key: cord-0333104-njnoic27 authors: Gao, C. X.; Broder, J. C.; Brilleman, S.; Berger, E.; Ikin, J.; Smith, C. L.; Campbell, T. C. H.; Wolfe, R.; Johnston, F.; Guo, Y.; Carroll, M. title: Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression date: 2021-04-04 journal: nan DOI: 10.1101/2021.03.28.21254516 sha: e97f5b46a36695bf16184907bc3b10705cb788aa doc_id: 333104 cord_uid: njnoic27 Background: Disasters and other community-wide events can introduce significant interruptions and trauma to impacted communities. Children and young people can be disproportionately affected with additional educational disruptions. With the increasing threat of climate change, establishing a timely and adaptable framework to evaluate the impact of disasters on academic achievement is needed. However, analytical challenges are posed by the availability issue of individual-level data. Methods: A new method, Bayesian hierarchical meta-regression, was developed to evaluate the impact of the 2014 Hazelwood mine fire (a six-week fire event in Australia) using only aggregated school-level data from the standardised National Assessment Program-Literacy and Numeracy (NAPLAN) test. NAPLAN results and school characteristics (2008-2018) from 69 primary/secondary schools with different levels of mine fire-related smoke exposure were used to estimate the impact of the event. Using an interrupted time-series design, the model estimated immediate effects and post-interruption trend differences with full Bayesian statistical inference. Results: Major academic interruptions across NAPLAN domains were evident in high exposure schools in the year post-mine fire (highest in Writing: 11.09 [95%CI: 3.16-18.93], lowest in Reading: 8.34 [95%CI: 1.07-15.51]). The interruption was comparable to a three to four-month delay in educational attainment and had not fully recovered after several years. Conclusions: Considerable academic delays were found as a result of a mine fire, highlighting the need to provide educational and community-based supports in response to future events. Importantly, this work provides a statistical method using readily available aggregated data to assess the educational impacts in response to other disasters Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression performance could provide unique insights into the level of impact of disasters on schoolaged children and adolescents. Indeed, many studies have demonstrated the link between disaster exposure and academic challenges. [18] [19] [20] [21] Nonetheless, accessing individual students' academic records is often difficult and requires complex ethics procedures, which can be particularly challenging following disaster events. In contrast, de-identified aggregated schoollevel data is more accessible. Hence there is a need for statistical models that can incorporate aggregated standardised academic testing results to evaluate the impact of disasters without losing substantial statistical power. In February 2014, a bushfire ignited the Morwell coal mine adjacent to the Hazelwood Power Station (in the Latrobe Valley, Victoria, Australia) and burned for approximately six weeks. Whilst the flames themselves did not directly threaten homes or cause loss of life, heavy smoke concentrations throughout the six-week period resulted in physical ill-health and psychological distress in the local community and caused considerable school disruption. 22, 23 The Hazelwood Health Study (HHS; www.hazelwoodhealthstudy.org.au), established to evaluate the health and wellbeing impact of the mine fire, 23,24 conducted a school survey to evaluate the psychological outcomes of the mine fire on students. A subsequent evaluation of National Assessment Program-Literacy and Numeracy (NAPLAN) results of survey participants suggested academic delays in highly smoke-exposed areas. 25 However, the low participation rate in the survey, as is frequently the case in post-disaster studies, introduced risk of bias. 26,27 Hence the aggregated school-level NAPLAN data from all Victorian schools were obtained to further consolidate our findings. In this study, we developed a Bayesian interrupted time-series hierarchical meta-regression model to evaluate the impact of the Hazelwood mine fire on academic performance. Using this method, instead of individual-level data, only aggregated school-level data from standardised academic tests is required for evaluating spatial and temporal profiles of community-wide Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression Socio-Educational Advantage (ICSEA) based on school location, were provided by ACARA for each year. School characteristics (in 2014) and NAPLAN participation rate (2008) (2009) (2010) (2011) (2012) (2013) (2014) (2015) (2016) (2017) (2018) were first compared across the three exposure groups. School-level mean NAPLAN scores pre-and post-mine fire were visualised using box plots by exposure group for each educational domain and student grade level. To increase interpretability of results, the NAPLAN scores were first centred against the matching mean regional scores (for the same year, grade and educational domain) to represent the difference from the regional Victorian average. Hierarchical two-level meta-regression models were carried out in a Bayesian modelling framework to estimate the association between mine fire exposure and centred NAPLAN scores. The first level random effects (random intercepts) were modelled at the school-level, and the nested second level random effects (random intercepts) were modelled as student cohorts (e.g. the cohort of students progressing from Grade 3 in 2014 to Grade 5 in 2016 at the same school). The centred mean NAPLAN