Table 1 Comparison of analysis methods

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