This is a question I have always struggled with - suppose you have medical data on patients over a period of time. This includes information on how long they spent in different states: Admission, Discharge and Death

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You have data for patients between the years 2010 and 2020. Suppose you have data for patients that entered the study in 2010, patients that entered the study in 2011, patients that entered the study in 2012, ... all the way to patients that entered the study in the 2019 (the last full year before the end of the study). This means that patients who entered the study earlier will have more data compared to patients later, possibly creating some types of biases.

I thought of an example to explain this: Suppose a storm broke John's fence 20 years ago and John still hasn't fixed his fence - Suppose a storm broke Jason's fence last week and Jason still hasn't fixed his fence : Can we conclude that John and Jason are equally lazy? Obviously Not! We would have to give Jason at least a few years to see if he repairs his fence to conclude if he is as lazy as John!

In the case of Multistate Models, suppose the patients who were recruited towards the end of the study - at that time they were recruited, suppose they were not admitted in the hospital (and were obviously not dead) and remain in the "Discharge State" for the remainder of the study, thus experiencing no transitions whatsoever. However, they might have been admitted to the hospital within a year of the study terminating - but this transition will not have naturally been recorded in the data. It sounds plausible that this might bias the calculations for the Hazard Rates and Transition Probabilities calculated within the medical study.

Logically, the "lower risk" (in terms of incurring less bias) option would be to only include patients who began in 2010, but we would then be missing out on potentially valuable information from patients who entered the study at later times. To counter for this, we might be able to create a "cutoff" that balances both of these biases - for instance, we might decide to include patients who entered the study from 2010 to 2015, thus guaranteeing that we at least 5 years of data for any patient in the study. But the "elephant in the room" still remains - why not make the cutoff at 2014 or 2016?

This brings me to my question:

  • Are there any "statistical techniques" that can be used to consider potential cutoffs for including patients (e.g. some minimum number of time for the estimations to be statistically valid, e.g. analogous to sample size n = 30) - or is this something that is inherently arbitrary? Should this kind of decision be left to the subject matter experts (e.g. medical professionals) who possess a more sophisticated understanding of the domain and can thus advise on how to create the "cutoff" based on their knowledge of different exogenous factors that might be present and influence the data in different ways (e.g. Swine Flu H1N1 outbreak in 2009)?

  • Specifically for Multistate Models , is this requirement for patients being in the study for similar amounts of times as important when compared to standard Survival Models? Or since we are estimating the transition probabilities between different states of a Markov Chain, the "Markovian Assumption" might not make this requirement might not be as important? E.g. John enters the study on June-01-2019 and is recorded spending June-01-2019 to Feb-02-2020 outside of the hospital (i.e. Discharge State), but is then admitted to the hospital on Feb-03-2020 (study is now over). Even though we have such little information on John, we still know that he spent June-01-2019 to Dec-31-2019 outside of the hospital, and this information might still be able to make a valid and useful contribution in estimating transition/hazard rates for John's cohort?




1 Answer 1


The premise of your question--that you need to ensure similar times at risk for all individuals and thus should identify lower-limit cutoff times for inclusion in data analysis--is inconsistent with standard approaches of survival analysis.

... patients who entered the study earlier will have more data compared to patients later, possibly creating some types of biases.

This is the standard situation with right censoring in survival models. Those observed for shorter times provide information for as long as they are at risk for an event (or a state transition in a multi-state model). Some forms of censoring, like informative censoring that is associated with outcomes, can pose difficulties for reliable modeling. To evaluate that you would want to call upon expert opinion. Censoring per se, however, is standard in survival analysis. This review on Censoring Issues in Survival Analysis is a good introduction.

That's even the case for your hypothetical situation of someone entering the study in the Discharge state but undergoing no state transition. That situation is not fundamentally different from a two-state alive/dead model when someone enters a study alive and doesn't die before the end of the study. The time for such an individual on the study does provide information about times to events that would have been possible (even if not experienced).

The John/Jason example also isn't quite on point for a survival model. Survival models do not give you information about the time to an event for any particular individual. They are best thought of as providing a probability of survival over time for a group of individuals who share modeled characteristics.

John provides information about time to fence repair for individuals like him through 20 years; Jason provides information about time to fence repair for individuals like him through 1 week. Those two individuals, on their own, don't even provide much information about relative laziness between the groups that they represent. You need multiple individuals and events to estimate a survival curve reliably.


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