Valuation of EQ-5D-3l Health States in Slovenia: VAS based and TTO based Value Sets

The study was a multicentre, population-based study, using face-to-face interviews. The sample was prepared by the Statistical Office of Slovenia using the Central Population Register. In the sample, 1,000 individuals aged 18+ from 40 Slovenian municipalities were included. At the first level, 40 municipalities were randomly selected and later on 25 individuals were selected from each municipality. Each person carried a name, last name, address, house number, postcode, municipality, age and gender. The investigators started the interviews in September 2005 and finished in April 2006. Participant recruitment was conducted primarily through landline telephone numbers for each participant in the sample. 225 participants agreed to participate in the survey. Interviews were conducted by three interviewers, who underwent one-day training on the health state valuations, the purpose of the interviews and TTO procedures. To facilitate the training, the interview book prepared by Gudex (14) was translated into Slovenian language and used for training of the interviewers and in the pilot training. Each investigator conducted 5 test interviews.

EQ-5D consists of a descriptive system and EQ visual analogue scale (EQ-VAS). The EQ-5D descriptive system consists of 5 dimensions: mobility (MO), self-care (SC), usual activities (UA), pain/discomfort (PD), and anxiety/depression (AD). Each dimension has 3 levels: no problems, some problems, and extreme problems (9). The respondent is asked to indicate his or her health state by ticking the box that marks the most appropriate level of problems in each dimension. A unique health state can be described by using a 5-digit vector formed according to the responses to the 5 questions. For example, no problems in MO and SC, some problems in UA and PD and extreme problems in AD can be referred to as “11223.” Health states defined in this way may be converted into a single summary index by applying a formula that attaches values to each of the levels in each dimension. A total of 243 possible health states can be defined.

In the valuation task, each investigator had 3 sets of health states, and investigators decided randomly which set to use with each respondent. The sets were named A, B and C. Each set contained 15 health states. Some health states were included in all three sets, but some were not. Health states in each set represent the complete scale of health states, from worst to best health states. Sets B and C were developed in 2000 (16). The number of all various directly valued health states in all three sets is 23 plus unconscious and dead. These states are 11211, 11111, 21111, 12111, 11112, 11121, 11122, 11113, 11131, 11133, 11312, 13311, 32211, 22222, 21232, 22323, 22233, 32223, 32313, 23232, 33321, 33323, 33333, unconscious and dead. Health states can also be divided into mild, moderate and severe states (17) in such a way that all the categories were represented in all three sets.

The questionnaire consists of four parts. In the first part, the respondent indicated his/her own health state on the day of the interview using an EQ-5D descriptive system. Furthermore, the respondent marks how good or bad his/her health state is on a visual analogue scale (VAS) from 0 to 100 (where 0 represents the worst health state imaginable and 100 represents the best health state imaginable).

The second part of the questionnaire is a valuation of the 15 selected health states. Once the respondent had familiarised himself/herself with the health states by reading them, he/she ranked the selected states from worst to best. After ranking he/she attached the value from 0 to 100 to all 15 health states.

The third part of the interview is the valuation of the same selected 15 health states using time trade off (TTO) method. The interviewers follow the adapted Measurement and Value of Health study (MVH) protocol (14). The MVH study was a large exercise, in which 3,395 respondents valued 13 different health states. Because of the limited budget, we included 23 health states altogether. Out of 23 health states, we made three different sets of 15 health states (sets A, B and C) as described in Chapter 2.3.

The objective of the TTO is to determine the length of lifetime the respondent would be willing to forego to live in a better health state (typically ‘full health’) and to avoid living in a bad health state. This is achieved by presenting respondents with a series of choice tasks, each involving two alternative hypothetical lives. The two lives are presented so that the respondent is forced to choose between a longer life in the health state of interest and a shorter life in better health (15).

The last part of the interview collects social demographic data: gender, age, education, work experience, smoking habits, experience with illness and postcode.

