Is it possible to calculate hazard ratio from median survival time? I am trying to perform a meta-analysis on time-to-event data.
However, some studies only provide median survival time with 95% CIs.
(for example, 5.54 +- 1.23 months)
Is it possible to use these data to estimate the hazard ratio?
 A: No.
There's a formula for the case of exponential distributions, but it doesn't hold for other distributions.
For example, taking a power transformation of exponential distributions gives Weibull distributions. These have the same hazard ratio, but the ratio of median survival is transformed by the same power
> library(survival)
> x<-rexp(1e5,1)
> y<-rexp(1e5,2)
> median(x)/median(y)
[1] 2.003155
> coxph(Surv(c(x,y))~rep(0:1,each=1e5))
Call:
coxph(formula = Surv(c(x, y)) ~ rep(0:1, each = 1e+05))

                           coef exp(coef) se(coef)   z      p
rep(0:1, each = 1e+05) 0.692791  1.999288 0.004711 147 <2e-16

Likelihood ratio test=21484  on 1 df, p=< 2.2e-16
n= 200000, number of events= 2e+05 
> 
> x1<-sqrt(x)
> y1<-sqrt(y)
> median(x1)/median(y1)
[1] 1.415329
> coxph(Surv(c(x1,y1))~rep(0:1,each=1e5))
Call:
coxph(formula = Surv(c(x1, y1)) ~ rep(0:1, each = 1e+05))

                           coef exp(coef) se(coef)   z      p
rep(0:1, each = 1e+05) 0.692791  1.999288 0.004711 147 <2e-16

Likelihood ratio test=21484  on 1 df, p=< 2.2e-16
n= 200000, number of events= 2e+05 
> 

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