score at Grade g level for cohort c students in given school s was modelled as follows: y s,g,c ∼ N(βX s,g + θ s,c + θ s + θ e , τ s,g,c 2 ) The terms θ s and θ s,c are the random effects for the school s and cohort c in that school, respectively. θ e is the random error term. We assume θ s,c ∼ N(0, σ 2 s,c ), θ s ∼ N(0, σ 2 s ) and θ e ∼ N(0, σ 2 e ). The fixed effect matrix X s,g includes values of potential confounding factors: school characteristics (ICSEA, total enrolments, percentage of girls, school sector, grade level, long-term trend (year) as well as mine fire exposure effect variables detailed below with an illustration of the Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression meaning of the effect coefficients β. τ s,g,c is simply the standard error of the mean NAPLAN score of the given school, student cohort and grade level (input data obtained from ACARA). The mine fire exposure effect was evaluated using the interrupted time-series design 31 with a time-specific interruption variable to capture the immediate effect of the mine fire on that year's NAPLAN results, and an interaction between the time interruption variable and year to capture any change in underlying trends from pre-to post-mine fire. It was assumed that there would be no interruption effect in the no/low exposure group, and mine fire interruption effects as well as post interruption trend differences were evaluated separately for the high and moderate exposure groups, summarised as follows: ). Therefore, β e1 and β e2 can be interpreted as the prior-mine fire differences when comparing moderate and high exposure schools with no/low exposure schools. These two coefficients are subsequently referred to as the fixed intercepts. The coefficients β e3 and β e4 can be interpreted as the mine fire interruptions effect (relative to the students' developmental trajectories) for moderate and high exposure schools, respectively. The coefficients β e5 and β e6 are the post-mine fire trend differences compared with the trend before the mine fire. Other than β e1 , β e2 . . . β e6 , the vector of coefficients, β, also contains coefficients of other confounding variables detailed above. Estimation was conducted by Markov chain Monte Carlo (MCMC) sampling implemented in the Stan 32 programming language via RStan package. 33 Stan is a platform for high-performance full Bayesian statistical inference using "No-U-Turn Sampler" (NUTS). 34 Weakly informative prior distributions were used for standard deviations (SDs) of random effects, namely, . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression σ s,c ∼ TN(10, 5 2 ), σ s ∼ TN(10, 5 2 ) and σ e ∼ TN(10, 5 2 ), where TN is the truncated normal distribution with support over the range [0, in f inity). The mean of 10 for prior distributions of the random effects was chosen based on preliminary exploratory evaluation of all Victorian schools. Weakly informative prior distributions N(0, 50 2 ) were used for all fixed effect parameters (non-informative priors base on uniform distributions can lead to a range of model fitting issues) 32,35 . Separate models were estimated for each testing domain. Results were reported as the posterior mean of estimated coefficients (4 Monte Carlo chains with 2000 iterations each), 95% credible interval (CI) and the probability of estimated coefficients (β) being greater or less than 0. Predicted centred NAPLAN score for schools were calculated and visualised for each testing domain and exposure group using line plots. A range of sensitivity analyses were undertaken to test the robustness of results, which included using different prior distributions and excluding cohort random effects. Also, two schools in Morwell were relocated during the mine fire event and remained at their relocation sites for an extended period afterwards; hence sensitivity analyses were conducted excluding the two relocated schools. Code for fitting the models using synthetic data is provided in the Supplementary Material I. The characteristics of schools across exposure groups are presented in Table 1 . ICSEA socioeducational advantage scores were lower for schools in the high exposure group (Morwell) compared to schools in moderate and no/low exposure groups. Other school characteristics, including the percentage of girls, number of students, school sector and NAPLAN test participation rates were comparable between exposure groups. Distributions of NAPLAN scores pre-6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression and post-mine fire for each domain and grade level were plotted by exposure group, see Figure 2 . While there was a general trend across all exposure groups for NAPLAN performance to decline post-mine fire, this was greater in higher exposure schools. Results from Bayesian hierarchical meta-regression models are displayed in Table 2 and Figure 3 . Compared with the Victorian regional average, there was an estimated downward trend for the schools in the three exposure groups across all domains of testing (see Figure 3 and Table S1 to S5 in Supplementary Material II). As shown in Table 2 , NAPLAN scores were found to be similar between schools in the moderate vs no/low exposure group pre-mine fire after controlling for other confounding factors (i.e. there was no evidence that the fixed intercept mode coefficients for moderate exposure differed from 0). However, pre-mine fire NAPLAN scores were estimated to be lower in schools in the high exposure group for most domains when compared with no/low exposure schools (fixed intercept for high exposure ranged between -3 to -14, Table 2 ). for writing. After the initial drop in academic performance, there was evidence that writing, grammar and punctuation scores began to recover (positive slope) in high exposure schools, see . