statistical models and corresponding software has been developed for such data, with most analyses being undertaken in a Bayesian setting using either Markov chain Monte Carlo (MCMC) simulation or integrated nested Laplace approximations (INLA). This paper presents a tutorial for undertaking spatio-temporal disease modelling using MCMC simulation, utilising the CARBayesST package in the R software environment. The tutorial describes the complete modelling journey, starting with data input, wrangling and visualisation, before focusing on model fitting, model assessment and results presentation. It is illustrated by a new case study of pneumonia mortality at the local authority level in England, and answers important public health questions including the effect of covariate risk factors, spatio-temporal trends, and health inequalities.

Estimating the changing nature of Scotland's health inequalities by using a multivariate spatiotemporal model.

Health inequalities are the unfair and avoidable differences in people's health between different social groups. These inequalities have a huge influence on people's lives, particularly those who live at the poorer end of the socio-economic spectrum, as they result in prolonged ill health and shorter lives. Most studies estimate health inequalities for a single disease, but this will give an incomplete picture of the overall inequality in population health. Here we propose a novel multivariate spatiotemporal model for quantifying health inequalities in Scotland across multiple diseases, which will enable us to understand better how these inequalities vary across disease and have changed over time. In developing this model we are interested in estimating health inequalities between Scotland's 14 regional health boards, who are responsible for the protection and improvement of their population's health. The methodology is applied to hospital admissions data for cerebrovascular disease, coronary heart disease and respiratory disease, which are three of the leading causes of death, from 2003 to 2012 across Scotland.

A Bayesian space-time model for clustering areal units based on their disease trends.

Population-level disease risk across a set of non-overlapping areal units varies in space and time, and a large research literature has developed methodology for identifying clusters of areal units exhibiting elevated risks. However, almost no research has extended the clustering paradigm to identify groups of areal units exhibiting similar temporal disease trends. We present a novel Bayesian hierarchical mixture model for achieving this goal, with inference based on a Metropolis-coupled Markov chain Monte Carlo ((MC)$^3$) algorithm. The effectiveness of the (MC)$^3$ algorithm compared to a standard Markov chain Monte Carlo implementation is demonstrated in a simulation study, and the methodology is motivated by two important case studies in the United Kingdom. The first concerns the impact on measles susceptibility of the discredited paper linking the measles, mumps, and rubella vaccination to an increased risk of Autism and investigates whether all areas in the Scotland were equally affected. The second concerns respiratory hospitalizations and investigates over a 10 year period which parts of Glasgow have shown increased, decreased, and no change in risk.

Multivariate space-time modelling of multiple air pollutants and their health effects accounting for exposure uncertainty.

The long-term health effects of air pollution are often estimated using a spatio-temporal ecological areal unit study, but this design leads to the following statistical challenges: (1) how to estimate spatially representative pollution concentrations for each areal unit; (2) how to allow for the uncertainty in these estimated concentrations when estimating their health effects; and (3) how to simultaneously estimate the joint effects of multiple correlated pollutants. This article proposes a novel 2-stage Bayesian hierarchical model for addressing these 3 challenges, with inference based on Markov chain Monte Carlo simulation. The first stage is a multivariate spatio-temporal fusion model for predicting areal level average concentrations of multiple pollutants from both monitored and modelled pollution data. The second stage is a spatio-temporal model for estimating the health impact of multiple correlated pollutants simultaneously, which accounts for the uncertainty in the estimated pollution concentrations. The novel methodology is motivated by a new study of the impact of both particulate matter and nitrogen dioxide concentrations on respiratory hospital admissions in Scotland between 2007 and 2011, and the results suggest that both pollutants exhibit substantial and independent health effects.

A model to estimate the impact of changes in MMR vaccine uptake on inequalities in measles susceptibility in Scotland.

An article published in 1998 by Andrew Wakefield in The Lancet (volume 351, pages 637-641) led to concerns surrounding the safety of the measles, mumps and rubella vaccine, by associating it with an increased risk of autism. The paper was later retracted after multiple epidemiological studies failed to find any association, but a substantial decrease in UK vaccination rates was observed in the years following publication. This paper proposes a novel spatio-temporal Bayesian hierarchical model with accompanying software (the R package CARBayesST) to simultaneously address three key epidemiological questions about vaccination rates: (i) what impact did the controversy have on the overall temporal trend in vaccination rates in Scotland; (ii) did the magnitude of the spatial inequality in measles susceptibility in Scotland increase due to the measles, mumps and rubella vaccination scare; and (iii) are there any covariate effects, such as deprivation, that impacted on measles susceptibility in Scotland. The efficacy of the model is tested by simulation, before being applied to measles susceptibility data in Scotland among a series of cohorts of children who were aged 2.5-4.5, in September of the years 1998 to 2014.