In the TTO procedure, the interviewers used a TTO board and a set of health state cards. A TTO board was made of three layers of thick cardboard and incorporated a sliding scale from 0 to 10 years. Both sides of the board were used, one for states better than dead and the other for health states worse than dead. The respondent was taken through each of 15 health states to be valued, one at a time, with the interviewer moving the scale as appropriate. The respondent needed to make a series of choices between two hypothetical lives: one involving x years of healthy life, followed by death (Life A) and the other involving t years in a worse health state (where x≤t), followed by death (Life B). Time t was fixed, whereas time x was varied until the respondent reached their point of indifference. This iterative procedure continued until the respondent was unable to choose between the two lives. In our study, the respondent started with a choice between living Life A (health state 11111) for 10 years followed by death and living Life B (worse health state) for 10 years followed by death. Life A was chosen – the next choice was between Immediate Death (x=0 for Life A) and 10 years of Life B, followed by death. In the next choice, x was set at 5 years; in case Life A was chosen, x was decreased and the opposite until the point of indifference was found. The value of Life B was calculated according to how much healthy time the respondent was willing to forgo at this point of indifference – the utility value of the health state was at this point calculated as x/10. In case of states worse than dead, the respondent was again given two alternatives, but this time Life A was a combination of health state I for y number of years followed by full health for x number of years (x+y=10), followed by death. Life B was a certain outcome of immediate death. Time x was again varied until the respondent was indifferent between both alternatives. At this point, the utility value for health state I was calculated as –x/(10-x). Respondents were allowed to trade time in months and weeks.

In VAS procedure, the respondents ranked the health states and, in the second phase, attached them a value from 0 to 100. VAS values were later rescaled using the mean observed values for state 11111 and death. Health state “Unconscious” was not used.

Historically, values for EQ-5D-3L have been modelled by use of ordinary least squares (OLS) regression, using dummy variables representing the presence or absence of different levels of problems on each of the five dimensions. Built on this framework, different interaction terms have been added in different national valuation studies. More recently, the introduction of the EQ-5D-5L has resulted in a range of innovations in terms of modelling, including hybrid models combining TTO and DCE data (24), random intercept models, censored/interval regression to account for censoring at −1, and use of constrained, non-linear regression models (18, 22, 23).

For EQ-5D-3L, the standard, additive 10-parameter model, hereafter referred to as ADD10, has parameters representing levels 2 and“ 3 for each dimension. Let y represent the observed disutility of a health state, represent x_dl the dummy variable indicating the presence of problems on dimension d at level l and β_dl the coefficient representing the estimated disutility of having problems on dimension d at level l (e.g. β_MO3 representing the disutility of having moderate problems on mobility). The mathematical function of ADD10 is as follows: (1)y=∑l∑dβdlxdl+e=βMO2xMO2+βSC2xSC2+βUA2xUA2+βPD2xPD2+βAD2xAD2+βMO3xMO3+βSC3xSC3+βUA3xUA3+βPD3xPD3+βAD3xAD3+e\begin{array}{l}y = \sum\nolimits_l {\sum\nolimits_d {{\beta _{dl}}{x_{dl}} + e} } \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\beta _{MO2}}{x_{MO2}} + {\beta _{SC2}}{x_{SC2}} + {\beta _{UA2}}{x_{UA2}} + {\beta _{PD2}}{x_{PD2}} + {\beta _{AD2}}{x_{AD2}} + {\beta _{MO3}}{x_{MO3}}\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + {\beta _{SC3}}{x_{SC3}} + {\beta _{UA3}}{x_{UA3}} + {\beta _{PD3}}{x_{PD3}} + {\beta _{AD3}}{x_{AD3}} + e\end{array}

