# Standard Gamble, Time Trade-off and Visual Analog Scale

Would you rather live for 5 years in perfect health or 10 years with some debilitating disease?  How much do you value living for a year with this debilitating disease compared to a year in full health?  These questions may seem like ones from philosophy, but they are ones that health economics ask all the time.  The goal of these questions is to try to determine how much value patients place on going from a poor health state to a better one.

Many treatments improve patient health but do not decrease mortality.  In these cases, health economists which to measure the value patients receive in terms of improvement in health status.  A paper by Stiggelbout and de Haes (2001) describe three approaches for measuring the value of different health states.  I review their paper below.

Standard Gamble (SG): In the SG method, a subject is offered the hypothetical choice between the sure outcome, A (living his remaining life expectancy in the state “alive, artificial speech”), and the gamble, B. The gamble has a probability p of the best possible outcome (optimal health, defined as 1) and a probability (1 – p) of the worst possible outcome (usually immediate death, defined as 0). By varying p, the value at which the subject is indifferent to the choice between the sure outcome and the gamble is obtained. The utility for the sure outcome, the state “alive, artificial speech,” is equal to the value of p at the point of indifference…Thus,if the subject is indifferent to the choice between his remaining life in “alive, artificial speech” and a gamble with a probability of 0.90 that his remaining life will be in optimal health and a probability of 0.10 of immediate death, the utility for “alive, artificial speech” is 0.90 (0.90 x 1 + 0.10 x 0).

Time Tradeoff (TTO).  In this approach, the subject is asked to choose between his remaining life expectancy in the state “alive, artificial speech” and a shorter life span in normal health. In other words, he is asked whether he would be willing to trade years of his remaining life expectancy to avoid artificial speech. As an example, a 65-year-old man is asked how many years x in a state of optimal health he considers equivalent to a period of 15 years (his remaining life expectancy) in the state “alive, artificial speech.” By vary- ing the duration of x, the point is found where he is indifferent to the choice between the two options. The simplest and most common way to transform this optimal- health equivalent x into a utility (ranging from 0 to 1) is to divide x by 15.

Visual Analog Scale (VAS).  This is basically the “thermometer” approach. In VAS, the subject is asked to rate the state by placing a mark on a 100-mm horizontal or vertical line, anchored by optimal health and death (or sometimes by best possible health and worst possible health). The score is the number of millimeters from the “death” anchor to the mark, divided by 100. The VAS does not reflect any trade-off that a subject may be willing to make in order to obtain better health, neither in terms of risk nor in years of life.

Source: