Start time requirements or assumptions for survival analysis 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.
 A: 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."

*

(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.
A: 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.
A: 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. 
A: @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