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression The choice of prior distributions for the SDs of random effects were found to have little impact on results; however, using a weakly informative prior distribution reduced the time taken to fit the Bayesian models compared with using a non-informative prior distribution. Sensitivity analysis excluding the cohort random effects (only the school level clustering is considered) produced very similar results except for a slightly larger mine fire interruption effect for high exposure schools (see Table S6 ). Models excluding the two relocated schools showed results that were consistent with all schools, but with slightly smaller interruption effects (see Table S7 ). This suggests that school relocation might have an adverse impact on NAPLAN performance additional to the mine fire exposure or the adverse effects were stronger in those schools (relocated) closest to the mine fire. This study provides an innovative method to evaluate the impact of disasters on students' academic performance using only readily accessible aggregated school-level data. Results suggest that the Hazelwood mine fire had a major impact on academic performance in schools in the high exposure area. The impact was consistent across all NAPLAN testing domains, with about a 10-point score reduction in the year of the event based on NAPLAN testing approximately three months post-mine fire. Typically, NAPLAN scores increase from an average score of approximately 400 in Grade 3, to 600 in Grade 9 (about 33 points per year), 36 which means that the delay in educational attainment in high exposure schools was equivalent to about three to four-month. While there was some recovery in academic performance in high exposure schools across all academic domains except for spelling, performance levels remained below those seen prior to the mine fire some four years afterwards. Both the results and method in this study are novel. We identified, for the first time, evidence of academic interruptions across all NAPLAN domains following a prolonged wildfire where 8 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression the fire, itself, did not directly threaten life and property, but caused extreme air pollution. This highlights the substantial vulnerability of children and young people resulting from a community-level traumatic event associated with poor air quality. The impact of the mine fire on academic performance may be due to numerous factors, including disruption to day-to-day operations, 22 traumatic symptoms caused by the mine fire, 37 known associations between air pollution and impaired cognitive function, 38,39 adverse physical health effects of exposure to the Hazelwood mine fire-related air pollution (e.g. respiratory symptoms), 40 ongoing distress experienced by students, teachers and parents 22,41,42 and possibly reduced support from family and community. Given academic underachievement can lead to unemployment, disadvantage and ill-health later in life, 43 it is critical that these impacts are recognised and responded to. Although the theoretical link between disasters and educational outcomes has been wellestablished, 14 most studies have only evaluated the disaster impact on school attendance or drop-out rates 19,20,44 and rarely on academic delays. One study suggested more than 75% of the African American children evacuated to escape Hurricane Katrina (which resulted in the loss of more than 1300 lives, 800,000 homes and 110 schools) experienced a decline in grades. 45 To our knowledge, only Gibbs and colleagues evaluated the impact of disasters using national standardised tests. 21 The authors reported that exposure to the 2009 Black Saturday bushfire in Australia (loss of 173 lives, 2,000 homes and 3 schools) was associated with delays in academic achievement from Grade 3 to 5 in reading and numeracy but not in writing, spelling, and grammar domains. 21 However, only one cohort of students (Grade 3 in 2011) were evaluated. Our study, on the other hand, endorsed the time-series design with more historical data which may increase the likelihood of identifying interruptions. Potential links between air pollution and cognitive development, educational and behavioral outcomes in children is an area of rapidly increasing research. Associations have been seen with chronic air pollution and cognitive function and educational attainment, 46 but we are not aware 9 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression of previous research evaluating associations between medium-duration air pollution episodes and long term outcomes. Although our study design cannot delineate the relative contributions of all possible factors such as psychological trauma, disruption to schooling, or air pollution exposure, it indicates a possible linkage which warrants further investigation. This paper provides an easily adaptable method to evaluate the impact of different types of community-level traumatic exposures (e.g. disasters and disease outbreaks) on school-aged children and adolescents using only aggregated school-level data. This method has a few advantages. Firstly, it enables the evaluation of the spatial and temporal profile of the impact, which could be used to inform policy and resource allocation in academic settings post disasters. Secondly, the proposed method uses only summary statistics at the school-level without losing substantial statistical power to detect meaningful differences. Accessing aggregated data avoids the research challenges faced when attempting to recruit