How to regress latent intervals with survival::survreg (interval regression w/ censored data)?

Question

I'm attempting an interval regression in R with censored data containing dependant values either as a number y or an interval [0, z ] containing y .

After searching, I found several sources with examples recommending survival::survreg (ie here ), though they're not dealing with exactly the same problem. However, I can't get it to work with my data and I assume I'm having some special case.

I'll give you a MWE. First I create some data and the latent intervals:

# data
set.seed(417699)
df <- data.frame(ind = rbinom(10, 1, .75))
df <- transform(df, 
                value = ifelse(df$ind == 1, sample(1:1000), NA),
                value1 = ifelse(df$ind == 0, sample(10:100) * 10, 0),
                cv1 = rbinom(10, 2, .7)  # 1st independent var.
                cv2 = rbinom(10, 2, .25)  # 2nd indep. var.
                )

# intervals depending if 'ind' equals 0
df$liv <- with(df, ifelse(ind == 1, value, 0))
df$uiv <- with(df, ifelse(ind == 0, value1, value))
df

##    ind value value1 cv1 liv uiv cv2
## 1    1   616      1   2 616 616   0
## 2    0    NA    450   2   0 450   0
## 3    1   236      1   2 236 236   0
## 4    1   130      1   1 130 130   1
## 5    0    NA    350   1   0 350   1
## 6    0    NA    250   2   0 250   0
## 7    1   241      1   1 241 241   0
## 8    1   950      1   2 950 950   1
## 9    1   557      1   2 557 557   1
## 10   1   453      1   2 453 453   1

As one can see, there are intervals or points now depending on whether ind = 1 or 0. In detail, if ind = 0, the value lies somewhere in the interval.

Now, with survival::Surv() and assuming it is left censored I'm creating the "survival object" as follows.

library(survival)
(Y <- with(df, Surv(liv, uiv, event = rep(2, nrow(df)), type = "interval")))
## [1] [837, 837] [  0, 340] [694, 694] [ 74,  74] [  0, 280] [  0, 640] [177, 177]
## [8] [650, 650] [368, 368] [179, 179]

summary(Y)
##      time1           time2           status 
##  Min.   :  0.0   Min.   : 74.0   Min.   :3  
##  1st Qu.: 18.5   1st Qu.:204.2   1st Qu.:3  
##  Median :178.0   Median :354.0   Median :3  
##  Mean   :297.9   Mean   :423.9   Mean   :3  
##  3rd Qu.:579.5   3rd Qu.:647.5   3rd Qu.:3  
##  Max.   :837.0   Max.   :837.0   Max.   :3     

All fine, but at the end survreg() fails with an error:

survreg(Y ~ cv1 + cv2, data = df, dist = "gaussian")
## Error in coxph.wtest(t(x) %*% (wt * x), c((wt * eta + weights * deriv$dg) %*%  : 
## NA/NaN/Inf in foreign function call (arg 3)

In Surv() I tried several values for the options event= and type= , most of them didn't work and I'm confused how to specify the right settings (ie I don't know if I'm wrong or the function is, see following note).

Note: survreg() seems to have had a bug a few versions ago, but which now should be solved (I don't know for sure).

Does anyone know what's going on and how to solve this issue? Moreover, at the moment I guess this seems to be the only promising way to calculate such kind of an interval regression in R, but maybe there is a better option. Thank you.

Answer 1

A tiny comment on this question finally brought me the solution. The trick is to set type = "interval2" and we can drop the mode= option.

(Y <- with(df, Surv(liv, uiv, type = "interval2")))
## [1] 616        [  0, 450] 236        130        [  0, 350] [  0, 250] 241  
## [8] 950        557        453 

summary(Y)
##     time1           time2           status   
## Min.   :  0.0   Min.   :  1.0   Min.   :1.0  
## 1st Qu.: 32.5   1st Qu.:  1.0   1st Qu.:1.0  
## Median :238.5   Median :  1.0   Median :1.0  
## Mean   :318.3   Mean   :105.7   Mean   :1.6  
## 3rd Qu.:531.0   3rd Qu.:187.8   3rd Qu.:2.5  
## Max.   :950.0   Max.   :450.0   Max.   :3.0  

coef(intreg <- survreg(Y ~ cv1 + cv2, data = df, dist = "gaussian"))
## (Intercept)         cv1         cv2 
##   -282.0126    326.4428    216.9370 

Compared to normal OLS the regression results seem to be accurate:

coef(reg <- lm(value ~ cv1 + cv2, data = df))
## (Intercept)         cv1         cv2 
##   -242.5294    364.1176    127.8235