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We have prospective data from an observational registry and wish to consider the affects of a gene on time to cardiovascular events. The data includes standard data like age, gender, ... and also the date(age) of a cardio event.

In general terms what are the conditions/assumptions/requirements of a starting time for survival analysis? Entry into the registry is at random times for each individual (as he or she is recruited into the registry).

This is obviously no data at which the registry participants' genes changed, and there no intervention. Is it valid to use the date of enrollment in the registry as the start time for the survival analysis?

We (group working on this) are asking as some work has been done and the the enrollment date was used as the start time for the survival interval and there is some disagreement now as to whether this is a valid approach.

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  • $\begingroup$ I think the answers to this question will be helpful to you. stats.stackexchange.com/q/3611/1036 $\endgroup$ – Andy W Oct 23 '10 at 2:43
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    $\begingroup$ Have you seen the August issue of The American Statistician? The article "Two Pitfalls in Survival Analyses of Time-Dependent Exposure" covers exactly this issue. Abstract at pubs.amstat.org/doi/abs/10.1198/tast.2010.08259 $\endgroup$ – whuber Oct 23 '10 at 2:44
  • $\begingroup$ @whuber Sorry, I can't see why that AmStat article is relevant. Where is the time-dependent exposure in the question? $\endgroup$ – onestop Oct 23 '10 at 7:25
  • $\begingroup$ Is the case that the gene change took place for all participants before they enrolled in the registry? The other possibility is that gene changes took place at some random time before/after enrollment but you simply do not know when it took place. Can you clarify this issue? $\endgroup$ – user28 Oct 26 '10 at 15:12
  • $\begingroup$ @Srikant Vadali They where born with these genes. There was not change in genes :-) This is the root of the problem/question. I have not seen this spelled out well but I assume the starting time could be birth. But it cannot be unrelated to the outcome event? But what if age is part counted is used as an exogenous variable, I not clear on how this effect the estimation. Does this help. If so I will edit the original question to include this. $\endgroup$ – Vincent Oct 26 '10 at 18:06
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The starting time of the study is immaterial: it's just an origin for the clock. What you want to consider are the states in which the subjects can be found and the ages at which they transition from one to another. In this situation a minimum set of states would be

  • [Born]: "Born with gene." This always happens at age 0, of course.
  • [Enrolled]: "Enrolled in study."
  • [Endpoint]: "Cardiovascular event identified."
  • [Death]: "Death."

(This framework will allow multiple "endpoint" states to be modeled.)

The multistate analysis supposes there is a transition probability from some of these states to others. The relevant ones would be

  • [Born] --> [Death]. These account for people who never enrolled.
  • [Born] --> [Endpoint]. Are you considering these people? Are they even allowed into the study?
  • [Born] --> [Enrolled]. These are all the people selected for the study (who haven't died and don't already exhibit the cardiovascular disease).
  • [Enrolled] --> [Endpoint]. These are people in the study diagnosed with a cardiovascular disease.
  • [Enrolled] --> [Death]. These people died in the study without a diagnosis of cardiovascular disease.

The Nelson-Aalen estimator can be generalized to estimate the rates of these transitions. It's a simple estimator, summing the ratios of events occurring to the numbers of people at risk for them to occur. The conclusion of the recent TAS article Two Pitfalls in Survival Analyses of Time-Dependent Exposure is that if you get your multistate model wrong, you will miscount the number of people at risk in various states and that will bias the results. Its message is clear: get the multistate model right. If the study truly is prospective--that is, if you identify people with the gene at birth and follow them--then there is no question about the right model. Similarly, if enrollment in the study is independent of the presence of the gene, there will be no bias. Otherwise, this framework calls out for incorporating the study selection probabilities into the model and shows how to account for deaths and prior disease before enrollment was possible.

This paper also illustrates a nice tool for analyzing these subtleties: the Lexis Diagram. (Look at the figures in the end of this rather technical paper.) I believe these diagrams can be produced with the epi package in R. You might find them helpful for having discussions with your colleagues about the appropriate model to adopt.

ASA members and people with university library privileges probably already have online access to this article: it's worth reading.

