Study design and samples

This study used data from the project “EQ-5D-3L and EQ-5D-5L population norms in Thailand [38].” A cross-sectional survey was conducted using face-to-face interviews with 2,000 Thai adults. To ensure national representation, a four-stage stratified random sampling method was applied to select provinces, districts, sub-districts, and villages. Data were collected from 12 provinces, representing all geographic regions of Thailand: Bangkok, Samut Prakan, Nonthaburi, Chonburi, Nakhon Pathom, Chiang Mai, Nakhon Sawan, Nakhon Ratchasima, Khon Kaen, Buriram, Nakhon Si Thammarat, and Phatthalung.

Participants were eligible if they (1) were aged 18 years or older, (2) were able to understand the interview process as assessed by the researcher or trained interviewers, and (3) were fluent in Thai. Individuals with acute or life-threatening illnesses or severe cognitive impairments were excluded.

Data collection procedures

Trained interviewers read all questions and response options verbatim, and did not provide explanations or interpretations to minimize interviewer bias. All participants completed both the SF-12v2 and EQ-5D-5L questionnaires, with no missing responses. These face-to-face interviews with eligible participants were conducted at their home residences between 1^st May to 30^th June 2023.

Before data collection, participants received an information sheet outlining study objectives, procedures, and their rights to withdraw without consequences. Written informed consent was obtained from all participants. Questionnaires were administered in the following order: (1) demographic information, (2) EQ-5D-5L, and (3) SF-12v2. Details of the demographic variables are reported elsewhere [38]. The protocol and data collection process were approved by the ethical committees of Burapha University Institutional Review Board (IRB1–031/2566) and adhered to the principles outlined in the Declaration of Helsinki.

Source and target measures

SF-12v2 (source measure).

The SF-12v2 consists of 12 items grouped into eight subscales: physical functioning (PF: 2 items), role limitations due to physical problems (RP, 2 items), bodily pain (BP, 1 item), general health (GH, 1 item), vitality (VT, 1 item), social functioning (SF, 1 item), role limitations due to emotional problems (RE, 2 items), and mental health (MH, 2 items) [39]. Participants rated their health over a four-week recall period. Most items use a five-point Likert scale, except PF items, which use a three-point scale. Four items (GH1, BP1, VT1, MH1) were reverse-coded to ensure scoring consistency. Table 1 displays descriptions of the SF-12v2 items.

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Table 1. Descriptions of the SF-12v2 items.

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Subscale scores were transformed to a 0–100 scale, with higher scores indicating better health [39]. The Physical Component Summary (PCS) and Mental Component Summary (MCS) scores were calculated using a proprietary scoring algorithm to generate norm-based scores. SF-12v2 responses were also reclassified to derive SF-6D health states, allowing utility score estimation using the UK algorithm, with scores ranging from 0.29 to 1.00 [40].

Conceptual overlap between EQ-5D-5L and SF-12v2

Conceptual overlap between the EQ-5D-5L and the SF-12v2 was examined using Spearman’s rank-order correlation analysis. Pairwise correlation coefficients (r) were calculated between each SF-12v2 item and subscale score and each EQ-5D-5L dimension, as well as the overall EQ-5D-5L utility score.

An SF-12v2 item or subscale demonstrating at least a moderate correlation (r 0.4) with any EQ-5D-5L dimension or the utility scores was deemed to exhibit conceptual overlap [42]. Items and subscales meeting the criterion were subsequently selected as candidate independent variables for inclusion in the predictor set of the regression models.

Modeling approaches

Table 2 shows four predictor sets based on SF-12v2 dimensions and items in both direct and indirect mapping approaches. The explanatory variables were initially screened based on Spearman’s correlation between the SF-12v2 items/subscale scores and utility scores. The explanatory variables with p < 0.25 in the forward stepwise regression were included in the predictor sets. Furthermore, age was included as a covariate in all models due to its significant association with EQ-5D-5L utility scores and to reduce potential confounding effects. Accordingly, four predictor sets comprising subscale scores, polynomial transformation of subscale scores, and selected SF-12v2 items modeled as either continuous or categorical variables were evaluated using both mapping approaches.

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Table 2. Four predictors sets based on SF-12v2 dimensions and items for direct and indirect mapping.