individuals in communities postdisaster, and the associated costs for this more intensive approach. Lastly, the interrupted time-series design also allowed researchers to compare academic outcomes pre-and post-mine fire and to observe trends some years before and after the disaster. This provides essential information for teachers, schools and education departments to be able to plan and implement educational modifications and accommodate student's additional needs post-disaster. There are some limitations of this study. The model assumes that student NAPLAN scores within schools were normally distributed, which could be unrealistic if, for example, distributions were skewed. Although the number of schools in the high exposure group was modest, most of these schools had over 150 students enrolled, so the mine fire interruption effects identified are likely to be robust. Random slopes for schools, an extension of the model applied, was not considered due to the unwarranted increase in modelling complexity with limited data. Random slope and intercept models can be used where there are more schools and time points available. The aggregated nature of the data prohibited evaluating individual-level risk factors. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression More detailed region-specific data on other risk factors, such as service availability, were not available for this analysis but in principle could be included in the proposed model. This analysis shows that an extended air pollution event resulted in a delay in academic performance across multiple educational domains, which had not fully recovered after several years. While the available research to date has focused on the educational impact of major disasters, the current study shows that a community-wide traumatic event, with minimal immediate risk to life and property, can also have considerable long-term educational impacts. This highlights the need to respond to community-wide disaster events, providing targeted support during and following the event, in the hope of preventing or ameliorating any educational impacts. This paper provides a novel statistical method for using readily available aggregated data to assess educational impacts of disasters. Implementing research programs post-disasters is enormously challenging. Accordingly, an approach that enables accurate and timely assessment of educational impacts without impost on the community is invaluable. The model provided here could readily be used to look at the impact of other extended events, such as the COVID-19 pandemic, which has impacted on access to, and delivery of, schooling worldwide. This work was funded by the Victorian Department of Health and Human Services. The paper presents the views of the authors and does not represent the views of the Department. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression All procedure of the study was approved by the Monash University Human Research Ethics (project number: 5834) and the Victorian Department of Education and Training. There are no disclosures to report. All authors report no conflict of interest. The data underlying this article were provided by Australian, Curriculum, Assessment and Reporting Authority (ACARA). Data will be shared on request to the corresponding author with the permission of ACARA. However, a synthetically generated data set based on the source data for the tutorial part of the paper is available at https://github.com/CarolineXGao/NAPLAN _ impact. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; https://doi.org/10.1101/2021.03.28.21254516 doi: medRxiv preprint Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression . It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; https://doi.org/10.1101/2021.03.28.21254516 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. 20 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression Gelman . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression Berger . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; Import library packages library(pacman) p _ load(c("tidyverse", "rstan", "bayesplot","kableExtra"), character.only = TRUE) The data as well as the analysis code used in this tutorial can be directly downloaded from Github repository: https://github.com/CarolineXGao/NAPLAN_impact. naplan <-read.csv(here::here("Data","naplan _ fake _ data.csv")) The variables in the data set are: . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; A number of variables need to be changed for Bayesian modeling with Stan. Categorical variables, including grade (Grade) and exposure group (Exposure_group), need to be re-coded as dummy variables. Binary variables should be 0 or 1 (Government vs non-Government). In order to intemperate intercept of the model here we also center the numeric variables at the mean value and year at the start of the cohort (2008). Finally, interaction effects need to be created prior to the modelling. Grade 7 and 9 were combined due to relatively smaller numbers. Also the estimated effect size were also very similar when included separately. Moderate _ exposure = ifelse(Exposure _ group == "Moderate exposure", 1, 0), High _ exposure = ifelse(Exposure _ group == "High exposure", 1, 0), Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. When using Rmarkdown file, stan code can be directly included as a block of code with specification of {stan output.var = "StanModel"} in the code block. In this model we use weakly informative priors, N(10, 5), for the SDs of the random school effects, random cohort effects as well as random error N(10, 5). 10 was chosen because when using two-level mixed-effects models with the mean score differences as the outcome variable, the estimated error terms are close to 10. