This valuation study was conducted following the International Valuation Protocol of the EQ-5D-Y-3L and reported according to the Checklist for Reporting Valuation Studies of the EQ-5D (CREATE) [30, 46]. Details of the CREATE can be found in the Supplementary Information 1. A two-step valuation approach using independent surveys with different samples and modes of administration was conducted in this study: an online structured self-completed survey with discrete choice experiment (DCE) tasks and face-to-face computer-assisted personal interviews with cTTO tasks. The language of DCE and cTTO surveys was Brazilian Portuguese. Both surveys included information on the study, informed consent, three introductory questions (i.e., age, gender, and experience with severe illness), the self-reported version of the EQ-5D-Y-3L, the valuation task, feedback questions, and complementary questions (e.g., educational level, marital status, socioeconomic level, religious beliefs, general health, health conditions, and pain conditions).

This study was approved by the Human Ethics Committee of the Universidade Cidade de São Paulo (UNICID) (CAAE: 45241321.6.0000.0064). DCE and cTTO surveys were conducted in a sample of adults aged 18 years or above from the general population who provided informed consent to participate in this study. The respondents were adults asked to do the tasks considering a child’s perspective (i.e., adults imagined the health state of a 10-year-old child). This choice was made on the basis of previous studies to possibly avoid ethical issues associated with the consideration of dead if a sample of children was used [27, 44].

This study used the Brazilian Portuguese version of the EQ-5D-Y-3L [6]. The EQ-5D-Y-3L is a child-friendly version adapted from the EQ-5D-3L instrument for measuring general health-related quality of life. The EQ-5D-Y-3L is composed of two parts: a descriptive system and a Visual Analog Scale (EQ-VAS). The descriptive system consists of five dimensions with appropriate age wording: walking about (mobility), looking after myself (self-care), doing usual activities (usual activities), having pain or discomfort (pain/discomfort), and feeling worried, sad, or unhappy (anxiety/depression). Each dimension has three levels of severity: (1) no problems/no pain or discomfort/not worried, sad, or unhappy; (2) some problems/some pain or discomfort/a bit worried, sad, or unhappy; and (3) a lot of problems/a lot of pain or discomfort/very worried, sad, or unhappy [6]. The responses generate a five-digit numeric code that expresses the child’s health state ranging from 11111 (full health, representing no problems in any domain) to 33333 (the worst health state, representing a lot of problems in all domains), totalizing 243 health states. The EQ-VAS ranges from 0 to 100, where 0 represents “the worst health state you can imagine” and 100 represents “the best health state you can imagine” [6].

The DCE and cTTO tasks were conducted using the EuroQol Valuation Technology (EQ-VT) software (v2.1) [28]. Two valuation methods were used in this study: DCE and cTTO. The DCE and cTTO tasks were collected in two samples considering the perspective of the respondents for a 10-year-old child. In the DCE tasks, respondents expressed their preference between two different EQ-5D-Y-3L health states, classified as options A or B, and no specification of the duration of living in the health states was included [30].

The cTTO task consisted of a conventional time trade-off to elicit values for the health states considered “better than dead” (i.e., 10-year time trade-off) and a lead-time to elicit values for the states considered “worse than dead” [47] (i.e., 20-year time trade-off, 10 years in full health followed by 10 years in the health state), in which, the lowest tradable time trade-off was 6 months. Thus, respondents were asked to trade-off life-years in one hypothetical situation to identify the number of life-years in full health, where they would be indifferent for a kid to be living a shorter period of life-years in full health and a longer period of life-years in a specific health state [26, 30]. In this hypothetical situation, the respondent can prefer “life A,” “life B,” or consider “life A and B about the same” [26]. “Life A” corresponds to living with full health for a few years before death, and “life B” corresponds to living with full health before living a few years in a hypothetical health state from the EQ-5D-Y-3L before death [26]. Depending on the answer, the time of full health in “life A” changed, and the task finished when the respondent answered that “life A and B are about the same” (i.e., respondent’s point of indifference).

The DCE design consisted of 150 pairs of health states distributed over 10 blocks of 15 pairs. Each respondent was randomly allocated to complete one of the ten blocks. The order of the health state pair presentation and right/left presentation was randomized in each block. A two-dimension overlap was imposed for all pairs. Thus, the health states in each pair presented two dimensions with the same level of severity and three dimensions with different levels of severity. To help responders identify the differences between health states and reduce attribute non-attendance, a bold font was applied in the dimensions with level overlap [48]. The bold font was used as there is no color coding in the International Valuation Protocol [30]. Each respondent also completed three fixed dominant pairs for quality control. These dominant pairs were presented in the first pair, in the last pair, and at a random point. A dominant pair represents the health state that was always obviously better than the other (e.g., three dimensions with equal severity levels and two with worse severity levels). Thus, each respondent completed a total of 18 DCE tasks (15 health state pairs for valuation and three dominant pairs for quality control that were extensions of minimum requirements of the International Valuation Protocol). As DCE generates values on a latent scale, another valuation method is needed to anchor the utilities ranging from 1 to 0, where 1 represents “full health”, 0 represents “dead”, and negative values represent health states considered “worse than dead” [30]. The anchored utilities were developed through the cTTO task. The samples of the DCE and cTTO tasks were different, and those answering one did not participate in the other.