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A direct mapping approach was applied to predict EQ-5D-5L utility scores from SF-12v2 items and subscale-level scores. Multiple regression models were estimated, including OLS, Tobit, CLAD, GLM, TPM, ALDVMM, and Betamix. These models were selected based on their capacity to accommodate key features of EQ-5D-5L utility data, including boundedness, skewness, multimodality, and the discontinuity between the second-best and full-health states inherent in the Thai-specific value set.

In all direct mapping models, the EQ-5D-5L utility score served as the dependent variable, while SF-12v2 item/subscale scores and participant age were included as independent variables. For GLM and TPM specifications, disutility scores (1 – utility) were modeled to satisfy the non-negativity assumption of these approaches [43,44].

The modified Park test indicated that both Poisson and Gamma variance functions were plausible for the disutility outcome, as the estimated Gamma coefficient lay between 1 and 2 [45]. Based on Box-Cox regression results, a logarithmic link function was identified as optimal for both GLM and TPM models across all predictor sets [46].

Tobit and CLAD models were estimated to account for right-censoring, with utility scores censored at the upper bound of 1.0000 [31]. In contrast, ALDVMM and beta mixture models explicitly accommodated the multimodal distribution of utility scores while constraining predictions to the feasible utility range [37]. Accordingly, these models imposed lower and intermediate constraints at −0.4212 (worst health state) and 0.9436 (second-best health state), with truncation at 1.0000 for full health. Both mixture models were restricted to single-component specification, as models with additional components failed to converge across most predictor sets.

For the indirect mapping approach, each EQ-5D-5L dimension was modeled separately as a dependent variable, with SF-12v2 item/subscale scores serving as predictors. To estimate response-level probabilities, generalized ordered logistic (GOLOGIT), ordinal logistic (OLOGIT), or multinomial logistic (MLOGIT) models were evaluated.

GOLOGIT models failed to converge, and OLOGIT models were deemed inappropriate due to violations of the proportional odds assumption, indicating that predictor effects varied across response levels. Consequently, MLOGIT was selected as the final modeling strategy.

Using the most-likely-probability method, MLOGIT generated the most probable response level for each EQ-5D-5L dimension, producing a five-digit health-state profile that was subsequently converted into a utility score using the Thai-specific value set.

Notably, predicted utility scores were truncated at the theoretical boundaries of the Thai EQ-5D-5L value set when estimated values exceeded the feasible utility range. Specifically, values greater than 1 were truncated to the upper bound of 1.0, while values less than –0.4212 were truncated to the lower bound of –0.4212.

Model performance

Model performance was evaluated using ten-fold cross-validation (CV), whereby the dataset was randomly partitioned into 10 approximately equal-sized subsets (n ≈ 200 per fold). In each iteration, nine subsets were used for model estimation, and the remaining subset served as the validation sample. This procedure was repeated 10 times so that each subset functioned as the validation set exactly once.

Predictive accuracy was assessed using the mean absolute error (MAE) and root mean square error (RMSE) across all predictor sets. The optimal model was identified based on the lowest values of these metrics, where discrepancies arose, RMSE was prioritized due to its greater sensitivity to large prediction errors [44].

Model agreement was further evaluated using the intraclass correlation coefficient (ICC) derived from a two-way mixed-effects model with absolute agreement and single-measurement specifications. ICC values were interpreted as poor (ICC < 0.50), moderate (0.50 ≤ ICC <0.75), good (0.75 ≤ ICC <0.90), or excellent (ICC ≥ 0.90) agreement [47].

In accordance with NICE guidelines [48], mean utility score plots were constructed across the full range of WHOQOL-BREF total scores to identify systematic prediction bias. Additionally, cumulative distribution plots were used to examine discrepancies between predicted and observed utility values. The optimal model was expected to demonstrate the highest agreement and minimal divergence across these visual diagnostics. Notably, this study was conducted and reported in accordance with the Mapping onto Preference-Based Measures Reporting Standards checklist [49] and the reporting standards guidance outlined in the 2017 by International Society for Pharmacoeconomics and Outcomes Research (ISPOR) Task Force Report [50], as throuroghly described in Tables in S1-S2 Table.

All statistical analyses were conducted using Stata version 17 (StataCorp LLC, College Station, TX, USA) and Microsoft Excel. A two-sided p-value <0.05 was considered statistically significant.

