Hello,

Would anyone be able to clarify the following three questions about the methods Stata uses to calculate confidence intervals for the survivor function with respect to the sts list command?

The main sts manual (https://www.stata.com/manuals/ststs.pdf) states on page 17 that while the standard error for survivor functions is calculated using Greenwood's formula, the confidence intervals are calculated using the ln[−ln S(t)] approach:
The standard error reported is given by Greenwood’s formula (Greenwood 1926) ... These standard errors, however, are not used for confidence intervals. Instead, the asymptotic variance of ln[−ln S(t)] ... is used.
1. I presumed that, because this manual applies to confidence intervals generated using the sts graph and sts list commands, the ln[−ln S(t)] approach is used to calculate all confidence intervals for the survivor function using the sts list command. Is this accurate?

The reason I am asking for clarification is that the manual specific to sts list (https://www.stata.com/manuals/ststslist.pdf) states on page 3 that the level option for sts list,
specifies the confidence level, as a percentage, for the Greenwood pointwise confidence interval of the survivor or failure function
In my analyses, I am using the risktable(numlist) option with the sts list function to describe an sts graph Kaplan Meier curve at 3 specified time points. I am finding that, in some cases, the sts list command and the sts list command with the risktable() option produce different survivor function results at the same time points. Namely, when sts list with risktable() is used, some time points within the extent of my survival data (but with only one participant at risk) are not assigned a survival estimate, while the sts list command alone assigns an estimate. I have attached images of the three outputs I am referring to below.

2. What could be causing the difference in survivor function & confidence interval availability between sts list and sts list, risktable()?
3. Could you explain how I should interpret a missing survivor function result that is within the extent of my data and displays a confidence interval in my Kaplan-Meier graph and sts list, but cannot be assigned a confidence interval according to sts list, risktable()?

I greatly appreciate your time and assistance with this,
Andrew

Code:
sts list, risktable(6 12 24)
Array





Code:
sts list, at(6 12 24)
Array





Code:
sts graph, ci risktable risktable(0(6)24)
Array