# Calculating sensitivity and specificity from survival data

I have a diagnostic test performed on 100 participants at baseline. I then follow up these participants for variable periods of time and have data regarding survival.

I have used a Cox regression model to calculate a hazard ratio, and used the Mantel-cox log rank to test whether a positive test predicts death.

I would like to calculate time specific version of sensitivity and specificity of the test. I have been using the 'survivalROC' package in R to do this.

library(survivalROC)
num_subj = NROW(data)
survivalROC(Stime = data$survival_time, #time till censoring marker = data$positive_test, #1 for positive, 0 for negative
status = data$death, #whether subject dead or alive predict.time = 2, #cutoff time span = 0.25*num_subjects^(-0.20))  From this I get 'True positive' and 'False positive values' If I then run the same code but this time with marker = data$negative_test, #1for negative, 0 for positive


I will get different True/false positive values.

My question is: can I put these 4 numbers in a 2x2 table (the values from the marker = data\$negative_test used as the values for true and false negative) and calculate sensitivity and specificity in the usual manner (e.g. sens = TP/(TP+FN))?

Or please let me know if this whole approach is misguided and there are superior alternatives.

• The fact that this give the same results for sensitivity and specificity as the td.sesns.spec function from: rdrr.io/bioc/survcomp/man/td.sens.spec.html reassures me that this may be an ok solution – RobMcC Sep 15 '17 at 10:37