Design of Health Technologies lecture 19 John Canny 11/14/05

Medical Decision-Making The perils of probability: HIV test is positive 98% of the time on individuals carrying the HIV virus. The same test is negative 99% of the time on individuals without the virus. Q: In a population where 1 out of every 1000 people have the virus, what is the probability that a person who tests positive actually has the virus? A: Only 10%!

Bayes rule V = individual has the virus, NV = doesnt P = individual tests positive, NP = doesn’t Pr(P | V) = 0.98 Pr(NP | NV) = 0.99 What is Pr(V | P) ? Use Bayes rule: Pr(A | B) = Pr(A and B) / Pr(B)

Bayes rule Bayes rule: Pr(A | B) = Pr(A and B) / Pr(B) So Pr(V | P) = Pr(V and P) / Pr(P) Use Bayes again Pr(V and P) = Pr(P | V)Pr(V): Pr(V | P) = Pr(P | V) Pr(V) / Pr(P) We know Pr(P | V) = 0.98, Pr(V) = 0.001, need to find Pr(P)…

Bayes rule Pr(P) = Pr(P and V) + Pr(P and NV) Pr(P) = Pr(P | V) Pr(V) + Pr(P | NV) Pr(NV) = 0.98 * *  Substitute back to Pr(V | P) = Pr(P | V) Pr(V) / Pr(P) = 0.98 * /  0.09

Human uses of probability Terms used by doctors and range of probabilities encoded:

Human probability heuristics Representativeness: How similar is user A to users with condition B? Availability: How available is the physician’s memory of cause B for symptoms A? Anchoring and Adjustment: Physician makes an initial estimate of probability based on coarse information, and then refines it based on further facts.

Objective Estimates Prevalence: is the probability of occurrence of a condition in the general population. Prevalence can be estimate from reported rates of the disease, but that may underestimate because of undiagnosed cases. A random sample of all users can be used in conjunction with a diagnostic test to estimate prevalence.

Objective Estimates Clinical Subgroup: is a group of users with certain attributes who prevalence is known. E.g. users who have been referred to a urologist for possible prostate problems may have the problem at 50% rate. Referral Bias: disease prevalence is usually much higher in a group of referred patients such as the above, e.g. 50% vs. 5-14%.

Testing Many diagnostic tests produce continuous values. Thresholds must be set to declare positive/negative results.

Testing Sensitivity: Likelihood that a diseased patient tests positive. i.e. Pr(P | V) in our example. Specificity: Likelihood that a non-diseased patient tests negative. i.e. Pr(NP | NV) in our example. Note: Sensitivity corresponds to recall in information retrieval. IR precision is Pr(V | P), so it does relate directly to specificity.

Expected Values The expected value of a variable is: E[X] =  v i Pr(X = v i ) i.e. it weights the value of events by their likelihood. It makes a lot of sense over populations of people. Maximizing the expected value of a person’s survival also maximizes the number of people who would survive this procedure in a large population.

Decision Trees A natural representation for a series of clinical test. Decision nodes represent tests. Probabilities are easily computable given parent probabilities and conditional probabilities for each node given its ancestors.

QALYs A QALY is a Quality-Adjusted Life Year. It’s a way to weigh a patient’s preference for life quality over duration. e.g. you can ask the patient “how many years of normal mobility would be equivalent to 10 years in a wheelchair?” This quality adjustment allows you to compare the trade- offs among therapies with various outcomes.

QALY-adjusted decision tree

Time Dependence Many disease processes have a relatively fixed probability of occurring in a given amount of time. Markov models model such processes very well. A Markov model has a fixed time step, and can transition from one state to another in one time step. The probabilities of transition are fixed. Annual probabilities are shown at right

Influence diagrams Represent actual observable data, and latent (unobservable) events. By adding these latent data, more accurate inference can often be made.

Latent Variable Models Represent actual observable data, and latent (unobservable) events. By adding these latent data, more accurate inference can often be made. Applies either to influence diagrams (Bayes nets) or Markov models (DBNs or Dynamic Bayes Nets).

Discussion Questions With the growth of home monitoring etc. there are new possibilities for medical and health data-gathering. But there are also new types of biases that can occur. Discuss these new possibilities, the types of bias that might occur, and how to guard against them. Discuss some weaknesses of the QALY model: e.g. how well do you think users address the tradeoffs? Would their attitudes change over time? What could you do about this in terms of decision-making?