Participant characteristics

Among the 2,000 participants drawn from the general Thai population, mean SF-12v2 subscale scores ranged from 64.07 ± 24.94 for GH to 86.83 ± 17.89 for RE. The mean PCS and MCS scores were 50.28 ± 8.44 and 53.61 ± 7.11, respectively. Most SF-12v2 subscales exhibited both ceiling effects (scores of 100) and floor effects (scores of 0). An exception was observed for the MH subscale, which demonstrated only a ceiling effect, affecting 14.50% of respondents. Detailed descriptive statistics for participant characteristics and EQ-5D-5L utility scores are reported elsewhere [38].

Conceptual overlap between EQ-5D-5L and SF-12v2

Table 3 presents the absolute Spearman’s rank correlation coefficients between SF-12v2 items and subscale-level scores and EQ-5D-5L utility scores. All pairwise correlations were statistically significant (p < 0.001), except for the correlation between MH1 and SC, MCS, and MO, and MCS and SC.

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Table 3. Spearman’s correlation coefficients between SF-12v2 items or subscale scores and the EQ-5D-5L dimensions and utility scores.

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At the subscale level, PF, RP, BP, and GH demonstrated the strongest correlations with EQ-5D-5L utility scores (|r| = 0.5904–0.6109) and showed moderate to strong correlations with at least one EQ-5D-5L dimension. These subscales were therefore retained for inclusion in the predictor sets used in the mapping models. In contrast, VT exhibited the weakest correlation with EQ-5D-5L utility scores (|r| = 0.2879) and was excluded from further analyses.

At the item level, GH1, PF1, PF2, RP1, RP2, RE1, RE2, BP1, and MH2 showed at least moderate correlations with EQ-5D-5L utility scores (|r| > 0.4). However, the inclusion of RP1, RP2, RE1, and RE2 concurrently raised concerns regarding multicollinearity, given their conceptual and statistical overlap within subscales. Consequently, RP2 and RE1 were excluded from the predictor sets, as their correlation coefficients were lower than those of RP1 and RE2, respectively.

Model selection

Table 4 summarizes predictive performance metrics across all regression models for both direct and indirect mapping approaches. For direct mapping, predictor set 4 demonstrated superior performance relative to the other sets, yielding the lowest average MAE and RMSE.

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Table 4. Predictive performance of all regression models for predicting EQ-5D-5L utility scores from ten-fold cross-validation.

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Although both Tobit and ALDVMM-1 component models achieved the lowest post-cross-validation (CV) MAE (0.0402 and 0.0410, respectively), the ALDVMM-1 component model produced the lowest post-CV RMSE (0.0625). In contrast, the Tobit model ranked 16th in terms of RMSE among all evaluated models.

Based on overall predicted accuracy, the ALDVMM-1 component model was selected as the best-performing direct mapping model. As illustrated in Fig 1, this model exhibited less variability in predicted utility scores across the full distribution compared with the Tobit model. Although cumulative distribution plots indicated that the Tobit model more closely regressed observed values at the upper boundary (1.0000), this was primarily attributable to truncation at the maximum utility value. In contrast, the ALDVMM-1 component model generated predictions without truncation at either end of the scale. Similar to the distribution plots, ALDVMM-1 component model outperformed the other models because it could predict the utility scores more closely aligned with the observed utility scores, particularly at the maximum utility score of 1.00 (50%) and for values below zero as shown in Figure in S1 Fig.

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Fig 1. Comparison of the cumulative plots of observed and predicted utility scores across all regression models for direct and indirect mapping.

ALDVMM-1 component adjusted limited dependent variable mixture model with 1 component CLAD censored least absolute deviation GLM generalized linear model MLOGIT multinomial logistic regression OLS ordinary least squares Trunc truncated predicted utility values for the OLS, Tobit, and CLAD models. Their plots were generated with predicted values truncated at theoretical boundaries of the Thai EQ-5D-5L value set: an upper bound of 1.0 for values exceeding 1 and a lower bound of –0.4212 for values less than –0.4212. Truncation did not affect the comparative assessment of model performance. Non-truncated predictions are shown for GLM-poisson, ALDVMM-1 component, and MLOGIT, which generate predicted utility values within the Thai-specific value set by model structures.

