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I am new to survival analysis, and I am confused about time origin, or what's called calendar data format and survival data format.

I have the following dataset, subjects were continuously entering study since the study start, and we record the days after study start when they entered. I am trying to use the following two ways to plot survival curve, why they are so different? I am guessing it's about the time origin, but I am not understanding the story behind it.

Here is the dataset: enter image description here

Here is the two ways of code:

Proc phreg data=ds; model actual_follow_up_days*censor(1)=;run;

Proc phreg data=ds; model Calendar_Days*censor(1)= \ entry=delay_entry ;run;

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The difference here is between when the study started administratively (presumably Study Start) and when each Subject entered the study (presumably on Study Start plus the days of Delay_Entry). Then the Actual_Follow_Up_Days represents the follow-up time for each Subject after that Subject's entry into the study.

The Actual_Follow_Up_Days is almost certainly what you care about. Say you are studying how long Subjects survived after diagnosis of a type of cancer, with each Subject entering the study at the date of diagnosis. The fact that you happened to start your study on 8/5/2018 doesn't matter for any Subject's survival after diagnosis. If the diagnosis for an individual was on 8/5/2019 (Delay_Entry = 365) you would presumably care about survival after that date. I could imagine some study designs where survival from a common fixed date like Study_Start might be of interest, but without further information on your particular study design I think that would be unlikely.

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  • $\begingroup$ Thank you so much EdM for your response. 08/05 is a date we start our project, and on that date, some patients had diagnosis, and after that people continuously got diagnosis and enter study, all we care is the Actual_Follow_Up_Days. Regarding the two ways of coding, which one should be the correct one to use? I assume the first one would be the correct one for us, but why the second one won't work, since the option entry=delay_entry is considered? $\endgroup$ – Z.Gary Aug 5 '19 at 22:44
  • $\begingroup$ @Z.Gary the first coding is correct for those diagnosed after the study entry. For those who entered the study already diagnosed, however, you need to consider them as being "left censored." That is, for those already diagnosed at the start of the study, all you know when they have their event is that the time between diagnosis and event is at least as long as the time since the study started. This is a more complicated type of analysis than simple time from diagnosis to event, and you should consult an experienced statistician for help. $\endgroup$ – EdM Aug 6 '19 at 0:47
  • $\begingroup$ @Z.Gary with respect to the second coding, that would only make sense if what you cared about was the time between the start of your study and the times of individual events. Unless there is something special about the design of your study, that type of analysis would seldom make sense even if it is technically an option. $\endgroup$ – EdM Aug 6 '19 at 0:48
  • $\begingroup$ Thank you EdM for your clear logic and explanation. I feel much clearer now. We don't have patients in the study who were diagnosed before the study start, so we don't have left censored data. $\endgroup$ – Z.Gary Aug 6 '19 at 15:58
  • $\begingroup$ @ EdM For the second coding, I got the idea when I search online asking how to handle delayed entry problem. Many say it's left truncation problem, and SAS phreg with entry option can handle that. but I am not quite getting it from those articles. Would you mind to explain a little bit about left trunction, and whether our design has the left truncation issue? $\endgroup$ – Z.Gary Aug 6 '19 at 15:59

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