# Comparing coefficients of survival analysis with Gompertz distribution in R

I am performing Gompertz analysis of survival to calculate initial mortality rate (IMR) and Gompertz coefficient (rate of ageing) of different strains of worm. I am doing this by using the package flexsurv. Gompertz analysis is represented by the equation:

S = A*eGx

Where S is mortality rate, A is initial mortality rate, and G is Gompertz coefficient.

Below is the code that I am using to run it:

> # Creating sample dataset for single strain
> sampledf <- data.frame(c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30),
+                        c(9,9,10,11,11,11,13,13,13,14,15,15,16,16,16,17,18,18,19,19,19,19,19,20,20,20,21,21,21,21),
+                        c(1,1,1,1,1,0,0,1,1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,1,1,1,1,1,1))
> colnames(sampledf) <- c("Worm_ID", "Day", "Status")
> ### convert to Surv object
> s1 <- with(sampledf, Surv(Day, Status))
> ### get parameters for Gompertz distribution
> f1 <- flexsurvreg(s1 ~ 1, dist="gompertz")
> f1
Call:
flexsurvreg(formula = s1 ~ 1, dist = "gompertz")

Estimates:
est       L95%      U95%      se
shape  0.322705  0.210768  0.434642  0.057112
rate   0.000755  0.000118  0.004833  0.000715

N = 30,  Events: 23,  Censored: 7
Total time at risk: 484
Log-likelihood = -68.28754, df = 2
AIC = 140.5751


Here, the rate value estimated is IMR and Gompertz coefficient is shape parameter. I am performing this analysis in 8 different strains of worm and want to compare the significance between these values in different strains of worm (compare IMR values of between any two strains of worm and same for Gompertz coefficient value, not IMR and Gompertz coefficient of same strain) as reported in (Bansal, 2015) paper where they have performed likelihood ratio test. I performed LR test as well, but it compares two models not individual coefficients estimated. I have tried to test the difference by comparing 95% CIs (by checking if there's any overlap in the CI values). But, I am not sure if it is a statistically valid way. I want to know the statistically valid way to compare these values across any two different strains of worm.