Mapping the PHQ-8 to EQ-5D, HUI3 and SF6D in patients with depression

Statistical analyses were carried out using the STATA software version 13 (StataCorp LP, College Station, TX). The overlap between the source and the target instruments were calculated using the Spearman correlation coefficient. Since the distribution of utility scores derived from generic preference-based measures such as EQ-5D are often not normally distributed and have a higher ceiling effect at a value of 1 [18], we used a beta regression mixture model (betamix) to map the utility scores. In this study, a beta mixture regression model was used as a primary statistical model to predict different points of health instruments. The model has an advantage over other regression models in terms of its flexibility and ability to capture different points of health utility scores, including negative values (health state worse than death), the peak of observation at full health or death, the gap between boundary values and a mixture of number components of beta distributions. The results were compared against two common regression methods, including Ordinary Least Square (OLS) and Tobit regression models [19]. The beta regression mixture model is a two-part model that incorporates a multinomial logit model and a beta mixture model in their algorithms. Studies have increasingly suggested that this regression method outperforms the linear regression model [20‐22]. In order to determine the best performance of the prediction model, three regression methods with 18 different model specifications consisting of three model specifications in each OLS and Tobit, and 12 model specifications in the beta mixture regression models with up to two components with and without truncation and probability mass at full health and truncation point were included in the current analyses. The first model included only PHQ-8 total scores as a main predictor for the utility score; the second model included PHQ-8 total scores, age, and gender. The third model included PHQ-8 total scores, PHQ-squared, age, and gender. The performance of regression methods was assessed using the following criteria. Both mean absolute error (MAE) and root mean square error (RMSE) were used as the main criterion to compare the performance of regression methods. Values from both indices were ranked and summed to get an average ranking. The regression model with the lowest average ranking values (ARV) was considered to be the best prediction model [6, 22, 23].

The descriptive statistics are presented in Table 1. The sample included 249 participants with depression. The mean age of the overall sample was 36.2 years (SD = 11.1), 69.9% were Chinese, 13.7% were Malays, 14.4% were Indians, and 2% belonged to other ethnicities. The EQ-5D-3L showed a mean (SD) index score of 0.615 (0.317) with minimum and maximum scores of − 0.2999 and 1, while the mean (SD) EQ-5D-5L index was 0.709 (0.212) with minimum and maximum scores of − 0.027 and 1, respectively. The mean (SD) HUI3 index score was 0.461 (0.331) with minimum and maximum scores of − 0.289 and 1, while the mean SF-6D was 0.607 (0.105) with minimum and maximum scores of 0.385 and 0.958, respectively. The distribution of the EQ-5D-3L, EQ-5D-5L, and HUI3 utilities showed a substantial skew to the right, that is, toward a better quality of life (Fig. 1). The mean (SD) PHQ-8 total score was 11.526 (6.590), with minimum and maximum scores of 0 and 24, respectively.

Table 2 shows the Spearman ‘s correlation coefficient results between the source and the target instruments. A strong inverse correlation was observed between the source instrument, i.e., PHQ-8, and the four target instruments (EQ-5D-3L, EQ-5D-5L, HUI3, and SF-6D). The correlation coefficient ranged between -0.61 and -0.78, suggesting a significant overlap between the source and the target instruments.

Table 3 shows the performance of three regression methods (beta mixture regression, OLS, and Tobit) for mapping PHQ-8 to the EQ-5D-3L utility scores. Among the three regression methods and 18 model specifications, beta mixture regression method with two components with truncation, probability mass at full health (1), and the truncation point (0.8538) was the most parsimonious prediction model for the EQ-5D-3L utility scores. It produced the smallest average ranking of MAE (0.1765) and RMSE (0.2326) values compared to other regression methods and model specifications (Table 3). This regression model revealed that PHQ-squared scores were significantly and negatively associated with EQ-5D-3L utility scores in the first component and found that the PHQ-8 total scores and PHQ-squared were negatively and positively associated with the full health (Supplementary Table 1).

Table 4 shows the performance of three regression methods for mapping the PHQ-8 to the EQ-5D-5L utility scores. Among the three regression methods and 18 model specifications, beta mixture regression method with two components with truncation and probability mass at full health (1) and truncation point (0.879) was the most parsimonious prediction model for the EQ-5D-5L utility scores. It produced the best prediction performance index (MAE = 0.1208 and RMSE = 0.1620) than other regression methods and other model specifications. In this regression model (Supplementary Table 2), age was significantly and negatively associated with the EQ-5D-5L utility scores in the first component utility scores. In contrast, PHQ-squared was significantly and negatively associated with the EQ-5D-5L utility scores in the second component and PHQ-squared and age were significantly and negatively associated with the full health (Supplementary Table 2).

Table 5 shows the performance of three regression methods for mapping the PHQ-8 to the HUI3 utility scores. Among the three regression methods and 18 model specifications, the OLS regression method with model 3 specification performed as the most parsimonious prediction model for the HUI3 utility scores. It produced the best prediction performance index (MAE = 0.1584 and RMSE = 0.2024). In this regression model, those with lower PHQ-8 total scores and of younger age were significantly associated with higher HUI3 scores (Supplementary Table 3).

Table 6 shows the performance of three regression methods for mapping the PHQ-8 to the SF-6D utility scores. Among the three regression methods and 18 model specifications, beta mixture regression method with two components without truncation and probability mass at full health (1) was found to be the most parsimonious prediction model for the SF-6D utility scores. It produced the smallest average ranking of MAE (0.0519) and RMSE (0.0683). In this regression model, PHQ-8 total scores and age were significantly and negatively associated with the SF-6D utility scores in both components. Meanwhile, the female gender was significantly and negatively associated with the SF-6D utility scores in the first component (Supplementary Table 4).