# Balancing "Delayed Entry Bias" and "Survivorship Bias"?

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

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?

Thanks!

Reference:

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).