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I have a question about survival analysis with a gaussian distribution of the response variable. I have interval censored data, that look something like this (just an example):

structure(list(Ylower = c(2, 3, 2, 6, 1, 4, 9, 5, 6, 4, 15, 13, 8, 9, 4, 6, 7, 6, 5, 5, 2, 1, 3),Yupper = c(4, 7, 3, 10, 4, 8, 14, 9, 11, 9, 16, 16, 11, 10, 9, 8, 11, 10, 6, 6, 5, 3, 6), F = c("A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B", "B"), X = c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 1.2, 2.5, 2.8, 4.5, 4.7, 5.5, 6.2, 7, 9, 10.2)), row.names = c(NA, -23L), class = c("tbl_df", "tbl", "data.frame"))

The response variable Y is only available as an interval within which the real time Y lies, given as Ylower and Yupper. The data contains a continuous variable X and I am interested whether there is a (linear) relationship between Y and X, I thus assume a gaussian distribution of X. The data further conatins a factor with the two levels A and B. I want to know whether the relationship of X and Y depend on the level of F.

options(contrasts=c('contr.treatment','contr.poly'))
Y = with(example_data, Surv(Ylower, Yupper, event = rep(3, nrow(example_data)), type = "interval"))
  mod = survreg(Y ~ X * F, example_data, dist="gaussian")
  summary(mod)

Output:

Call:
survreg(formula = Y ~ X * F, data = example_data, dist = "gaussian")
             Value Std. Error     z       p
(Intercept)  0.962      1.159  0.83  0.4067
X            1.024      0.158  6.48 9.2e-11
FB           8.949      1.631  5.49 4.1e-08
X:FB        -1.736      0.253 -6.85 7.4e-12
Log(scale)   0.538      0.194  2.77  0.0056

Scale= 1.71 

Gaussian distribution
Loglik(model)= -26.5   Loglik(intercept only)= -39.4
    Chisq= 25.75 on 3 degrees of freedom, p= 1.1e-05 
Number of Newton-Raphson Iterations: 5 
n= 23 

I have not found an awful lot about information on gaussian distribution survival models. I understand that for example for a Weibull or exponential distribution, the scale parameter is the lamda of the survival function exp(-\lamda *x^a) or exp(-\lamda *x).

But what is the scale parameter for a gaussian distribution and what is my interpretation of it?

And from the output of the model, can I say that per one unit increase in X, Y increases 1.024 units (for F=A)?

How do I check whether the model assumptions are met (assuming I have compared log-likelihoods of survival models with different distribuitons)?

I appreciate any help!

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