Different ways of summarizing medical risks

Pete Lindstrom writes:

I was wondering if you could blog on the points discussed in the WSJ at this link. Apparently, there is a controversy over ways to use clinical data to calculate risks – one method adjusting for time and another using absolute numbers for the entire length of the study.

My (wholly inadequate) reply: This is interesting, but I have to say, I find the article pretty confusing. It’s written in the standard journalistic style of going forward and backward in time, rather than in the scientific-journal style of presenting the data and models all in one place. If this was something I had to do, I’d puzzle through what’s happening here. Luckily for me, I’m blogging just for fun and so I’ll just let the question sit for others to worry about.

2 thoughts on “Different ways of summarizing medical risks

  1. I would argue that what the WSJ calls the "actuarial method" (i.e., using time) is a much better way to measure risk. Without accounting for time, there is no way to factor in possible deaths for competing risks. For instance, while someone might have developed an adverse condition from the treatment, they never had the opportunity for it to present because they died in a traffic accident or died of another disease. It's morbid to think about, but the longer something takes to present, the more likely it is that these other risks intervene in the meantime.

  2. one student in my class has charged me on this news as well. Here is my answer to the whole class.

    The Biogen Inc. is using cumulative incidence to calculate the risk of
    PML disease among those who took Tysabri. 6 cases among 52,000 patients during the first introduction. which is one in 8,700. After reintroducing the drug to market, 11 new cases among 56,500 patients. which is about one in 5,140.

    The key here is the time unit of analysis. In cumulative analysis, we don't explicitly put time in the denominator. The assumption of cumulative incidence is that it assumes all patients are followed up the same time period. That is, the way Biogen did is to assume all 56,500 has been followed for all three years.

    This is not true. We discovered that not all 56,500 patients have taken drug for the whole three years. about 56,500-30,600=25,900 are in the first year of taking the drug; about 20,600 = 30,600-10,000 are at their second years; and only about 10,000 are at their third year.

    The journalist suggests we should use the actuarial method, which is commonly used in survival analysis. The way actuarial method does is to calculate risk of disease by each follow up year, and then get a summary risk. This method takes account of people who withdraw from the study, lost of follow up, died, or not having been observed enough time etc. It is a better way to calculate the risk of developing disease over time.

    However, the interpretation of the summary risk needs to be careful. If the longer patients stay on drug, the more likely to develop the disease, then the longer follow up, there will likely be more diseased cases. The summary risk will be higher anyway.

    So the Biogen company is certainly playing down drug risk, but the journalist may be ignorant about the interpretation of summary risk.

    The only correct interpretation is from Dr. Robert Fox of Cleveland Clinic. The summary risk from the actuarial method suggests that the longer patients stay on drug, the more likely to develop the PML (from 0 to 0.01% to 0.07% over three years). Time is the key. Rotating drugs may be the correct way to administer the drug.

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