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A brief comment on proportional hazard assumption;
Many RCTs use «TIME-TO-EVENT» as a primary endpoint. Cox regression model is used to get summary measure (HR) and 95% CI.
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Many RCTs use «TIME-TO-EVENT» as a primary endpoint. Cox regression model is used to get summary measure (HR) and 95% CI.
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Key assumption of Cox model is PROPORTIONAL HAZARD assumption (PHA). PHA means that the ratio of hazards between any two fixed sets of covariates not vary with time. If PHA is largely violated, Cox cannot be used! HR given by Cox, only reflects average tx effect which useless 2/ 
The most used methods for PH assumption are:
1)log (-log S) plot and
2)Smoothed Schoenfeld residual
3)Fitting time dependent covariates
*In this trial, it is clear that the PH assumption was violated.
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1)log (-log S) plot and
2)Smoothed Schoenfeld residual
3)Fitting time dependent covariates
*In this trial, it is clear that the PH assumption was violated.
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When we suspect that PHA was violated, look at the KM curve?
KM plots are useful to assess PHA, however PHA should be assess with more proper methods.
1-Crossing curves (most important sign)
2-Early/late seperation with early/late overlap
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KM plots are useful to assess PHA, however PHA should be assess with more proper methods.
1-Crossing curves (most important sign)
2-Early/late seperation with early/late overlap
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What do we do after violation of PHA?(Therneau)
***The first two questions to ask are "does it matter" and "is it real;" it will often turn out that nothing is required.
*violation of PH may make no difference to the interpretation, particularly for large sampIe sizes.
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***The first two questions to ask are "does it matter" and "is it real;" it will often turn out that nothing is required.
*violation of PH may make no difference to the interpretation, particularly for large sampIe sizes.
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*It is also possible to have a "significant" test for nonproportionality that is unreliable upon further examination (it is important examining plots, rather than just relying on test statistics).
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Alternatives:
1-If violation of PHA is minor and sample size is large>>continue with Cox model
2-Stratifed cox
3-Partition the time axis
4-Model by time-dependent covariates
5-Different model (AFT, GAM..)
6-Weighted cox, piecewise
7-KM based: RMST, wKM
8-Frailty model
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1-If violation of PHA is minor and sample size is large>>continue with Cox model
2-Stratifed cox
3-Partition the time axis
4-Model by time-dependent covariates
5-Different model (AFT, GAM..)
6-Weighted cox, piecewise
7-KM based: RMST, wKM
8-Frailty model
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Maybe wee need power calculation to allow for non-PH in clinical trials
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