An EQ-5D-3L variant of the constrained model approach used in the Chinese and Malaysian EQ-5D-5L valuation studies employs six primary parameters: one for each dimension, representing the disutility of having problems at level 3 (β_MO,β_SC,β_UA,β_PD,β_AD), which for level 2 are multiplied by parameters for level 2 (L2). Thus, the disutility of having moderate problems on mobility is β_MO × L₂. The mathematical function of this model, hereafter MULT6, is as follows (note that x_dl still represents the dummy variable representing the presence of problems on dimension d at level l): (2)y=∑l(∑dβdxdl)Ll+e=(βMO2xMO2+βSC2xSC2+βUA2xUA2+βPD2xPD2+βAD2xAD2)L2+βMO3xMO3+βSC3xSC3+βUA3xUA3+βPD3xPD3+βAD3xAD3+e\begin{array}{l} y = \sum\nolimits_l {(\sum\nolimits_d {{\beta _d}{x_{dl}}){L_l} + e} } \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = ({\beta _{MO2}}{x_{MO2}} + {\beta _{SC2}}{x_{SC2}} + {\beta _{UA2}}{x_{UA2}} + {\beta _{PD2}}{x_{PD2}} + {\beta _{AD2}}{x_{AD2}}){L_2}\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + {\beta _{MO3}}{x_{MO3}} + {\beta _{SC3}}{x_{SC3}} + {\beta _{UA3}}{x_{UA3}} + {\beta _{PD3}}{x_{PD3}} + {\beta _{AD3}}{x_{AD3}} + e \end{array}

This constrained model assumes that the relative severity of level 2, “moderate problems”, is similar across dimensions. This assumption reduces the number of parameters to be fitted, and thereby provides more robust results than unconstrained models, particularly with smaller samples of data.

We tested the ADD10 and MULT6 models, with and without the inclusion of a constant term (intercept) representing any deviation from full health. The model variants including intercept are denoted with an “i”, e.g. ADD10i. We also tested an extension of MULT6 in which the full expression is exponentiated by a separately fitted parameter P: (3)y=((βMO2xMO2+βSC2xSC2+βUA2xUA2+βPD2xPD2+βAD2xAD2)L2+βMO3xMO3+βSC3xSC3+βUA3xUA3+βPD3xPD3+βAD3xAD3)p+e\begin{array}{l} y = (({\beta _{MO2}}{x_{MO2}} + {\beta _{SC2}}{x_{SC2}} + {\beta _{UA2}}{x_{UA2}} + {\beta _{PD2}}{x_{PD2}} + {\beta _{AD2}}{x_{AD2}}){L_2} + {\beta _{MO3}}{x_{MO3}}\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, + {\beta _{SC3}}{x_{SC3}} + {\beta _{UA3}}{x_{UA3}} + {\beta _{PD3}}{x_{PD3}} + {\beta _{AD3}}{x_{AD3}}{)^p} + e \end{array}

This model, hereafter MULT6P, was included under the assumption that respondents may display diminishing sensitivity to health problems when combined, so that the perceived disutility of problems on two separate dimensions at the same time may be smaller than the sum of the disutility of each problem in isolation.

Standard error estimation is non-trivial in regression models involving multiplication of two or more (presumably normally distributed) parameters. Consequently, standard errors for model parameters and modelled values were estimated for MULT6 and MULT6P using bootstrapping (22). Briefly, 10,000 bootstrap samples were drawn (with replacement) at the level of individual study participants, each subsample of the same size as the observed data. The regression models were fitted to each bootstrap sample, and standard errors were calculated by taking the standard deviation for the resulting coefficients and the predicted health state values.

Given the limited number of valued health states, and the relatively small sample size used in this study, we were concerned that regular regression models might produce results that were highly susceptible to random error. We, therefore, tested the included model variants using penalised regression, including Lasso (20), Ridge regression (17,18,19), and Elastic net (21).

Model selection was informed by two primary criteria, being monotonicity/logical consistency. Modelled state values should reflect the hierarchical structure of the EQ-5D descriptive system, so that further problems on any dimension should always result in worse (lower) values. Monotonic models were compared in terms of out-of-sample predictive accuracy for observed means. This was compared using leave-out-by-state cross-validation (18, 22). Predictive accuracy was assessed in terms of mean square difference between out-of-sample predictions and corresponding observed means, as well as Lin’s Concordance Correlation Coefficient.

The final Slovenian TTO model was compared visually to the Polish EQ-5D-3L value set (25) and the UK MVH value set (26), and the final VAS model was compared visually to the EU VAS value set (27).

All statistical analyses were performed in the R statistical package, version 3.3.2, in the RStudio environment, using ggplot for graphical output (28,29,30). Regression models were run in the xreg package (31).