CENSORING PATIENTS
 

 

 

 

 

 

 

 

 

 

 

 

 

So you identify 100 patients, give them the treatment, and their cancers seem to be cured. You follow them for several years. During this time, seven patients celebrate their newfound health by visiting Iceland. In a horrible tragedy, all seven happen to die in an avalanche caused by a submerged volcano. What is the effectiveness of your treatment on cancer mortality? Just looking at the data, it is tempting to say there is a 7 percent mortality rate. However, this mortality is clearly not related to the treatment, so the answer does not feel right. And, in fact, the answer is not right. This is an example of competing risks. A study participant might live, might die of cancer, or might die of a mountain climbing accident on a distant island. Or the patient might move to Tahiti and drop out of the study. As medical researchers say, such a patient has been “lost to follow-up.” The solution is to censor the patients who exit the study before the event being studied occurs. If patients drop out of the study, then they were healthy to the point in time when they dropped out, and the information acquired dur­ ing this period can be used to calculate hazards. Afterward there is no way of knowing what happened.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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They are censored at the point when they exit. If a patient dies of something else, then he or she is censored at the point when death occurs, and the death is not included in the hazard calculation. TI P The right way to deal with competing risks is to develop different sets of hazards for each risk, where the other risks are censored. Competing risks are familiar in the business environment as well. For instance, there are often two types of stops: voluntary stops, when a customer decides to leave, and involuntary stops, when the company decides a cus­ tomer should leave—often due to unpaid bills In doing an analysis on voluntary churn, what happens to customers who are forced to discontinue their relationships due to unpaid bills? If such a customer were forced to stop on day 100, then that customer did not stop vol­ untarily on days 1-99. This information can be used to generate hazards for voluntary stops. However, starting on day 100, the customer is censored, Censoring customers, even when they have stopped for other reasons, makes it possible to understand different types of stops.