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Consistent with these findings, the ALDVMM-1 component model demonstrated the highest agreement between predicted and observed utility scores, with an ICC of 0.8192, exceeding that of all alternative regression models.

For indirect mapping, all five predictor sets were initially evaluated. However, the GOLOGIT model failed to converge, and the OLOGIT model violated the proportional odds assumption across all predictor sets. Consequently, MLOGIT was implemented.

Model convergence was achieved only for predictor set 1, yielding post-CV MAE and RMSE values of 0.0401 and 0.0703, respectively. Agreement between predicted and observed utility scores was good, with an ICC of 0.7810.

Fig 2 presents plots comparing predicted and observed mean utility scores stratified by WHOQOL-BREF total scores across all regression models. All models exhibited a consistent upward trend in predicted utility scores with increasing WHOQOL-BREF scores. For WHOQOL-BREF scores below 80, the GLM-poisson produced the most accurate predictions, whereas other models tended to overestimate utility.

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Fig 2. Mean observed and predicted utility scores by WHOQOL-BREF Total Score as the conditioning variable across all regression models for direct and indirect mapping.

ALDVMM-1 component adjusted limited dependent variable mixture model with 1 component CLAD censored least absolute deviation GLM generalized linear model MLOGIT multinomial logistic regression OLS ordinary least squares Trunc truncated predicted utility values for the OLS, Tobit, and CLAD models. Their plots were generated with predicted values truncated at theoretical boundaries of the Thai EQ-5D-5L value set: an upper bound of 1.0 for values exceeding 1 and a lower bound of –0.4212 for values less than –0.4212. Truncation did not affect the comparative assessment of model performance. Non-truncated predictions are shown for GLM-poisson, ALDVMM-1 component, and MLOGIT, which generate predicted utility values within the Thai-specific value set by model structures.

https://doi.org/10.1371/journal.pone.0351064.g002

For WHOQOL-BREF scores between 80 and 105, the ALDVMM-1 component model demonstrated superior predictive performance compared to other regression models. In contrast, for scores exceeding 105, where data density was lower, the OLS model yielded more accurate predictions than other approaches. Notably, the MLOGIT model systematically overestimated utility scores across the entire WHOQOL-BREF score range.

Algorithm for direct and indirect mapping

Based on the above evaluations, the ALDVMM-1 component model with predictor set 4 and the MLOGIT model with predictor set 1 were identified as the best-predicting models for direct and indirect mapping, respectively.

The mathematical specification for predicting EQ-5D-5L utility scores using the selected direct mapping model is shown below:

where:

( denotes response to SF-12v2 items GH1, PF1, PF2, RP1, RE2, BP1, and SF1 (response levels for PF1 and PF2 ranged from 1–3; all others ranged from 1–5);

represents the estimated coefficient corresponding to the item

Age refers to the respondent’s age in years.

Estimated utility scores were subsequently used to calculate predicted utility values using algorithms derived from the StataCorp LLC implementation [51]. The predicted utility values were subsequently calculated using the following formula.

Where:

: The predicted value of dependent variable (utility scores) for each individual

: The summation operator over C possible categories; however, it is one for this study because the best-predicting model is ALDVMM with one component.

: Cumulative distribution function of the standard normal distribution for upper limit

: Cumulative distribution function of the standard normal distribution for lower limit

: Upper bound is 0.9436 (the second highest values for the Thai-specific value set)

: Lower bound is -0.4212 (the lowest values for the Thai-specific value set)

: The standard deviation of the error term for category c where it is 0.0795847 for

this study

: Estimated utility value from the exploratory variable and regression coefficients

of the STATA output

: Probability density function of the standard normal distribution for upper limit

: Probability density function of the standard normal distribution for lower limit

Detailed coefficients and standard errors are provided in Table in S3 Table, with a worked example illustrated in Text in S1 Text.

Table in S4 Table reports the coefficients for the selected SF-12v2 items used in indirect mapping (predictor set 1), while Text in S2 Text provides a step-by-step example of utility scores calculated via the indirect mapping approach.

The predicted utility scores may be applied in future economic evaluations. The variance-covariance matrices are available in Microsoft Excel format to facilitate probabilistic sensitivity analysis in S2 File.