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; https://doi.org/10.1101/2021.03.28.21254516 doi: medRxiv preprint y~normal(mu, sigma); } } Input data is needed to be saved in a list. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; https://doi.org/10.1101/2021.03.28.21254516 doi: medRxiv preprint print(fited _ model, pars = c("alpha", thetas, paste0("beta[",1:length(predictors),"]")), probs = c(0.5, 0.025, 0.975)) ## Inference for Stan model: 832db374c6d4af44fc1e1f951141a4d4. ## 4 chains, each with iter=4000; warmup=2000; thin=1; ## post-warmup draws per chain=2000, total post-warmup draws=8000. Full model diagnostics can be evaluated using an interactive shinystan package. Here we provide a few static diagnostic plots. Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; color _ scheme _ set("mix-brightblue-gray") mcmc _ trace(posterior, pars = c("alpha",thetas, paste0("beta[",1:length(predictors),"]"))) + xlab("Post-warmup iteration") Markov chain Monte Carlo (MCMC) plot shows no signs of poor mixing for each coefficient. There was no warning of divergent transitions (using non-centred parameterisation centered parameterisation can help with avoiding divergent transitions), which can be diagnosed using diagnostic plots for the NUTS. All continuous variables are confounding variables (we are not interested in estimating effect sizes from these parameters), hence they were all standardised in the analysis to improve model fitting speed. If any variable of interest is a continuous variable, the original parameters can be easily recovered (see Stan manual) post standardisation. The mcmc_pairs function is used to visualize the univariate histograms as well as bivariate scatter plots for key parameters. It is useful in identifying multicollinearity (strong correlation) and other non-identifiability issues (banana-like shapes). Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. There is a negative association between sampled coefficients of the intercept term (alpha) and school sector (government, beta [7] ). This is possible as school sector (government vs non-government ) is the most important predictor of school-level NAPLAN results. Hence the sampled intercept will be impacted by the sampled coefficient of the school sector. Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression Supplementary material I -9 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; Mean and credible intervals summary <-summary(fited _ model, pars = c("alpha",thetas, paste0("beta[",1:length(predictors),"]")), probs = c(0.5, 0.025, 0.975)) names _ coef <-c("Intercept", thetas _ names, names) summary <-summary$summary %>% as.data.frame() %>% mutate(Variable = names _ coef ) %>% select(Variable, everything()) Summary. Table <- . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. Summary. Table %>% kable(align = c("l","c","c","c","c"),booktabs = T,linesep = "") %>% kable _ styling(bootstrap _ options = "striped", full _ width = F, latex _ options = "hold _ position") Mean 95% CI p (x<0) p (x>0) Here we obtain predicted margins using the posterior distribution of coefficients using the following steps: • Obtain design matrix with confounding variables fixed at reference values . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. ; Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 4, 2021. ; https://doi.org/10.1101/2021.03.28.21254516 doi: medRxiv preprint Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 4, 2021. ; https://doi.org/10.1101/2021.03.28.21254516 doi: medRxiv preprint Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression Table S6 : Estimated intercept, mine fire interruption effect and post-mine fire trend difference for moderate and high exposure schools estimated from Bayesian hierarchical meta-regression models (excluding cohort effect) Moderate exposure High exposure β 95% CI P(β < 0) P(β >0) β 95% CI P(β < 0) P(β > 0) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. Evaluating the impact of Hazelwood mine fire event on students' educational development with Bayesian interrupted time-series hierarchical meta-regression Table S7 : Estimated intercept, mine fire interruption effect and post-mine fire trend difference for moderate and high exposure schools estimated from Bayesian hierarchical meta-regression models (excluding relocated schools) Moderate exposure High exposure β 95% CI P(β < 0) P(β >0) β 95% CI P(β < 0) P(β > 0) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted April 4, 2021. Annual disaster statistical review 2016: The numbers and trends Research on the Epidemiology of Disasters (CRED) C for. CRED crunch 58 -disaster year in review Wildfires, global climate change, and human health 000 disaster victims speak: Part i. An empirical review of the empirical literature Children and disasters Psychological impact of disasters on children: Review of assessment and interventions Post-traumatic stress disorder, depression and generalised anxiety disorder in adolescents after a natural disaster: A study of comorbidity. Clinical Practice and Epidemiology in Mental Health 2018, 1)) + theme _ bw() + theme(axis.text.x = element _ text(hjust = -0.7,v = -0.1), legend.text = element _ text(size = 12), legend.title = element _ text(size = 12), axis.title.x = element _ text(size = 12 We wish to thank the Latrobe Valley and Gippsland communities for their support and participation in the Hazelwood Health Study. We also like to acknowledge Prof Rob Hyndman for his generous sharing of the Rmarkdown LaTex template (https://github.com/robjhyndman/ MonashEBSTemplates) for writing this paper in the Rmarkdown environment.