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  • $\begingroup$ Can anyone figure out why link #2 is not working correctly? Maybe there's a problem with using square brackets elsewhere in the text? $\endgroup$ – whuber Oct 29 '10 at 19:46
  • $\begingroup$ Looks like my edit overlapped with shabbychef. Hope we did not break anything. $\endgroup$ – user28 Oct 29 '10 at 19:58
  • $\begingroup$ there was a space in the URL. fixed. $\endgroup$ – shabbychef Oct 29 '10 at 19:58
  • $\begingroup$ Thanks guys. You are not only smart and sharp-eyed but helpful, too. $\endgroup$ – whuber Oct 29 '10 at 20:01
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You need to be careful to distinguish two different "start times" in studies such as this:

  • The origin for the time variable, i.e. the point which you're calling t=0 for each participant
  • The time at which an individual enters the study, i.e. the time from which you would record an event if one happened

In the simple cases first taught in survival analysis, these times are assumed to be the same. For long-term cohort studies, it's usually much better to allow them to differ. The most suitable time origin for cohort studies of chronic diseases (such as cardiovascular disease here) is usually date of birth, as Srikant suggests above. That's because for chronic diseases the baseline hazard varies strongly with age. But (unless it's a birth cohort) individuals don't enter the study when they are born. If they have an event before they enter the study you wouldn't record this, and that could cause bias if you don't handle it properly by distinguishing entry time from time origin. This is sometimes called delayed-entry.

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Since the individuals were born with the 'genetic change' I would use their birth as the starting time instead of the time at which they entered the registry.

The following is my reasoning: First, ignore the effect of other variables on survival such as gender, income levels, exercise levels etc. For the sake of illustration we will assume that these variables have no differential impact on the time at which they have a cardio event.

Second, I am assuming that you wish to investigate the following question: Does the difference in gene types (broadly speaking) result in a differential impact on the time it takes for a person to have a cardio event? I suppose that there is an underlying theory which states that the answer to the above question is 'yes'.

Now, consider two individuals both of whom had the gene change. One, enters the registry just before a cardio event and the other has a cardio event several years after entering the registry. However, for the sake of dicussion assume that the ages of both people are the same. Thus, the time to cardio event is technically the same (their age). However, if you use the starting time as the time at which they enter the registry you would draw different conclusions about how long it takes for the cardio event to happen which would bias your conclusions.

I am assuming that my interpretation of your goals and the situation is correct. Please correct me if I am wrong about some aspect.

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  • $\begingroup$ "However, if you use the starting time as the time at which they enter the registry....bias your conclusions." Thanks for your answer. I agree with your answer I am trying to convince others that using time of enrollment is wrong as it is not related to outcome or genetics. Age could be the endog which is equivalent to starting the survival interval at birth. Do you have a reference that would indicate that using time of enrollment is wrong. $\endgroup$ – Vincent Oct 26 '10 at 20:06
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    $\begingroup$ @Vincent At risk of being repetitive, I would refer you again to the TAS article ("Two Pitfalls in Survival Analyses...") because the authors address precisely this issue. They use "multistate modeling" to examine "specific types of survival bias such as length bias and time-dependent bias." You should be particularly concerned about length bias, which is a form of sample selection bias. (What about people who died before they had a chance to ever make it into your study?) This article, as is typical for TAS, has a good bibliography for further research. $\endgroup$ – whuber Oct 26 '10 at 21:33
  • $\begingroup$ @Vincent No, I do not know of any reference. Perhaps, the reference pointed out by whuber may help. Alternatively, you can perform a simulation study and demonstrate what the right choice is. By the way, if people enroll roughly at the same age then the issue is not relevant as enrollment time and age will be synonymous. The issue of incorrect estimates becomes more prominent as enrollment times vary a lot vis-a-vis age. Or, at least that is my intuition. $\endgroup$ – user28 Oct 27 '10 at 0:55
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@Skirant you lost me on your last comment, but I agree with Whuber that by using birth at start start you are distorting your sample as it doesn't take into account people with that gene change that actually already had the event or died from it. On top of it once people enter the regstry there is a chance that they change their behaviour to compensate for the higher risk. I suggest you use entry into the registry as start time and age (at entry) as a covariate or age at event as a time dependent covariate

Let me know how you go

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  • $\begingroup$ Which comment of mine confused you? By the way, I am not the OP. Just wanted to clarify as it feels as if your response including the last line is addressed to me. $\endgroup$ – user28 Oct 27 '10 at 12:07
  • $\begingroup$ There is no change in the genes, they are born with them. Therefore entering the registry does not increase risk. I don't expect a change in behavior but it is possible. There care does not change it is just tracked in the registry. $\endgroup$ – Vincent Oct 28 '10 at 4:16
  • $\begingroup$ sorry for addressing the wrong person. I understand that the gene doesn't change in their life time my English is failing me here I thought you used that term as gene mutation. But regardless of that thanks for clarifying that you think that being in the registry doesn't change their risk. $\endgroup$ – tosonb1 Oct 29 '10 at 0:10
  • $\begingroup$ @Vincent, even if their care does not change, becoming part of a register will probably lead to changes in how they represent their health to themselves, and thus cause changes in their behaviour /end(somewhat irrelevant psychology tangent} $\endgroup$ – richiemorrisroe Oct 31 '10 at 15:56

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