Comparing regression modeling strategies for predicting hometime

Hometime, the total number of days a person is living in the community (not in a healthcare institution) in a defined period of time after a hospitalization, is a patient-centred outcome metric increasingly used in healthcare research. Hometime exhibits several properties which make its statistical analysis difficult: it has a highly non-normal distribution, excess zeros, and is bounded by both a lower and upper limit. The optimal methodology for the analysis of hometime is currently unknown.

Using administrative data we identified adult patients diagnosed with stroke between April 1, 2010 and December 31, 2017 in Ontario, Canada. 90-day hometime and clinically relevant covariates were determined through administrative data linkage. Fifteen different statistical and machine learning models were fit to the data using a derivation sample. The models' predictive accuracy and bias were assessed using an independent validation sample.

Seventy-five thousand four hundred seventy-five patients were identified (divided into a derivation set of 49,402 and a test set of 26,073). In general, the machine learning models had lower root mean square error and mean absolute error than the statistical models. However, some statistical models resulted in lower (or equal) bias than the machine learning models. Most of the machine learning models constrained predicted values between the minimum and maximum observable hometime values but this was not the case for the statistical models. The machine learning models also allowed for the display of complex non-linear interactions between covariates and hometime. No model captured the non-normal bucket shaped hometime distribution.

Overall, no model clearly outperformed the others. However, it was evident that machine learning methods performed better than traditional statistical methods. Among the machine learning methods, generalized boosting machines using the Poisson distribution as well as random forests regression were the best performing. No model was able to capture the bucket shaped hometime distribution and future research on factors which are associated with extreme values of hometime that are not available in administrative data is warranted.