Data management & analysis

Data analysis was conducted using SAS 9.4 (SAS Institute, Cary NC). All hospital episodes of care related to the same event were linked to form a period of care. Chi-square tests were used to compare characteristics of cases and matched peers. The number of ED visits, hospital admissions, and hospital length of stay (LOS) (measured in days) during and after the index admission were identified for cases and matched peers and compared using Mann-Whitney U tests. The calculation of hospital LOS was cumulative and included transfers between hospitals. All chi-square and Mann-Whitney-U tests were two-tailed with an alpha level set at 0.05.

Generalized linear mixed modelling was used to examine risk of not achieving the NMS for each NAPLAN assessment for cases and matched peers across school years 3, 5, 7 and 9. Each multilevel model was fitted using a binary distribution, log link function, and Kenward-Roger approximation of denominator degrees of freedom. The residual option of the random statement was used to model R-side covariance and data were analyzed to account for within student correlation in the longitudinal data and repeated measurements using an autoregressive covariance structure. Generalized linear modelling was used to examine risk of not completing high school years 10–12 for cases and matched peers. Each generalized linear model was fitted using generalized estimating equations with binomial distribution and a log link function. All generalized linear mixed models and generalized linear models were fitted using mixed selection method (i.e., combined forward selection and backward elimination), whereby non-collinear covariates were sequentially added to and removed from the model, with p-value thresholds set at 0.05 to enter and 0.10 to leave the model. The variables included in each final fitted model are listed in the footnotes of Supplementary Table 3. Cases and matched peers with missing values for socioeconomic status and language background were excluded from the model fitting procedures. As young people in the comparison cohort could have nil hospital LOS, a small constant value was added to hospital LOS before log transformation. Adjusted relative risks (ARR) with 95% confidence intervals (CI) were derived from each final fitted model. The family-wise error rate arising from multiple comparisons (i.e. five NAPLAN assessments) was controlled for using the Bonferroni-Holm procedure.