eTable 7. Subgroups of amputations according to etiology.

Random effects	Value
Tsurgical groups*1	1.159
Residual ICC*2	0.261
n surgical groups	104
n patients	203 327
Marginal R2 / conditional R2*3	0.1433 / 0.3665

Presented are random effects (i. e. variances and intraclass correlations [ICC]) from the two-level regression model predicting prolonged postoperative opioid use (PPOU) from types of surgery (random intercept) and pre-existing risk factors. Of relevance for interpretation is the row which shows the importance of pre-existing risk factors and surgical group in predicting PPOU. Conditional R² of 0.3665 (or 36.65%) represents the overall amount of variance in PPOU explained by both pre-existing risk factors and surgical group. Marginal R² of 0.1433 (or 14.33%) gives the amount of variance in PPOU explained by pre-existing risk factors. Finally, the difference of 0.2232 (or 22.32%) is the amount of variance in PPOU explained by the surgical group which is not explained by pre-existing risk factors. This result shows that surgical group remains important for predicting the risk of PPOU even after controlling for many pre-existing risk factors, and that the type of surgery is more important for risk of PPOU than the measured pre-existing risk factors taken together.

*¹ T_{surgical groups} is the variance of the random intercept, i.e., the between-group variance of the surgical groups.

*² Residual ICC is a standardized measure of the heterogeneity of PPOU among surgical groups under statistical control of the patient-level risk factors.

*³ Marginal R² is the proportion of explained variance by the fixed part η only (i.e., by pre-existing risk factors). Conditional R² is the proportion of explained variance by the fixed part η and the random part (i.e., including the unique variance explained by the surgical groups T_{surgical groups}).