Quantifying the Spatial Inequality and Temporal Trends in Maternal Smoking Rates in Glasgow.

Maternal smoking is well known to adversely affect birth outcomes, and there is considerable spatial variation in the rates of maternal smoking in the city of Glasgow, Scotland. This spatial variation is a partial driver of health inequalities between rich and poor communities, and it is of interest to determine the extent to which these inequalities have changed over time. Therefore in this paper we develop a Bayesian hierarchical model for estimating the spatio-temporal pattern in smoking incidence across Glasgow between 2000 and 2013, which can identify the changing geographical extent of clusters of areas exhibiting elevated maternal smoking incidences that partially drive health inequalities. Additionally, we provide freely available software via the R package CARBayesST to allow others to implement the model we have developed. The study period includes the introduction of a ban on smoking in public places in 2006, and the results show an average decline of around 11% in maternal smoking rates over the study period.

Controlling for localised spatio-temporal autocorrelation in long-term air pollution and health studies.

Estimating the long-term health impact of air pollution using an ecological spatio-temporal study design is a challenging task, due to the presence of residual spatio-temporal autocorrelation in the health counts after adjusting for the covariate effects. This autocorrelation is commonly modelled by a set of random effects represented by a Gaussian Markov random field (GMRF) prior distribution, as part of a hierarchical Bayesian model. However, GMRF models typically assume the random effects are globally smooth in space and time, and thus are likely to be collinear to any spatially and temporally smooth covariates such as air pollution. Such collinearity leads to poor estimation performance of the estimated fixed effects, and motivated by this epidemiological problem, this paper proposes new GMRF methodology to allow for localised spatio-temporal smoothing. This means random effects that are either geographically or temporally adjacent are allowed to be autocorrelated or conditionally independent, which allows more flexible autocorrelation structures to be represented. This increased flexibility results in improved fixed effects estimation compared with global smoothing models, which is evidenced by our simulation study. The methodology is then applied to the motivating study investigating the long-term effects of air pollution on respiratory ill health in Greater Glasgow, Scotland between 2007 and 2011.

Using spline models to estimate the varying health risks from air pollution across Scotland.

The health risks associated with long-term exposure to air pollution are often estimated from small-area data by regressing the numbers of disease cases in each small area against air pollution concentrations and other covariates. The majority of studies in this field only estimate a single health risk for the entire region, whereas in fact the risks in each small area may vary because of differences in the exposure level and the extent to which the population are vulnerable to disease. This paper proposes a natural cubic spline model for estimating these varying health risks, which allows the risks to depend (potentially) non-linearly on additional risk factors. The methods are implemented within a Bayesian setting, with inference based on Markov chain Monte Carlo simulation. The approach is illustrated by presenting a study based in Scotland, which investigates the relationship between PM (10) concentrations and respiratory related hospital admissions.

Bayesian latent variable modelling in studies of air pollution and health.

This paper describes the use of Bayesian latent variable models in the context of studies investigating the short-term effects of air pollution on health. Traditional Poisson or quasi-likelihood regression models used in this area assume that consecutive outcomes are independent (although the latter allows for overdispersion), which in many studies may be an untenable assumption as temporal correlation is to be expected. We compare this traditional approach with two Bayesian latent process models, which acknowledge the possibility of short-term autocorrelation. These include an autoregressive model that has previously been used in air pollution studies and an alternative based on a moving average structure that we describe here. A simulation study assesses the performance of these models when there are different forms of autocorrelation in the data. Although estimated risks are largely unbiased, the results show that assuming independence can produce confidence intervals that are too narrow. Failing to account for the additional uncertainty which may be associated with (positive) correlation can result in confidence/credible intervals being too narrow and thus lead to incorrect conclusions being made about the significance of estimated risks. The methods are illustrated within a case study of the effects of short-term exposure to air pollution on respiratory mortality in the elderly in London, between 1997 and 2003.

Time-varying coefficient models for the analysis of air pollution and health outcome data.

In this article a time-varying coefficient model is developed to examine the relationship between adverse health and short-term (acute) exposure to air pollution. This model allows the relative risk to evolve over time, which may be due to an interaction with temperature, or from a change in the composition of pollutants, such as particulate matter, over time. The model produces a smooth estimate of these time-varying effects, which are not constrained to follow a fixed parametric form set by the investigator. Instead, the shape is estimated from the data using penalized natural cubic splines. Poisson regression models, using both quasi-likelihood and Bayesian techniques, are developed, with estimation performed using an iteratively re-weighted least squares procedure and Markov chain Monte Carlo simulation, respectively. The efficacy of the methods to estimate different types of time-varying effects are assessed via a simulation study, and the models are then applied to data from four cities that were part of the National Morbidity, Mortality, and Air Pollution Study.