Conjoint Analysis

Conjoint Analysis with Ratings, Rankings, Choices and Part-Worths in Health Preference Research

Conjoint analysis turns judgements about whole profiles, such as two ways of running a clinic, into a value for each feature that makes up the profile. In health economics it puts numbers on aspects of care outside standard health outcomes, such as waiting time or place of treatment, and it has been tested as a source of outcome weights in health technology assessment. Studies use one of three task formats (ratings, rankings and choices) and an additive part-worth model, from which relative importance and trade-offs follow, and an illustrative worked example later uses regression on ratings. Whether discrete choice experiments belong in the same family remains debated. Choice tasks have their own page on choice-based conjoint.

From conjoint measurement to a preference method

Conjoint analysis began in mathematical psychology and passed through marketing to health care. Hauser and Rao trace it to work on conjoint measurement by Luce and Tukey in 1964 and by Krantz and colleagues in 1971, who were exploring the behavioural axioms, such as additivity and independence, under which an overall judgement can be decomposed into parts. According to Hauser and Rao, Green and Rao adapted that theory to marketing and product development in 1971. Green and Srinivasan later defined conjoint analysis as any decompositional method that estimates the structure of a person's preferences, such as part-worths or importance weights, from overall evaluations of alternatives described by attribute levels.

Ryan and Farrar described its arrival in health care during the 1990s to elicit patients' and the community's views, on the premise that a service's value depends on the levels of its characteristics. An ISPOR task force report by Hauber and colleagues notes that early health applications quantified process utility and that later ones turned to patient preferences for health status, treatments and tests.

Ratings, rankings and choices as three ways to elicit preferences

All conjoint studies show respondents profiles built from attributes and levels, usually selected by an experimental design, but differ in the task. The ISPOR statistical methods report describes conjoint analysis as a broad term for methods in which respondents rate, rank or choose among such profiles, and the ISPOR checklist asks whether the format (rating, ranking or choice) suited the research question and whether it should allow for indifference.

The table follows Green and Srinivasan's framework, which pairs measurement scales with metric, nonmetric and choice-probability estimation; Louviere, Flynn and Carson note that rank orders can be expanded into implied choices. Ryan and Farrar reported that ranking had not yet been used in health care and that the choice approach was preferred because choices more closely resemble real decisions; choice tasks are covered on the discrete choice experiment page. Self-explicated, hybrid and adaptive methods, which ask respondents to value attributes directly, are not solely decompositional.

The part-worth model and how it is estimated

Most conjoint studies assume that the overall value of a profile is the sum of the values of its attribute levels. Each of these values is a part-worth utility. With ratings treated as an interval scale, the additive model can be estimated by linear regression as follows.

$$R_j = \beta_0 + \sum_{k=1}^{K} \sum_{l=1}^{L_k} \beta_{kl} \, x_{jkl} + e_j$$

where $R_j$ is the rating of profile $j$, $\beta_0$ is the intercept (the predicted rating of a reference profile), $\beta_{kl}$ is the part-worth of level $l$ of attribute $k$, $x_{jkl}$ equals 1 if profile $j$ shows that level and 0 otherwise, $K$ is the number of attributes, $L_k$ the number of levels of attribute $k$ and $e_j$ the residual. One level of each attribute is the reference, with a part-worth of zero. The terms other than $e_j$ give the profile's overall value under the additive model.

Green and Srinivasan describe the part-worth function as more general than the vector (linear) and ideal point (linear plus quadratic) models, at the cost of more parameters, and Hauser and Rao note that regression needs at least as many observations as parameters. Ryan and Farrar, analysing choices, used a random effects ordered probit model.

The additive form rests on preferential independence, meaning that the trade-off between two attributes must not depend on the levels of the others. Hauser and Rao point out that an orthogonal main-effects design implicitly assumes this and cannot estimate interactions, so any interaction effect has to be planned at the design stage.

