We appreciate Cella et al.'s letter and their interest in the algorithm for predicting EuroQol five-dimensional (EQ-5D) questionnaire scores using Functional Assessment of Cancer Therapy - Prostate (FACT-P) questionnaire scores, published in Wu et al. In the letter, the authors raised two primary issues with the algorithm and proposed a modification. We welcome the opportunity to reply to these concerns.

First, the authors pointed out that while using the proposed algorithm, the predicted mean EQ-5D values were out of range. In response to this issue, we would like to emphasize a crucial step in the algorithm. Table 4 on page 412 provides the final full algorithm with and without EORTC. The algorithm, however, also requires a truncation of the predicted value of EQ-5D at the final step to ensure the correct range of the predicted value. This has been mentioned in page 410 of the published article:
    If the predicted value of EQ-5D fell outside the defined range of [−0.594, 1.000], then it was truncated to the appropriate boundary value.

Note that the proposed model is not a linear model but a truncated linear model in which the predicted values are truncated with a floor and ceiling (−0.594, 1.000). Using only the linear model with the coefficients reported in Table 4 on page 412 can produce mean EQ-5D values outside that range; hence, it is crucial to use the truncation step of the algorithm. We believe that using the prediction algorithm along with this truncation step will ensure mean EQ-5D values within the correct range.

Second, we acknowledge the typographical error made on page 410 (“an average BMI of 72.4 (SD = 9.0)”) as pointed out by the authors. Based on the original result of this study, the correct summary statistics for BMI should be mean = 27.3 and SD = 4.1. This typographical error, however, affects only this particular sentence of the article and does not by any means affect the validity of the algorithm. We are really sorry for this mistake and any confusion this may have caused to the readers, including the authors, and to Value in Health.

We would also like to point out that even though the authors made an interesting approach to modify the algorithm by matching the mean of the predicted utility with the predicted value at mean covariate values, the general approach of the proposed modification is incorrect because it assumes a key result in the context of a linear regression model that does not hold for a truncated or nonlinear regression model. More importantly, the modified model is a prediction model without age or body mass index as potential predictors, which has limited interpretability as well as generalizability for individual-level prediction in other samples, because age and BMI are important predictors of EQ-5D (as mentioned in Table 3 of the article).

Once again, we thank the authors as well as the editor for identifying the typographical error. After reviewing the original data, we believe that the published algorithm is correct. We sincerely hope we were able to address the concerns the authors raised and were able to emphasize the key step in using the published algorithm in a correct way to predict utility.