# BIOS601 AGENDA: Tuesday November 04, 2014

### Agenda for November 04, 2014

• Discussion of issues in C&Hs Chapter 07 (Competing Risks), and JH's Notes and Assignment on this chapter

Answers to be presented by students on Thursday November 06 for: : (Supplementary) Exercises 7.1, 7.2

Remarks on Notes:

These notes were developed to supplement the Clayton and Hills chapter, which was aimed at epidemiologists, and which does not give the derivations (the 'wiring' and 'theory') below the results (the user's view of the car).

It is important to read C&H first, before JH's notes.

The core topic in this chapter is a very old one, going back at least to Daniel Bernoulli in 1760, when he published 'an attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it.'

In medical follow up studies, one of the ways to deal with deaths from unrelated causes is to simply censor these observations at the time the patient dies of the other cause. But, as is clear if one applies the 're-distribution-to-the-right' principle to these so-called 'censored observation', we see that we are effectively 'resurrecting' them and putting them at future risk of the cause-of-death or 'event' of interest. In effect, at each time t, this approach forces everyone to be in one of two states: either the 'initial (event-free)' state, or the 'post-event-of-interest' state. It is as though nobody is allowed to died of an unrelated cause.

A better way is to recognize that at any time t, one can be one one of 3 states. Thats why JH calls the competing curves in the JAMA article '3-ply' curves. A Kaplan-Meier curve is a '2-ply' curve: below the curve are those still in the initial state, and above it are those who have transited from the initial state to the 'other' (absorbing) state.

A compelling example is how to display the progress of PhD students towards a PhD. When JH went back over the records of our department to see how long, from when one enters the program, it takes to get a PhD, he encountered some censored' observations, in that the student was still pursuing a PhD at the time he was doing the analysis. But he was also confronted with the fact that a fraction of those who entered long before did not remain in the program until they got a PhD, preferring instead to transit to a different absorbing state, namely "it is not for me". It would be misleading to treat these as 'censored' at the time they withdrew (say after 4 years), since if we treat them as such in a K-M analysis, it effectively gives them a PhD at the same rate as the others who had not gotten a PhD by the end of the 4th year, but did get the degree in year 5, 6, 7, ... The more transparent thing to do is to have 3 columns in the life table that describes, out of (every) 100 who entered the program, who is in which state at the end of the year in question

........... . ..... State ....... . State ....... State ............

End of Year . Still Pursuing PhD . HaveGivenUp ... Have PhD .........TOTAL

..... 1 ............ 95 ............... 5 ............ 0 ........... 100

..... 2 ............ 88 .............. 12 ............ 0 ........... 100

..... 3 ............ 87 .............. 13 ............ 0 ........... 100

..... 4 ............ 60 .............. 15 ........... 25 ........... 100

..... 5 ............ 25 .............. 20 ........... 55............ 100

..... 6 ............ 13 .............. 22 ........... 65 ........... 100

..... 7 ............. 5 .............. 25 ........... 70 ........... 100

..... 8 ............. 0 .............. 25 ........... 75 ........... 100

Competing risk analysis is particularly relevant in medical follow-up studies of cause-specific mortality or morbidity (eg from a specific type of cancer) when the follow up extends into ages where there is substantial mortality from other unrelated causes.

The approach we take is not applicable for 2 disease processes that are the result of a common agent. Thus, it might be reasonable to think of deaths from prostate cancer and all other causes as arising from independent processes, and so if we were to eradicate all prostate cancer, the other process would continue as before. But if we were to eradicate most lung cancer by getting people to not smoke, we would also alter the death rates from heart disease and other diseases caused by smoking. that