Pros and cons of regression trees
We analyzed our data with regressions trees, a statistical tool from the CART family. This method has some advantages compared to linear regression. First, the result of CART analysis, i.e. the regression tree, is very easy to implement and interpret. The predicted value for the outcome is found by simply following subsequent splits from top to bottom, based on the known values of the predictor variables. Second, being a non-parametric method, no assumptions need to be made about linearity of the association or distribution of the variables. Issues such as multicollinearity, complex interactions, and outliers are also dealt with by the specific design of CART. Finally, missing values can be replaced by surrogate variables [
16,
29].
However, CART analysis presents some disadvantages as well. First, it is not very suitable for continuous predictor variables. When these are inserted in the model, they will be dichotomized automatically to create the best fitting model, a practice that is strongly discouraged [
13]. Although still leading to loss of data, categorization of continuous data should be done before attempting to run the model. In our dataset, we had only three continuous variables: attendance, age and temperature. Attendance ranged from 10,000 to over 1000,000 and was split into five categories. We created four classes for the age distribution of patients, not only taking into account median age, but also the IQR, thus making use of as much information as possible. We were able to keep the temperature variable in its original continuous form, by not inserting it in the regression tree, but adjusting the results from the regression tree with a regression equation based on a linear association between ambient temperature and PPR instead. That way, we combined the advantages of regression trees with those of linear modelling.
A second drawback is that a regression tree is prone to instability: small changes in the data can result in completely different trees. Finally, as with linear models, overfitting is a risk in CART modelling as well [
16,
29]. We applied 10-fold cross-validation to counteract the risks of instability and overfitting [
12,
29]. Additionally, we limited the number of candidate predictor variables to those found relevant in the literature [
10] to ensure that EPV would be higher then 10, which is a rule of thumb to prevent overfitting [
13].
Assessment of predictor and outcome variables
Our regression tree indeed failed to predict PPR and TTHR for specific types of manifestations, and certainly for those that were different from the events the tree was built upon. This finding suggests that some important predictors of MUR have been overlooked, or at least not optimally used, in our model.
MG category was an important determinant of predicted PPR and TTHR, but there is room for improvement. As discussed above, outdoor music is a broad category, containing one-day concerts to four-day festivals, and music genres such as folk music, world music, rock, and heavy metal. Adding either a categorical variable with music genres [
5,
25] or a variable representing “crowd mood”, which is assumed to be related to music genre [
21], can probably improve predictive power of the model. The same is true for the category of sports events, which may be split into running vs cycling, and/or competitive vs recreational. However, the current number of sports events in the MedTRIS database is too small to allow for sufficiently stuffed subcategories.
Ambient temperature was not measured onsite. Instead, we retrospectively used data central data from the central weather station in Uccle (Brussels), operated by the RMI. Although Belgium is a small country with limited variation in elevation and latitude, daily maxima may be more than 10 °C higher in the Campine region than at the coast on warm spring and summer days.
Consumption of alcohol and other drugs is assumed [
20,
21,
25] and has been shown [
30] to increase patient needs. However, we have no data on the prevalence of drugs use at the MGs in MedTRIS, and we could only roughly estimate alcohol consumption by a variable indicating “no” (a festival for children only), “limited” (active sports events) or “unlimited” (all other events) access to alcohol.
Proper prediction of PPR and TTHR is important for organizations such as BRC to optimize onsite medical care at MGs, but in reverse, characteristics such as number, location, visibility, and size of care posts can also influence the influx of patients, as illustrated anecdotally with the examples of I Love Techno and Dranouter above. Unfortunately, information on these characteristics of medical care provided at MGs in MedTRIS was scattered and unusable for our analysis.
The number of attendees is indispensable to calculate PPR and TTHR. Yet, it was not recorded in the course of the years, and we had to construct this variable retrospectively by contacting organisers and sifting through online press releases. As a result, we obtained rough estimates (usually rounded to the nearest 1000) for most MGs and needed to estimate attendance for some events by interpolation or deduction (see Methods). Moreover, for multi-day MGs (except Rock Werchter), we obtained only the overall number of attendees. As a consequence, we treated these MGs as a single data line and used temperatures averaged over the course of the event, thus missing potential fluctuations in PPR due to weather conditions.
We had no missing data for other predictor or outcome variables, but referral place after dismissal from the care post was lacking in about 10% of all PEFs. Because the vast majority of patients qualified as “back to the event” (94% of all patient presentations), it is possible that this category was more easily forgotten when completing the PEF than the rare (2% of presentations) and more important category of “transported to hospital by ambulance”. This would imply that overall TTHR was slightly overestimated in our analysis.
From the results and discussion above, it is clear that the prediction model performs well for PPR on future editions of most MGs included in the development dataset, but fails to predict PPR and TTHR at many other MGs. This limitation is not new, as earlier models for PPR and TTHR prediction [
2,
3,
6] all revealed poor predictive performance and generalizability when applied to external datasets [
7‐
10].
Just like earlier prediction models for MGs [
2‐
6,
24], our model predicts overall PPR and TTHR, regardless of temporal variation during the event. However, PPR, and hence the need of medical care, fluctuates over the course of the event.