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