 Research
 Open Access
 Published:
Evaluation of the performance of algorithms mapping EORTC QLQC30 onto the EQ5D index in a metastatic colorectal cancer costeffectiveness model
Health and Quality of Life Outcomes volumeÂ 18, ArticleÂ number:Â 240 (2020)
Abstract
Background
Costeffectiveness models require quality of life utilities calculated from generic preferencebased questionnaires, such as EQ5D. We evaluated the performance of available algorithms for QLQC30 conversion into EQ5D3L based utilities in a metastatic colorectal cancer (mCRC) patient population and subsequently developed a mCRC specific algorithm. Influence of mapping on costeffectiveness was evaluated.
Methods
Three available algorithms were compared with observed utilities from the CAIRO3 study. Six models were developed using 5fold crossvalidation: predicting EQ5D3L tariffs from QLQC30 functional scale scores, continuous QLQC30 scores or dummy levels with a random effects model (RE), a most likely probability method on EQ5D3L functional scale scores, a beta regression model on QLQC30 functional scale scores and a separate equations subgroup approach on QLQC30 functional scale scores. Performance was assessed, and algorithms were tested on incomplete QLQC30 questionnaires. Influence of utility mapping on incremental cost/QALY gained (ICER) was evaluated in an existing Dutch mCRC costeffectiveness model.
Results
The available algorithms yielded mean utilities of 1: 0.87â€‰Â±â€‰sd:0.14,2: 0.81â€‰Â±â€‰0.15 (both Dutch tariff) and 3: 0.81â€‰Â±â€‰sd:0.19. AlgorithmÂ 1 and 3 were significantly different from the mean observed utility (0.83â€‰Â±â€‰0.17 with Dutch tariff, 0.80â€‰Â±â€‰0.20 with U.K. tariff). All new models yielded predicted utilities drawing close to observed utilities; differences were not statistically significant. The existing algorithms resulted in an ICER difference of â‚¬10,140 less and â‚¬1765 more compared to the observed EQ5D3L based ICER (â‚¬168,048). The preferred newly developed algorithm was â‚¬5094 higher than the observed EQ5D3L based ICER. Disparity was explained by minimal diffences in incremental QALYs between models.
Conclusion
Available mapping algorithms sufficiently accurately predict utilities. With the commonly used statistical methods, we did not succeed in developping an improved mapping algorithm. Importantly, costeffectiveness outcomes in this study were comparable to the original model outcomes between different mapping algorithms. Therefore, mapping can be an adequate solution for costeffectiveness studies using either a previously designed and validated algorithm or an algorithm developed in this study.
Background
Measurement of healthrelated quality of life (HRQoL) with generic questionnaires (e.g. EQ5D3L) and disease specific questionnaires (e.g. EORTC QLQC30) are of great interest to clinicians and researchers, especially in the context of costeffectiveness research. In oncology, costeffectiveness research becomes more important rapidly, as it provides information for decisionmakers in establishing the content of the basic benefit package of a health insurance in some countries. Costeffectiveness outcomes are more often reported in addition to clinical outcome parameters, and the incremental cost per quality adjusted life year (QALY) is generally chosen as primary outcome in costeffectiveness models [1]. To calculate the total QALYs gained due to treatment, both length and quality of life have to be established. Quality of life can be measured through a generic preferencebased quality of life questionnaire such as the commonly used EQ5D3L questionnaire, which is requested by some reimbursement authorities [2]. Based on this questionnaire, patient scores are transformed into healthrelated quality of life utilities, on a scale of 1  being full health to 0  reflecting death (and even negative values reflecting health states worse than death), which can be combined with the duration (survival) of a patient to calculate the QALY [1, 3].
