Comparing different methods for analysing hierarchical composite endpoints: two illustrative case studies with post hoc analyses of the BALANCE (Bacteraemia Antibiotic Length Actually Needed for Clinical Effectiveness) and CAMERA2 (Combination Antibiotics for methicillin-resistant Staphylococcus aureus) randomized clinical trials

Objectives
Hierarchical composite endpoints (HCEs) are increasingly being used in infectious disease research. In this paper, we illustrate different methods for analysing HCEs in post hoc analyses of the Bacteraemia Antibiotic Length Actually Needed for Clinical Effectiveness (BALANCE) and Combination Antibiotics for MEthicillin Resistant Staphylococcus aureus (CAMERA2) clinical trials.

Methods
We constructed post hoc HCEs for each trial by combining clinical efficacy and safety outcomes: (a) mortality, relapse of bacteraemia, and antibiotic adverse events for BALANCE, and (b) mortality, primary treatment failure, infectious complications, and antibiotic adverse events for CAMERA2. For both trials, we additionally included length of stay or duration of antibiotic treatment as tiebreakers after the primary HCE in separate analyses. We applied these analytic methods: (a) logistic regression using a binary composite outcome, (b) generalized pairwise comparisons using different outcome permutations, (c) Wilcoxon rank sum approach for an ordinal outcome, (d) proportional odds model, and (e) probabilistic index model. We estimated the probabilistic index, win ratio, win odds, net treatment benefit, or odds ratio where possible using each method.

Results
For the BALANCE trial, all analyses of the primary HCE resulted in the same conclusion of no evidence of differences between treatment groups. Inclusion of length of stay as a tiebreaker resulted in 7 of 11 analyses finding the 7-day treatment arm superior to the 14-day arm, whereas inclusion of antibiotic duration resulted in all analyses concluding superiority of the 7-day treatment arm. For the CAMERA2 trial, all analyses found no evidence of differences between the two treatment groups. For all analyses, there were only minor differences in estimates across different analytic methods.

Conclusions
In these post hoc analyses, different methods for analysing HCEs resulted in similar effect estimates and conclusions consistent with the primary analyses of the BALANCE and CAMERA2 trials. These analyses illustrate how different HCEs can be constructed and analysed, and may be useful to other researchers in designing future studies that use HCEs.