25 Sept 07 FF8 - Discrete Choice Data Introduction Tony O’Hagan

25 Sept 07FF8 - Discrete Choice Data The basic idea We have a finite collection of statuses: S 1, S 2, …, S N We want to assign utility values to these: u(S 1 ), u(S 2 ), …, u(S N ) We ask people to compare two or more statuses, and say which they prefer From many such expressed preferences, we aim to make inference about the underlying utilities

25 Sept 07FF8 - Discrete Choice Data The basic problem Preferring S i to S j basically means u(S i ) > u(S j ) But if all we learn from the data is these inequalities, then all we can infer is the ordering of the utilities We cannot infer values for the utilities E.g. If S 1 has highest utility, then ›I will always choose this in any comparison ›I can infer it has higher utility than any other status ›But not how much higher

25 Sept 07FF8 - Discrete Choice Data Just add noise In practice, people aren’t that consistent Model ›Person states preference for S i over S j if v(S i ) > v(S j ) ›Where v(S) = u(S) + e ›And e is an error term »May be due to the person not evaluating their utilities accurately, or because of variation between people Now if two statuses have similar utilities there is a chance that the preference will be stated the other way round ›We can infer differences in utilities from the frequency of preferences

25 Sept 07FF8 - Discrete Choice Data But … We have to assume a distribution for e ›Including variance »which will strongly affect frequency of preference reversal ›And it is usual to assume independence »which I don’t believe I can’t think of any other problem where getting better quality data would make the problem worse ›Which suggests there is something unsatisfactory about this solution

25 Sept 07FF8 - Discrete Choice Data Health states We will hear about various versions of this approach In the context of health economics, the statuses we wish to value are those describing health A health state descriptive system typically represents health by a level in each of a number of dimensions ›E.g. EQ-5D has 5 dimensions and 3 levels in each dimension ›So this system has 3 5 = 243 distinct health states

25 Sept 07FF8 - Discrete Choice Data Alternative choice systems Consider the EQ-5D state ›Mobility – some difficulties with mobility ›Self-Care – no problems, can care for self ›Usual Activities – can engage in all usual activities ›Pain/Discomfort – some pain/discomfort ›Anxiety/Depression – severe anxiety/depression Status ›The statuses are whole state descriptions like above (N = 243) ›The statuses are individual levels (N = 15) »Utility for whole state is then obtained by assuming additivity Task ›Compare all in a set, to get a full ranking from best to worst ›Identify only the best and worst in a set (best-worst method)