In industry sponsored oncology studies, both the EORTC QLQC30 and the EQ5D questionnaires are often used to capture clinically meaningful changes in quality of life and enable healtheconomic evaluations [2, 4]. However, the lack of generic preferencebased questionnaires in for instance academic clinical studies or clinical registries hamper the calculation of healthrelated quality of life utilities for costeffectiveness research. To overcome this issue, researchers often revert to the translation of disease specific quality of life outcomes (such as those captured by QLQC30 in oncology) into utilities (such as captured by EQ5D3L) using so called â€˜mapping algorithmsâ€™ for their costeffectiveness models. Mapping algorithms are regression models developed and tested in specific patient population datasets, which make them â€˜sample dependentâ€™. Consequently, Doble et al. [5] demonstrated that in oncology only two out of 10 eligible mapping algorithms, performed sufficiently well in the estimation of utilities (Versteegh et al. using a Dutch tariff for EQ5D3L, developed in a multiple myeloma and nonHodgkin lymphoma dataset, and Longworth et al. for EQ5D3L, developed in a multiple myeloma and breast cancer dataset) [5,6,7]. As shown by Doble et al., QLQC30 outcomes between development and validation datasets demonstrated clinically relevant differences on multiple QLQC30 dimensions, although congruence of QLQC30 outcomes between datasets was not predictive for mapping algorithm performance [5]. Even so, disease related effects could influence the outcomes of mapping algorithms and it has been previously advised to use a mapping algorithm with similar clinical characteristics compared to the sample on which the mapping is to be applied [8]. More recently, Marriott et al. proposed a mapping algorithm developed with a metastatic colorectal cancer (mCRC) patient dataset using an U.K. tariff for EQ5D3L [9]. Even so, we question whether the currently available mapping algorithms, which were not all developed with mCRC datasets and an mCRC disease specific algorithm based on a U.K. tariff, are sufficiently suitable to translate QLQC30 outcomes to Dutch EQ5D3L based utilities for mCRC patients.
Our first objective was to evaluate the accuracy of available mapping algorithms for conversion of QLQC30 outcomes to EQ5D3L utilities in a population of mCRC patients. Our second objective was to design an mCRC specific mapping algorithm using a Dutch tariff for the conversion of QLQC30 outcomes to EQ5D3L based utilities. Finally, we evaluated the influence of utility mapping on the incremental cost per QALY gained (ICER) in an existing mCRC costeffectiveness model [10].
Methods
Patient population
The CAIRO3 study is a randomized phase 3 study (NCT00442637) sponsored by the Dutch Colorectal Cancer Group (DCCG), in which mCRC patients with stable disease or better (nâ€‰=â€‰558) following 6 cycles of initial therapy with capecitabine, oxaliplatin and bevacizumab (CAPOXB). Patients were either randomized to the observation strategy or capecitabine (625â€‰mg/m^{2} orally twice daily continuously) and bevacizumab (7.5â€‰mg/kg intravenously every 3â€‰weeks) (CB) maintenance treatment [11]. Patients completed both the disease specific QLQC30 version 3.0 and generic EQ5D3L questionnaires every 9â€‰weeks simultaneously [2, 4]. Only patients participating in the completion of QLQC30 and EQ5D questionnaires were selected and all time points were pooled for this study. Descriptive statistics were used for baseline characteristics.
Questionnaires
The EORTC QLQC30 questionnaire version 3.0 comprises 30 questions evaluating quality of life in five functional scales (physical, role, cognitive, emotional and social functioning), three symptom scales (fatigue, pain, nausea and vomiting), global health status and single items for the assessment of symptoms commonly reported by cancer patients (dyspnea, appetite loss, insomnia, constipation, diarrhea and financial difficulties) [4]. QLQC30 outcomes were calculated using the EORTC QLQC30 scoring manual. After linear transformation and calculation of raw score for the questions ranging not at all (0) to very much (4) for functional and symptom scale scores and very poor (0) to excellent (7) for global health, scale scores range 0 to 100. For functional scales and global health, a high score represents a higher level of functioning, while for the symptoms scales a low outcome represents less symptomatology [12].
The EQ5D3L contains 5 questions each addressing a different domain: mobility, selfcare, usual activities, pain/discomfort and anxiety/depression. Each of these domains has 3 levels [2]. An EQ5D3L based utility is derived from an EQ5D questionnaire using a country specific value set, i.e. tariff. EQ5D3L outcomes in this study were transformed to Dutch and U.K. tariff EQ5D3L based utilities [13, 14].
