# 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 $$\checkmark$$ $$\checkmark$$ x
Confidence interval for effect $$\checkmark$$ 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 