Asymmetric Information

Your doctor says you have six months to live. How accurate is this figure? Do you really have 4 moths to live? One year?

A paper by Alexander and Christakis (2008) analyzes physicians predictions of patient survival. The authors find that physicians systematically overestimate how long the patient will live. This bias is exacerbated when 1) the physician has a closer relationship with the patient or 2) the physician has to communicate their survival prediction directly to the patient.

In the paper, the authors collect data from a number of large hospices in Chicago. Before the patient was admitted to the hospice, the researchers asked the patient’s physician–usually the referring physician–to estimate how long the patient would survive. This was done using 3 measures:

(1) the point prediction is an answer to a question about the physicians’ best estimate of how long this patient has to live; (2) the communicated prediction is an answer to a question about what prognosis the doctor would communicate to the patient if the patient or the family insisted on receiving an estimate of survival; (3) the subjective distribution prediction is the physicians’ stated percent estimate that the patient would still be alive 7, 30, 90, 180 and 360 days after referral.

The closeness of the physicians to the patient is proxied with measures of the duration of their relationship, the frequency of their contact, and the date of their most recent contact.

Why would doctors overestimate survival? We assume predictions in the general case may be incorrect, but that estimates on average do not over- or underestimate survival probabilities. The lack of bias is due to the fact that we usually assume that individuals hope to reduce the mean-squared error of their prediction. The loss function, however, may not always be symmetric. One example of asymmetric loss functions comes from Varian’s 1974 paper, which investigates property value assessments in California. The paper showed that underestimate of property values cost the town money (in terms of the property tax received), but an overestimate could trigger the homeowner to file a lengthy and costly appeal process. Similarly, one would expect that doctors do not feel guilty giving the patient optimistic survival estimates, compared to the emotional stress which occurs when one has to communicate a pessimistic survival estimate to the patient.

The paper also finds evidence for two other types of biases: information bias and physician referential bias.

Information bias says that overestimates are more likely when the physician has less information about a disease. For this reason, we see that physicians have more accurate, less biased predictions for cancer patients. Why is this the case? Since cancer was the most likely reason why a person was admitted to a hospice, physicians have more experience caring for cancer patients. As the physician’s knowledge of a disease and frequency of dealings with patients who have a disease increase, the physician’s survival estimate becomes less biased.

Also, the physician’s physical observation (physician referential bias) will make predictions less accurate and more prone to overestimation. The authors claim that “[w]hen the patient is physically active, and able to function with little assistance on a daily basis, the physicians’ prognosis becomes more inaccurate and doctors inflate the estimates of their patients survival.”

• Varian, 1974 H.R. Varian, A Bayesian approach to real estate assessment. In: S.E. Fienberg and A. Zellner, Editors, Studies in Bayesian Econometrics and Statistics, North-Holland, Amsterdam (1974), pp. 195–208.