Evaluation of existing algorithms
The algorithms by Versteegh et al. and Longworth et al. were initially selected as these performed best in the analysis by Doble and Lorgelly, and is appropriate to the Dutch setting as both can predict Dutch tariff EQ5D3L utilities [5, 6]. The mapping algorithm by Marriott et al. was additionally selected as this algorithm was developed in an mCRC patient dataset appropriate to a U.K. setting [8]. All three mapping algorithms were used for prediction of an EQ5D3L based utility using concurrently collected EORTC QLQC30 outcomes. As the algorithm by Versteegh et al. was based on version 2 of the QLQC30 questionnaire, while version 3 was used in the CAIRO3 trial, QLQC30 question 1 through 5 were converted into a binary response to fit the mapping algorithm. All algorithms were developed for nonpatient level modelling purposes and the performance analysis is therefore focused on their sample means. Some individual level performance characteristics were also used for the mapping algorithms, albeit the well documented suboptimal performance of these algorithms on the individual level in the lower utility ranges. The algorithms were compared to the observed EQ5D3L based utilities using the root mean square error (RMSE), mean absolute error (MAE), ttest and Spearman correlation. The data was formatted in STATA. All analyses were performed using R.
Mapping algorithm design
Methodology according to the MAPS statement was used for developing the mapping algorithm [15]. The mCRC specific mapping algorithms that were developed with commonly used statistical methods and evaluated used 5fold crossvalidation.
Each fold provided a test set in which the trained model, which was developed based on the other 4 folds, could be tested, resulting in 5 estimates for each performance measure.
First, the EQ5D3L based utility was regressed on the QLQC30 functional and symptom scale scores using a random effects model (RE) with a random intercept: model 1. In a second RE model (model 2), the QLQC30 questions were treated as continuous variables and in a third model as dummy variables (model 3). Dummy variables essentially are a redefinition of the four QLQC30 answer categories (categories: 1 (no problem at all) to 4 (very much a problem)) and seven categories (categories: 1 (very poor) to 7 (excellent)) for the last two QLQC30 questions. For each QLQC30 question dummies for outcome categories were regressed on utility prediction. All abovementioned RE models assume a continuous and normal distribution for EQ5D utilities. Although this assumption is hardly realistic considering the wellstudied skewed distribution of utilities, it is by far the most popular form of mapping in the literature and generally performs quite well compared to more complex models [16].
Model 4 is a twostep model, also known as a response mapping model. The advantage of a response mapping model is that it is independent of tariff calculations and it can therefore compute any country utility score for which tariffs are available. First, in model 4, ordered logit regression was used to predict the EQ5D3L domain score. An ordered logit model was chosen to preserve the ordering of the categories in the dependent variable.* For this method, input variables were the QLQC30 functional scale scores. Secondly, a utility was calculated using the most likely probability method. With the most likely probability method, the probabilities of the EQ5D3L response levels (no problem, some problems and severe problems) per EQ5D domain (mobility, selfcare, usual activities, pain/discomfort and anxiety/depression) were predicted based on the QLQC30 functional scale scores. The following formulas were used for this:
Footnote * A multinomial logit model was also developed; however the ordered logit model outperformed the multinomial logit model. Hence, we only report on the ordered logit model in this manuscript.
Where level stands for the EQ5D3L response level, EQ. 5D stands for the latent EQ5D functional or symptom scale score regressed on the QLQ dimensions, Îº stands for the estimated threshold between different response levels. These predicted probabilities were subsequently scored with the EQ5D scoring system [17].
Model 5 used beta regression to restrict the EQ5D3L utilities to the 0,1 interval. The advantage of this method is that it cannot lead to unrealistic utility predictions exceeding 1. However, it will not be able to produce negative utilities. In the current analyses, the number of individuals with negative utilities was so small (0.2%) that this is unlikely to notably affect the results. Moreover, it cannot model values of exactly 1 or 0, so these values were rescaled prior to the mapping. All utilities were first transformed to disutilities. All values â‰¥1 (which were utilities of 0 or less than 0) were selected to be approximated so that the disutilities would return a value <â€‰1 and thus included in the beta regression. To do so, a standardized value was subtracted from the disutility. All values of exactly 0 (which were utilities of 1) were selected to be adapted so that the disutilities would return values >â€‰0. The standardized transformation applied was: (disutility*(N1)â€‰+â€‰0.5)/N. Nevertheless, the beta distribution is in theory a better approximation of the EQ5D utility distribution compared to the normal distribution underlying OLS regression, at least in samples with very few health state observations worse than dead. This regression was also conducted on the QLQC30 functional scale scores.
