I am looking for a method in R to get the estimate of correlation (and the associated p-value) between a partially censored time-to-event data and a continuous variable (e.g. body length).
Here is the sample of my data - time observations censored at 900 (seconds):
length <- c(12.10, 11.00, 9.59, 10.38, 11.10, 9.39)
timeto <- c(149, 900, 26, 3, 0, 900)
event <- c(1, 0, 1, 1, 1, 0)
data <- data.frame(length, timeto, event)
It sounds like you want a time-to-event analysis where event rate is dependent on a continuous variable. You can do this using a Cox proportional hazards model, which is really easy to do with the survival package:
library(survival)
# Create a Surv object from times and events:
data$surv <- Surv(timeto, event = event)
# See the summary of the Cox model:
summary(coxph(surv ~ length, data = data))
#> Call:
#> coxph(formula = surv ~ length, data = data)
#>
#> n= 6, number of events= 4
#>
#> coef exp(coef) se(coef) z Pr(>|z|)
#> length 0.1698 1.1850 0.4808 0.353 0.724
#>
#> exp(coef) exp(-coef) lower .95 upper .95
#> length 1.185 0.8439 0.4618 3.041
#>
#> Concordance= 0.643 (se = 0.152 )
#> Likelihood ratio test= 0.12 on 1 df, p=0.7
#> Wald test = 0.12 on 1 df, p=0.7
#> Score (logrank) test = 0.13 on 1 df, p=0.7
Created on 2020-06-21 by the reprex package (v0.3.0)