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I have data that consists of lab test results for patients, cancer dates for those who got cancer, and time till death/censor from that cancer. This cancer is both rare (most of the patients never get it) and mostly non-lethal (even for the patients that do get it, most live with it for many years).

I would like to predict a risk score for patients before they have cancer, which will answer the question: "according to my lab tests, what's the risk for me to get a lethal cancer?".

I thought of 2 ways to get the most from my data, and using all populations (very lethal cancer, medium and non-lethal cancer and healthy):

  1. Survival analysis (training a model such as a random survival forest). For the cancerous patients I would enter their true death/censor time, and for healthy patients I would enter censor with the maximum follow-up time.
  2. Regression (training a model such as xgboost). The label would be some risk level such as: healthy=0, death-from-cancer-within-more-than-3-years=1, death-from-cancer-within-0-3-years=2. This method would require estimating time-to-death for censored-out cancer patients, e.g. by using a mean death time for the cancer patients with a recorded death-time.

Which of these 2 ways is preferable (if any)? Is it valid at all to mix healthy with cancer and ask that risk/survival question?

And most importantly - how can I measure which model is better? By using concordance index? - is it valid to assume healthy patients are censored-out in max follow-up time, as they are substantially different from patients that got cancer but lived with it for max follow-up time..

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  • $\begingroup$ In your data set, how many cases are there for those who got that cancer, and how many that died from it? Those numbers, rather than the total number of cases, will set the limit to getting the most from your data. $\endgroup$ – EdM Jul 28 '16 at 11:59
  • $\begingroup$ @EdM - about 14K censored out and 1.3K deaths. Why do you think I won't be able to get more from my data if I'll find a way to include the countless healthy cases I have? $\endgroup$ – ihadanny Jul 28 '16 at 12:24
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    $\begingroup$ The limiting factor in survival modeling is the number of events. See for example this Cross Validated page or Harrell's course notes, page 101. Relations of outcome to predictors are only evaluated when events occur. Having more total cases might improve estimates of hazard functions, but you still need about 10-20 events per predictor that you will evaluate. You have no problem with with modeling overall survival, but might if you only have a few dozen related to this cancer. $\endgroup$ – EdM Jul 28 '16 at 13:38
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You may want to look into the literature concerning relative survival.

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  • $\begingroup$ Thanks! it appears that the papers are mainly interested in how to incorporate the risk for a cancerous patient of dying from another factor (e.g. car accident), and do so mainly by using death certificates/registry or by estimating the risk for a similar healthy person. However - I couldn't find a paper about actually incoporating a healthy person into the model - is it because it is wrong to do so? $\endgroup$ – ihadanny Jul 30 '16 at 10:37
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    $\begingroup$ You cannot die of cancer if you don't have cancer. So you need to think carefully about what you want to estimate exactly. One possibility would be the excess mortality discussed in that literature, but you will probably need to adjust your estimator to take the specifics of your data into account. $\endgroup$ – Maarten Buis Jul 30 '16 at 15:28

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