The final model (model 6) consisted of a separate equations subgroup approach. In the first step, probabilities are calculated on the basis of a multinomial logistic regression for having a EQ5D3L utility score lower than 0.6 (related to scoring â€˜extreme problemsâ€™ on any EQ5D3L dimension [18], higher than 0.6 but lower than 1 and equal to 1. In the next step, RE models are trained on individuals with utility scores lower than 0.6 and higher than 0.6 separately. Finally, the predicted utilities of these two submodels and of having a 1 are combined with the probabilities from the first step. The advantage of this approach is that it relaxes the assumption of a continuous linear relation between EQ5D utilities and QLQC30 functional and symptom scale scores. Poor health states often adhere to a different (approximate) linear relation with the EQ5D utilities compared to higher scores, often leading to the overvaluing of low health states in the literature [18].
All models were developed using a backward selection procedure, where nonsignificant coefficients based on the QLQC30 items were removed onebyone (cutoff value pâ€‰=â€‰0.05) until all coefficients were at or below the cutoff value. Except for model 4 and 6 (in part), backward selection was performed to minimize the mapping algorithm length without compromising the model performance, which has previously been done by others [6, 7]. In a second step, nonlogical coefficients were removed. Nonlogical coefficients were defined as coefficients that carried an incongruous sign, for example a coefficient for nausea leading to a better utility when one would expect a reduction in the assigned utility. Random effects with cluster robust standard errors were introduced to correct for multiple responses from one patient for all OLS models (models 1, 2, 3, and 6 in part). The beta, ordered logit and multinomial logit regressions (models 4, 5 and 6 in part) used normal standard errors as there were no cluster robust standard errors available for these methods.
Validation of the developed mapping algorithms
After development of the six mapping algorithms using each of the five training data sets consecutively, the algorithms were tested in the corresponding folds. Performance of the algorithms was reported as mean predicted utility, the root mean squared error (RMSE) and mean absolute error (MAE). The RMSE will give a better insight into the performance of the mapping algorithm alongside MAE, as it is more sensitive to outliers and hence helps identify the mapping algorithm with the least extreme deviations between predicted and observed values. The resulting algorithms were analyzed for logical consistency using scatter plots comparing observed and predicted utilities, i.e. worse outcomes of the observed EQ5D3L based utility also lead to worse outcomes in the predicted utilities with the six methods described above. Lastly, Spearman correlation coefficients and ttests were used to illustrate the performance of the various algorithms. The model of preference was selected based on best fit: smallest value for RMSE, MAE and highest value for the Spearman correlation.
Performance of the mapping algorithms based on QLQC30 functional scale scores, developed with OLS, response mapping, beta regression and the separate equations model, were tested on incomplete QLQC30 questionnaires. Quality of life functional scale scores (e.g. physical functioning) can be calculated with a minimal completion of half of the questions included in the QLQC30 questionnaires [12]. Incomplete questionnaires, for which functional scale scores calculations remained possible and with a concurrently collected EQ5D3L, were selected to test mapping algorithm performance with those algorithms based on functional scale scores. No imputations were performed on QLQC30 questionnaires. Results were compared with concurrently collected EQ5D3L questionnaires. Outcomes were compared with observed utilities as previously described.
Algorithm influence on costeffectiveness model outcomes
The influence of the mapping algorithms on the primary outcome, the incremental cost per QALY gained (ICER), was evaluated using a Dutch costeffectiveness model comparing CB maintenance and observation following 6â€‰cycles of first line CAPOXB for patients with mCRC. For this purpose, a discrete event simulation model, developed in AnyLogic (multimethod simulation software, v.8.2.3, The AnyLogic Company (Chicago, IL, USA) was used for the current analysis [19]. ICERs comparing CB maintenance and observation were calculated for 1) observed EQ5D3L based utilities as was done in the original study, 2) utilities obtained with the mapping algorithm developed by Versteegh et al. [6] (mapping algorithm for a Dutch tariff conversion), 3) utilities obtained with the mapping algorithm developed by Longworth et al. using a Dutch tariff and 4) utilities obtained with the preferred mapping algorithm developed in this study (model 1). The mapping algorithm developed by Marriott et al. [9] uses a U.K. tariff conversion and was therefore not included. Only concurrently collected EQ5D and QLQC30 observations during either maintenance treatment and observation, defined as the first healthstate, were used in this analysis. Utilities in subsequent healthstates (reintroduction of therapy, salvage therapy, death) were derived from literature as these could not be derived from the CAIRO3 study [10].