Relative importance and trade-offs

Part-worths have no natural unit, so studies report quantities that compare them. The ISPOR statistical report measures an attribute's importance as the difference between the part-worths of its most and least preferred levels, over the range of levels in the study. Here that range is expressed as a share of the total, as follows.

$$RI_k = \frac{\max_l \beta_{kl} - \min_l \beta_{kl}}{\sum_{h=1}^{K} \left( \max_l \beta_{hl} - \min_l \beta_{hl} \right)}$$

where $RI_k$ is the relative importance of attribute $k$, the numerator is the range of its part-worths and the denominator sums the ranges of all $K$ attributes.

The ratio of two part-worths gives a marginal rate of substitution. If attribute $b$ is continuous, the change in $b$ that offsets a one-unit change in attribute $a$ is given below.

$$\Delta x_b = -\frac{\beta_a}{\beta_b}$$

where $\Delta x_b$ is the offsetting change in $b$, and $\beta_a$ and $\beta_b$ are the part-worths of one-unit changes in $a$ and $b$. With cost as $b$, the ratio is read as willingness to pay, but it is a welfare measure only for choice data analysed under random utility theory; Louviere, Flynn and Carson describe its use in rating-based studies as ad hoc. Ryan and Farrar used waiting time instead of cost. The 73 consistent traders retained from 157 completed questionnaires would accept about 1.3 extra months of waiting (0.77 divided by 0.59) for a local first orthodontic appointment rather than one in hospital.

Worked example of ratings-based part-worths for an outpatient clinic

The figures are hypothetical. A health board redesigning a follow-up clinic uses three two-level attributes, namely waiting time (4 or 12 weeks), location (hospital or local) and clinic lead (consultant or specialist nurse). The full factorial gives eight profiles, which one patient rates from 0 to 10. Coding is $W = 1$ for a 12-week wait, $L = 1$ for a local clinic and $N = 1$ for a nurse-led clinic, and 0 otherwise.

1. Estimate the part-worths. In a balanced orthogonal design each least-squares coefficient equals the difference in mean ratings between the two levels of its attribute, as follows.

$$\hat{\beta}_W = \bar{R}_{W=1} - \bar{R}_{W=0} = 3.25 - 6.25 = -3.00$$

where $\bar{R}_{W=1}$ is the mean rating of the 12-week profiles, (3 + 4 + 2 + 4) / 4, and $\bar{R}_{W=0}$ that of the 4-week profiles, (6 + 8 + 5 + 6) / 4. Likewise the local clinic part-worth is 5.50 minus 4.00, or +1.50, and the nurse-led part-worth is 4.25 minus 5.25, or -1.00. The mean rating is 4.75 and each dummy equals 1 in half the profiles, so the intercept is calculated as follows.

$$\hat{\beta}_0 = 4.75 - 0.5 \times (-3.00 + 1.50 - 1.00) = 4.75 + 1.25 = 6.00$$

where $\hat{\beta}_0$ is the predicted rating of the reference profile, which is a 4-week wait, in hospital, led by a consultant.

2. Check the fit. Fitted ratings match profiles 1, 2, 5 and 6 and miss the others by 0.5, so the residual sum of squares is 1.0 against a total of 25.5, which gives the fit below.

$$R^2 = 1 - \frac{1.0}{25.5} \approx 0.961$$

where $R^2$ is the share of rating variation explained by the additive model. Only four degrees of freedom remain, so real studies use more profiles per respondent or pool respondents.

3. Relative importance. The ranges are 3.00, 1.50 and 1.00, so the share for waiting time is calculated as follows.

$$RI_W = \frac{3.00}{3.00 + 1.50 + 1.00} = \frac{3.00}{5.50} \approx 0.545$$

where $RI_W$ is waiting time's share of the total range. Location takes 27.3% and clinic lead 18.2%.

