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Table 1 Comparison of analysis methods

From: Weighted composite time to event endpoints with recurrent events: comparison of three analytical approaches

  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