A total of 10,000 hypothetical patients per treatment strategy were simulated for a patientlevel outcome calculation. Subsequently, a probabilistic analysis was performed to calculate the ICERs with a 95% confidence interval based on 10,000 samples. To reflect parameter uncertainty in the probabilistic analysis, distributions for the utilities were defined according to the method of moments using the mean and a standard error for each of the utilities derived from the selected mapping algorithms in line with the original costeffectiveness evaluation of the CAIRO3 study. With the exception of the uncertainty around utilities only, distributions for the other parameters, such as costs, healthstate transitions, were defined as in the original costeffectiveness evaluation of the CAIRO3 study [10].
Results
From a total of 2440 observations, 1905 concurrently collected, complete QLQC30 and EQ5D3L questionnaires were included in this analysis. The concurrent observations were obtained from 473 patients enrolled in the CAIRO3 study (238 patients in the observation arm and 235 patients in the maintenance treatment arm). In TableÂ 1, characteristics of the QLQC30 and EQ5D data set are presented. The distribution of EQ5D based utilities can be viewed in AdditionalÂ FileÂ 1. Incomplete QLQC30 or EQ5D3L questionnaires were excluded for mapping algorithm development. For the purpose of the mCRC specific mapping algorithm design, we randomly divided the data in 5 folds (nâ€‰=â€‰381 each).
Performance of existing mapping algorithms on an mCRC dataset
The mean observed utility based on completed EQ5D3L questionnaires of the mCRC dataset included in this analysis was 0.834â€‰Â±â€‰sd: 0.171 (Dutch tariff) and 0.803â€‰Â±â€‰sd: 0.197 (U.K. tariff). The algorithm by Versteegh et al. resulted in a mean utility of 0.866â€‰Â±â€‰0.135 with a Spearman correlation of 0.76 (pâ€‰<â€‰0.01) (TableÂ 2). The algorithm by Longworth et al. resulted in a mean utility of 0.835â€‰Â±â€‰0.127 and 0.810â€‰Â±â€‰0.152, with a Spearman correlation of 0.77 and 0.79, for the Dutch tariff and the U.K. tariff respectively. The algorithm by Longworth for Dutch tariff performed very well and was not significantly different compared to observed utilities (pâ€‰=â€‰0.687). The algorithm by Marriott et al. (U.K. tariff) resulted in a mean utility of 0.813â€‰Â±â€‰sd:0.185 with a Spearman correlation of 0.75 (pâ€‰<â€‰0.01) (Table 2).
Design and validation of a new mapping algorithm on a mCRC dataset
Algorithm coefficients for the RE based algorithms are presented in TablesÂ 3 (model 1), 4 (model 2) and 5 (model 3). These algorithms concern the RE model with QLQC30 functional scale scores (model 1), RE model with QLQC30 question outcomes as continuous variable (model 2) and RE model with the QLQC30 questions as dummy variables (model 3). The ordered logit regressions for prediction of the EQ5D3L based utility (model 4) can be viewed in the AdditionalÂ fileÂ 2: Tables 13. The beta regression (model 5) output can be found in TableÂ 6 and the separate equations subgroup approach model (model 6) in Additional file 2 Tables 46.
