Table 1.

Comparison of analysis methods

	Wei-Lachin	Rauch	Bakal
Model assumptions	∙Stratified approach, i.e.	∙Stratified approach, i.e	Not applicable because no
	all 1st events in 1st stratum,	all 1st events in 1st stratum,	underlying model is specified.
	all 2nd events in 2nd stratum,	all 2nd events in second stratum,
	and so on. I.e. individuals are at	and so on. I.e. individuals are at
	risk for a subsequent event	riskrisk for a subsequent event
	only if a previous event has occurred.	only if a previous event has occurred.
Strong assumption	∙ Proportional hazards are	∙ Proportional hazards are
	assumed within strata	assumed within strata
	and event types.	and event types.
	→ Equal cause-specific	→ Equal cause-specific baseline
	baseline hazards.	hazards (or specific underlying
		event distribution)
	→ Baseline hazards can be	→ Baseline hazards can be
	strata-specific, i.e. risk for	strata-specific, i.e. risk for
	subsequent events	subsequent events
	is allowed to change.	is allowed to change.
Estimation assumptions	No difference to	Cause-specific hazards	∙ No difference between strata, i.e.
	model assumptions.	are different.	no risk change for subsequent event.
			∙ Individuals are at risk as long as
			they are under observation
			but their contribution to the
			event number and number at risk
			changes for subsequent events.
Weights	∙ pre-specified	∙ pre-specified	∙ pre-specified
	∙ non-negative	∙ non-negative	∙ non-negative
	∙ relative weights	∙ weights based on	∙ relative weights
		clinical relevance
	∙ sum up to 1	∙ proposed highest weight of 1	∙ highest weight of 1 (for 1 type)
		but could be higher
	∙ works multiplicatly on the	∙ works multiplicatly on the	∙ works accumulatively multiplicative
	logarithmized cause-specific	cause-specific hazards (event counts)	on the event count
	hazard ratios
Test statistic	multivariate procedure	stratified weight based	modified log-rank test
	(semi-parametric)	log-rank test	(not stratified)
Effect estimator	$✓$	$✓$	x
Confidence interval for effect	$✓$	only bootstrap	x
Interpretation	∙ Weighted cause-specific	∙ Weighted cause-specific	Weighted individual score
	logarithmic hazard ratios.	hazards work on	for event count and risk set.
	Thus influence of event counts is not	the event counts and hence is
	directely incoporated, i.e. a higher	also satisfying in terms of variablity
	cause-specific logarithmic hazard ratio	for a low event number.
	has a higher influence on	Thus the composite effect is
	the composite effect, which	determined by the distribution of
	results in a higher	the clinically more relevant event.
	variability when the estimation
	is based on a low event number.
	∙ weighted composite hazard ratio based	∙ weighted composite effect based on
	on weighted cause-specific	weighted cause-specific hazards
	logarthimic hazard ratios