Confidence Intervals for Hazard Ratios

[modedec]

How can the Hazard Ratio confidence intervals be calculated

1)survPen(...) -> model 2)predict(model,...) -> pred_1 and pred_2 3)HR=pred_1$haz/pred_2$haz

Could one just do error propagation? f(x,y)=x/y var(HR)=(1/y*dy)+(x/y^2 dx)^2+(1/y^2 dy dx)^2

[fauvernierma]

Hello @modedec and thank you for your question

The simplest way to do it is with the log hazard ratio :

log(HR) = log(haz1) - log(haz2) = (X1 - X2)%*%model$coef

where X1 and X2 are the model matrix associated with each log-hazard

Thus, the variance for the log hazard ratio is: Var(log(HR)) = (X1 - X2) %% model$Vp %% t(X1 - X2)

With survPen, you can use the option: type="lpmatrix" for the predict function to get X1 and X2, this would give:

conf.int=0.95 qt.norm<-qnorm(1-(1-conf.int)/2)

newdata1 <- .... newdata2 <- ...

myMat1<- predict(model,newdata1,type="lpmatrix") myMat2<- predict(model,newdata2,type="lpmatrix")

myMat<-myMat1-myMat2

log.haz.ratio<-as.vector(myMat%*%model$coef)

haz.ratio<-as.vector(exp(pred.haz.ratio))

confidence intervals for hazard

std<-sqrt(rowSums((myMat%%model$Vp)myMat)) haz.ratio.inf<-as.vector(exp(log.haz.ratio-qt.normstd)) haz.ratio.sup<-as.vector(exp(log.haz.ratio+qt.normstd))

[fauvernierma]

Don't hesitate if something is not clear and close the issue if this is ok for you

Thanks and have a great day

[fauvernierma]

Erratum, in my answer, one must read :

haz.ratio<-as.vector(exp(log.haz.ratio)) instead of haz.ratio<-as.vector(exp(pred.haz.ratio))

Also, there are * missing at the very end:

haz.ratio.inf<-as.vector(exp(log.haz.ratio-qt.normstd)) haz.ratio.sup<-as.vector(exp(log.haz.ratio+qt.normstd))

[modedec]

Thank you for taking the time to answer our questions. We gonna try to implement your answer in the next couple of days and will come back to you.

Thx for the great package, have a great day

[modedec]

We checked the result with the cox timesplitting approach. Your solution works fine:

  lpmatrix.risk <- predict(model,df.risk,type="lpmatrix")
  lpmatrix.ref <- predict(model,df.ref,type="lpmatrix")
  myMat<-lpmatrix.risk-lpmatrix.ref
  std<-sqrt(rowSums((myMat%*%model$Vp)*myMat))
  log.haz.ratio<-as.vector((myMat)%*%model$coef)
  haz.ratio.upper<-as.vector(exp(log.haz.ratio+1.96*std))
  haz.ratio.lower<-as.vector(exp(log.haz.ratio-1.96*std))
  haz.ratio<-as.vector(exp(log.haz.ratio))

Thank you for your support, we highly appreciate it.