4. Trade-offs in weeks. If value falls linearly between the two waits, the part-worth per week is calculated as follows.

$$\hat{\beta}_{week} = \frac{-3.00}{12 - 4} = -0.375$$

where $\hat{\beta}_{week}$ is the change in rating per extra week. The wait that offsets a local clinic is then as follows.

$$\Delta x_{wait} = -\frac{1.50}{-0.375} = 4.0$$

where $\Delta x_{wait}$ is the extra weeks this patient would accept to be seen locally. Keeping a consultant lead is worth about 2.7 weeks (1.00 divided by 0.375).

5. Interpretation. For this patient a local nurse-led clinic with a 4-week wait (predicted 6.5) beats the reference hospital consultant clinic with the same wait (6.0), but not if the wait rises to 12 weeks (3.5). These trade-offs rest on treating the scale as interval and on linearity between two observed waits, neither of which the data can test.

Conjoint analysis or discrete choice experiment

Whether choice tasks belong in the family is the main naming dispute. The ISPOR statistical report calls the discrete choice experiment the most common type of conjoint analysis in outcomes research.

Louviere, Flynn and Carson argued in 2010 that discrete choice experiments are not conjoint analysis. In their account traditional conjoint analysis rests on conjoint measurement, a mathematical theory about how numbers behave under factorial manipulation with no error theory, whereas discrete choice experiments rest on random utility theory, which goes back to Thurstone's 1927 work and was extended by McFadden. They argue that ratings do not translate readily into the choice data on which utility theory is based and that many studies claiming to be conjoint analyses are discrete choice experiments, and report that health economists stopped calling choice studies conjoint analyses in the late 1990s.

Hauser and Rao, writing from marketing, describe stated choice models as having all the characteristics of conjoint analysis except the data collection format. The dispute is partly about substance, since only choice data under a random utility model support welfare measures. The family name is used here as the ISPOR reports use it, and random utility models are treated on the choice experiment page.

Outcome weights in health technology assessment and device regulation

Conjoint results reach health decisions mainly as weights for combining outcomes and as evidence on how patients trade benefits against harms. Ryan and Farrar add service uses, such as scoring ways of providing care.

In health technology assessment, Germany's Institute for Quality and Efficiency in Health Care (IQWiG) piloted choice-based weights for its efficiency frontier in 2014, as described on the choice-based conjoint page. IQWiG's General Methods (version 7.0, 2023, section 4.3.3) state that results for several outcomes can be weighted using preference elicitation methods whose applicability is the subject of scientific debate, and that a health economic evaluation under section 35b of Social Code Book V does not include preference surveys conducted by the institute. Surveys submitted in a dossier can be assessed, depending on the commission, provided they contain the outcomes to be considered in the evaluation. Such preference-based outcome weights combine results within a multi-criteria decision analysis and are not the health state utilities behind a QALY.

In device regulation, the US Food and Drug Administration's 2026 guidance on patient preference information cites the ISPOR conjoint analysis checklist and names preference weights and maximum acceptable risk among parameters that can support a benefit-risk assessment.

Where conjoint results mislead

Most errors come from treating outputs as fixed properties of people when they depend on the design and the task. Relative importance depends on the levels chosen, so a 26-week maximum wait would raise waiting time's share in the worked example. Green and Srinivasan report that importance also rises when levels are added between a fixed minimum and maximum; adding two intermediate price levels raised price's importance by seven percentage points in one study.

Ratings-based trade-offs treat the rating scale as cardinal, an assumption Louviere, Flynn and Carson suggest avoiding by using only the order information in ratings; they add that main-effects designs assume untestable additivity and that many conjoint validity tests are hold-out predictions, not comparisons with real behaviour. In a 2011 editorial, Ryan wrote that internal validity tests dominate in health given the lack of a market for health care, called external validity the greatest challenge, and warned that too many attributes may push respondents to rules such as always choosing the cheapest option. Ryan and Farrar dropped inconsistent respondents and non-traders and flagged possible bias. The ten-item ISPOR checklist offers a standard for judging a health conjoint study without endorsing any one method.

Sources

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