In the cTTO design, an orthogonal design including 18 health states was used [49, 50]. In addition to the orthogonal array, we considered the worst health state (33333), five mild health states (21111, 12111, 11211, 11121, and 11112), and four moderate health states to maintain near-orthogonality. In this study, the cTTO design consisted of 28 health states divided into 3 blocks of 10 health states (i.e., 9 health states per block, and the worst health state “33333” were included in all blocks). At least one mild health state was included in each block. Each respondent was randomly allocated to complete one of the three blocks. The order of the health states was also randomized. Before respondents completed the ten health states for the valuation study, each respondent valued two wheelchair examples considering a situation better than dead and another worse than dead, as well as three health states: a mild (21112), a severe (32323), and a health state difficult to imagine (13311). After the cTTO tasks, a ranking with all ten health states was presented to the respondents as an opportunity to verify if they agree with the rank ordering that is inferred from their responses. If necessary, inconsistencies flagging one or more cTTO valuations could be detected at this stage [51]. The average time for completing the cTTO task was around 60 min.

The International Valuation Protocol for the EQ‐5D‐Y‐3L [30] recommends sample sizes of 1000 respondents for the DCE survey and 200 respondents for the cTTO survey. For the DCE, the respondents were recruited from general population, considering the proportional distribution of Brazilian regions according to the Brazilian Institute of Geography and Statistics (Instituto Brasileiro de Geografia e Estatística—IBGE) data (i.e., of the total sample, 8.9% were recruited from north region, 27% from northeast region, 7.8% from central-west region, 14.3% from south region, and 42% from southeast region) [52]. For the cTTO, the respondents were recruited from the general population in three urban centers from three Brazilian states: Sao Paulo (69.5% of the total sample, representing the southeast region), Rio Grande do Sul (17% of the total sample, from Rio Grande do Sul, representing the south region), and Ceara (27% of the total sample, representing the northeast region) states [52]. The total population from all these three urban centers represents 31.6% of the whole Brazilian population. Additionally, the population from Sao Paulo consisted of 45.5% immigrants from other Brazilian states, showing good cultural representativeness from different states of Brazil [53]. Furthermore, quotas were used for age (18–24 years, 25–34 years, 35–44 years, 45–54 years, 55–64 years, > 65 years), sex (male and female), educational level (primary, middle, and high), and socioeconomic level based on the household income per month according to the Brazilian Association of Survey Companies [classification ranges from A to D/E, as A represents a household higher than $9678 (R$25,000)/month and D/E represents a household lower than $278 (R$719)/month] [54]. All quotas were considered for the recruitment of both surveys (DCE and cTTO).

Respondents were invited through a recruitment panel company for both surveys (DCE and cTTO). In the DCE approach, the respondents received a unique link by e-mail to access the DCE task. In the cTTO, the respondents were asked to attend a face-to-face interview at the local university according to their geographical location (e.g., Universidade Cidade de São Paulo in the Southeast region; Universidade Federal de Ciências da Saúde de Porto Alegre in the South region; and Universidade Federal do Ceará in the Northeast region). The interviews were conducted in private rooms and the respondents received a compensation for their transport and a food voucher.

The cTTO interviews were conducted by five interviewers, all of them working in research positions in the health area. Principal investigators of this study (GCM and TPY) received training from the EuroQol group on the valuation methods, EQ-VT protocol, and the quality control procedure. After the training, each principal investigator conducted ten pilot interviews with family and friends before offering standardized training for the interviewers. Interviewers received a 1-day hybrid training and a written script on the cTTO approach in Brazilian Portuguese. After the interviewers’ training, each interviewer conducted 10 pilot interviews with family and friends followed by 20 pilot interviews with the general population (assuring diverse socioeconomic and level educational background) before the data collection commenced. Although not all interviewers conducted 40 interviews in data collection because they were in Ceara and Rio Grande do Sul states (which needed a smaller number of interviews compared Sao Paulo state), our three interviewers from Sao Paulo state [CMES (n = 50), (VSS n = 49), and GCM (n = 40)] completed the interviews. Our interviewers had intensive training in conducting more pilot interviewers when compared to other conventional studies, and the data collection started when we reached an adequate quality of the interviewers following the quality control criteria from the EuroQol. Thus, we ensured that all interviewers (background in health area) had sufficient training and were guided by the principal investigators and also by the EuroQol group to maintain the quality of the interviews. During the pilot interviews and data collection, the interviewers shared their experiences as a group, and the principal investigators provided daily feedback on their performance. During data collection period, each interviewer performed a maximum of ten interviews per week to not overload the capacity of each interviewer. Data collection of the DCE and cTTO was performed from October to December 2022.

