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Good morning,

I am building known fate survival models based on numerous covariates including study site. At some sites, all individuals survived for the entire study period, making the site's S = 1.000 in the models. While this result is accurate, it is causing the standard error for that site to become 0 or a very large value. In one of my competing models (which includes site as a covariate), all standard error values are 0, including sites that had mortality and therefore should have an estimable value for standard error. Models that do not contain site as a covariate seem completely fine.

This is what my code looks like for processing data, creating design data, creating a function for running competing models (I shortened the list of models for this example- the function actually contains ~40 total models), and examining real parameters from the top model:

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#Process Data and designate groups
Surv <- process.data(data, model = "Known", groups = c("Sex", "Site"))

#Create Design Data
Surv.ddl <- make.design.data(Surv)

#Create function to run models specified within function
run.surv <- function() {
  S.Sex <- list(formula= ~Sex)
  S.Site <- list(formula= ~Site)

   # Create model list
  model.list = create.model.list("Known")
  Surv.results = mark.wrapper(model.list, data = Surv,
                                     ddl = Surv.ddl, output = FALSE, silent = TRUE)
  # Return model table and list of models
  return(Surv.results)
}

#View results
Surv.results = run.surv()
Surv.results

#top model= site
summary(Surv.results$S.Site)


Here, also, is the output of that summary function where you can see the standard error values and confidence intervals that are odd for sites that have S=1.000 (Sites D and E, not the intercept site).

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Beta
                  estimate          se           lcl         ucl
S:(Intercept)    3.3063687    0.000000     3.3063687    3.306369
S:SiteB  0.6056572    1.009952    -1.3738480    2.585162
S:SiteC         1.8294433    1.002944    -0.1363261    3.795213
S:SiteD       24.3810510    0.000000    24.3810510   24.381051
S:SiteE        18.7342030 3913.228200 -7651.1933000 7688.661700


Since I am getting such odd values for standard error, I want to ensure that my other parameter estimates are accurate before moving on with manuscript preparation. Is there an alternative way to get a standard error or confidence interval for these models that have S=1.000 for some sites?

I apologize if previous answers have provided insight on this topic- this is my first survival analysis so I tried my best to read other answers but tend to get lost in the weeds. Thank you so much in advance for any insight you can provide!

Apologies for not responding sooner. Message got missed in my inbox. Several things you can try.

1. You might want to use ~-1+Site which estimates each site value separately and then use link="sin" in the formula which does a better job with parameters at boundaries.
2. If that doesn't help you can use profile likelihood intervals.

But is Site what you are realy interested in? Be careful you don't include Site and site-specific covariates in the same model.

--jeff