Scaling

Standard Gamble

The standard gamble (SG) offers respondents a series of choices between the certainty of spending a specified time period in the health state of interest and taking a hypothetical treatment that has an X% chance of immediate death and a (100 − X)% chance of full health. The health state of interest can be a patient's own health or a description of a hypothetical but plausible health state, often prototypical of a disease or condition. The chances of full health and death are varied, either by direct titration or by “ping-pong.” In the titration procedure, the first choice offered is between the health state of interest and a treatment that gives a 100% chance of full health and 0% chance of death. Once this is accepted, the chance of full health is decreased, usually by 5% at a time (95, 90, 85, etc.), and the chance of death increased (5, 10, 15, etc.), until the respondent indicates that he will not accept the gamble or cannot decide between the two choices. The point of indifference is either at this indecision or midway between the chance of full health that is accepted and the chance that is not accepted. In the ping-pong approach, the chance of full health is varied from high to low: 100%, 5%, 95%, 10%, 90%, and so on. The chance of death is always 100 minus the chance of full health. The ping-pong approach gradually closes in on the respondent's point of indifference between the choice of the gamble and the health state of interest. Utility for the health state is defined as 1 minus the probability of death at the point of indifference between the certainty and the risk. Thus, indifference between staying in current health and a potentially curative treatment with a 20% chance of death yields a utility of .80 for current health. If a health state is very undesirable the respondent should be willing to take a high risk of death to avoid it, and the respondent's utility for that health state will be low. Utilities for health states worse than death can be elicited by asking respondents to make a choice between certain death and a gamble in which full health occurs with a probability X and staying in the health state occurs with a probability of 1 − X. If the health state is very undesirable, the person would not take the gamble unless X is very high. Utility is calculated as −X/(1 − X) and therefore has a much larger range than the 0 to 1.0 limit for utilities for health states preferred to death. This can be corrected by assigning −1 to the least preferred health state and scaling the others between it and 0. Another method is to divide the negative utility by 1 minus itself; for [Page 1018]example, if X = .95, utility = −19, and −19/(1 − (−19)) = −.95. The resulting values should be interpreted with caution.

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