According to recommendations from previous studies, all respondents in the DCE tasks who failed in any of the three dominant tasks (i.e., respondents preferred the obviously worse health state), and those “fast respondents” (i.e., respondents completed the DCE survey in less than 150–8.3 s/DCE task) were excluded from the final sample [28, 39, 51].

The quality control process consists of two main steps: (1) ensuring the protocol compliance and (2) investigating the presence of interviewer effects. In the first step (protocol compliance), we assessed four main criteria: (1) whether there was no explanation of the worse than dead task (lead-time) on the wheelchair example to each respondent; (2) whether a short time was spent on explaining the wheelchair examples (less than 3 min); (3) whether a short time was spent to complete all cTTO tasks (less than 5 min total time for completing the ten health states); and (4) whether there was any inconsistency in the cTTO responses (i.e., 33333 should be the lowest or at least 0.5 value higher than the health state with the lowest value) [51]. If at least one of the four criteria was met, the interview was flagged as an indication of potential poor quality. In the second step (presence of interviewer effects), we have monitored interviewer effects to ensure the data quality. The quality of the cTTO data was assessed every ten completed interviews (by each interviewer), using the quality control process defined by the EuroQol group [51]. The quality control process assesses interviewers’ performance related to interviewer effects and cTTO protocol compliance. Every week the data quality was discussed with the EQ-VT support team until completing cTTO data collection. After EQ-VT support team considerations, every week, the principal investigators discussed feedback on the performance and quality of the interviews with each interviewer to improve their skills.

All statistical analyses were conducted with STATA v.15 (StataCorp, College Station, Texas, USA). Descriptive analysis was used to describe the characteristics of the respondents, the descriptive system of the EQ-5D-Y-3L, the EQ-VAS, and the cTTO values. Statistical analyses were conducted in two steps. In the first step, two different models were used to estimate the DCE values on a latent scale derived from the DCE responses, namely (1) a conditional logistic model and (2) a mixed-logit model. The DCE model was estimated using a mixed-logit model as it handles unobserved preferences heterogeneity by allowing the model parameters to vary across individuals [55]. The dependent variable was coded as 1 for the chosen option in each DCE task (e.g., ‘life A’) or as 0 for the alternative (e.g., ‘life B’). Dummy variables for response levels 2 and 3 in each EQ-5D-Y-3L dimension were included as covariates in both models. Bayesian Information Criteria (BIC) was used to select the best DCE model [56]. The coefficients derived from both models were used to calculate the predicted DCE values for all 243 health states of the EQ-5D-Y-3L (i.e., the DCE values).

In the second step, a mapping function was used to map the predicted DCE values onto the mean observed cTTO values for the 28 health states in the cTTO design exploring two mapping approaches: linear mapping (Eq. 1) and non-linear mapping (Eq. 2). The mapping function consisted of a regression model to identify the relationship between the predicted DCE values for the 243 health states and the mean observed cTTO values for the 28 health states considered in the cTTO survey design [36, 37, 57].

$$V_}} = \gamma_ + \gamma_} V_}}$$

(1)

$$V_}} = \gamma_ + \left( } V_}} } \right)^$$

(2)

“VcTTOh” is the mean observed cTTO value for health state “h”, “VDCEh” is the predicted DCE value for the same health state “h”, “γ0” is the regression intercept, “γ1” is the slope between the cTTO and DCE values, and “δ” is a power parameter that may adjust for any possible non-linearity in the relationship between cTTO and DCE data. Linear and non-linear mapping models with and without intercept (including or excluding γ0, respectively) were applied. We structured the cTTO and DCE values as “disutilities” instead of “utilities” to facilitate the analysis (i.e., the cTTO and DCE values were scaled with 0 being the lowest value and least disutility, and the other values that were positive indicated greater disutility). To estimate the utilities of the 243 EQ-5D-Y-3L health states, we rescaled the coefficients of both DCE models based on rescaling parameters (i.e., the coefficients of the mapping approaches were considered with and without intercept) [58]. The intercept in the mapping model indicates an estimated mean utility when all EQ-5D health dimensions are zero. In general population samples, a relatively high proportion of responders score no problems in all EQ-5D dimensions leading to a large intercept, which can result in a gap between full health and the second-best health state. To partially deal with this gap, the mapping can be performed without the intercept in which utility decrements depend only on health dimensions coefficients size [59]. The preferred mapping approach was selected based on model fit. A relatively higher R2 and a lower Akaike Information Criteria (AIC) value, root mean squared error (RMSE), and mean absolute error (MAE) indicate a better model fit and thus prediction accuracy [58].