Probabilistic choice models in health-state valuation research: background, theories, assumptions and applications

Figures & data

Figure 1. Schematic representation of the raw data and after sorting of the columns (health states) and the rows (patients) in order to arrive at the hierarchical Guttman/Rasch data structures (the check mark indicates that this health state is preferred over the next health state, the cross mark indicates a misfit).

Figure 2. Development of the class of probabilistic choice models over time and by area of research.

Figure 3. Deriving paired comparison data based on rank data.

Reproduced with permission from [47].

Table 1. Overview of techniques and probabilistic choice models for the measurements of health-state values.

Names/origins	Probabilistic models	Implying a choice-based task	For modeling preferences (utility)	Application in health-state valuation^†	Type of stimuli	Assumptions for statistical modeling	Statistical models
Rating: conjoint analysis (by Green)	No	No	Yes	No	Rating each of more than two options described with different characteristic levels	Normal distribution of disturbances	Regression
(Multi-item) visual analogue scale	No	Partially	Yes	Yes	Positioning of one or more health states on a scale	Normal distribution of disturbances	Regression
Standard gamble	No	Yes	Yes	Yes	Two alternative health states with different probabilities of occurrence	Normal distribution of disturbances	Regression
Time trade-off	No	Yes	Yes	Yes	Two alternative health states with different durations	Normal distribution of disturbances	Regression
Thurstone LCJ	Yes	Yes	No	Yes	Two alternative stimuli	Normal distribution of disturbances	Probit
Bradley–Terry–Luce	Yes	Yes	No	No	Two alternative stimuli	Extreme value type I disturbances	Binary logit
Bradley–Terry–Luce	Yes	Yes	No	Yes	More than two discrete alternative stimuli	Extreme value type I disturbances; IIA	Multinomial logit
Rasch	Yes	Yes	No	Yes	Separate judgments for a set of stimuli	Extreme value type I disturbances	Conditional logit
Ranking – conjoint analysis (by Green)	Yes	Yes	Yes	Yes	Ranking more than two alternative options described with different characteristic levels	Extreme value type I disturbances; IIA	Ordered logit
Discrete choice analysis (by McFadden)	Yes	Yes	Yes	Yes	Choosing one from two or more discrete options described with different characteristic levels	Extreme value type I IID disturbances; IIA assumption	Conditional multinomial logit
Discrete choice generalizations: rank-ordered logit	Yes	Yes	Yes	Yes	A series of selection from smaller and smaller groups of health states (usually most preferred to least preferred)	Extreme value type I IID disturbances; IIA assumption	Rank-ordered logit
Multinomial probit	Yes	Yes	Yes	Yes	Choosing one from two or more discrete options described with different characteristic levels	Normal IID disturbances	Conditional multinomial probit
Nested logit/probit	Yes	Yes	Yes	No	Choosing one from three or more discrete options described with different characteristic levels	Extreme value type I/normal IID disturbances; nested IIA assumption	Nested logit/probit
Ordinal logit	Yes	Yes	Yes	No	Choosing an ordinal strength of preference from two options described with different characteristic levels	Extreme value type I IID disturbances IIA assumption	Conditional multinomial logit
Logit-mixture	Yes	Yes	Yes	No	Choosing one from two or more discrete options described with different characteristic levels	Extreme value type I/variable IID disturbances	Logit-mixture
Hierarchical-Bayes	Yes	Yes	Yes	No	Choosing one from two or more discrete options described with different characteristic levels	Conditional independence (in addition to the ‘base’-model being used, for e.g., logit-mixture)	Hierarchical-Bayes

The authors do not claim that this table is complete, instead only the most applied models are presented.

^†To the authors’ knowledge.

Krabbe PF. Thurstone scaling as a measurement method to quantify subjective health outcomes. Med. Care 46(4), 357–365 (2008).

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