Observed and mean predicted utility resulting from the six developed mapping algorithms are presented in TableÂ 7. The mean observed utility was 0.834â€‰Â±â€‰0.171, while the mean predicted utilities for model 1 to 6 were nearly identical, 0.832â€‰Â±â€‰0.134, 0.832â€‰Â±â€‰0.134, 0.833â€‰Â±â€‰0.133, 0.830â€‰Â±â€‰0.145, 0.838â€‰Â±â€‰0.156 and 0.834â€‰Â±â€‰0.138, respectively. A utility prediction drawing close to the observed utility was achieved in all models. Differences between observed and predicted utilities were nonsignificant. The lowest RMSE and MAE was achieved by model 1 (RMSE 0.098, MAE 0.072) and model 4 (RMSE 0.098, MAE 0.072). Note that comparable to the Longworth algorithm, model 4 is an algorithm for EQ5D response prediction and is thus independent of country tariff. For the purpose of comparison between model performance, a Dutch tariff was applied to the Longworth algorithm and model 4. Mapping algorithms based on functional scale scores are more forgiving towards incomplete questionnaires, as quality of life functional scale scores (e.g. physical functioning) can be calculated with a minimal completion of half of the questions included in the QLQC30 questionnaires. Performance of all newly developed mapping algorithms using QLQC30 functional scale scores (model 1, 4, 5 and 6), were additionally tested in incomplete QLQC30 questionnaires for which functional scale scores could still be calculated for which EQ5D outcomes were concurrently available (nâ€‰=â€‰120). Patient characteristics of incomplete questionnaires are presented in AdditionalÂ fileÂ 3. The mean observed utility in 120 incomplete QLQC30 questionnaires was 0.760â€‰Â±â€‰0232. The best predicted mean utilities were 0.767â€‰Â±â€‰0.177, 0.756â€‰Â±â€‰0.222, 0.764â€‰Â±â€‰0.222, for model 1, model 4 and model 5 respectively (TableÂ 8). The lowest RMSE an MAE were achieved for model 1, which was chosen as preferred model. The algorithm based on the QLQC30 functional scale scores (preferred model) was regarded effective based on correlation between observed and mapped utilities (Fig.Â 1).
Figures depicting the error of predicted utilities compared to the observed utilities for each algorithm are available in the AdditionalÂ fileÂ 4: Figs. 2 and 3. As is well documented in the literature [18], all mapping algorithms show overestimation of lower utilities and underestimation of high utilities.
Algorithm influence on ICERs in a mCRC costeffectiveness model
The influence of the mapping algorithms on the ICER, was tested in an existing Dutch costeffectiveness model comparing two different treatment strategies (CB maintenance versus observation following 6â€‰cycles of first line CAPOXB) in an mCRC patient population. For the first health state in this costeffectiveness model, utilities were estimated using a total of 1654 observations (709 observations for 223 patients in the observation arm and 945 observations for 225 patients in the maintenance arm), utilities of subsequent health states (first progression and theirafter) were derived from literature as was done in the original costeffectiveness study. The ICERs presented in TableÂ 9 were obtained with 1) observed EQ5D3L based utilities, 2) utilities obtained with the mapping algorithm developed by Versteegh et al., 3) utilities obtained with the mapping algorithm developed by Longworth et al using a Dutch tariff and 4) utilities obtained with the preferred model 1. The calculated ICER based on observed utilities in this analysis was â‚¬168,048/QALY. Previously developped mapping algorithm by Versteegh et al. compared to the observed EQ5D3L based utility lead to a negative ICER difference in the point estimate of â‚¬10,140 per QALY gained, while a positive difference of â‚¬5094 and â‚¬1765 was shown for the preferred algorithm (model 1) and the Longworth algorithm, respectively (Fig.Â 2).
Discussion
We have shown that the previously developed algorithm by Versteegh et al. and Marriott et al. for conversion of the diseasespecific questionnaire EORTC QLQC30 into EQ5D3L based utilities resulted in a statistically significant difference between predicted and observed utilities. Still, the existing algorithms performed well as the mean predicted utilities drew close to the mean observed utilities (mean differences between the observed and respectively the mapped utilities by Versteegh et al., Longworth et al. and Marriott et al. were 0.03, 0.001 and 0.01 for the Dutch tariff EQ5D utilities). No significant difference between, observed and predicted utilities were seen with the algorithm developed by Longworth et al. Even though the predicted utilities calculated with the algorithms by Versteegh et al. and Marriott et al. were significantly different, the outcome differences were not considered clinically meaningful. Previously, the minimal clinically relevant difference in utility for cancer patients was found to range 0.08â€“0.16, although this difference might vary per patient population [20, 21]. Moreover, patients with different cancers types and stages of disease experience different symptoms and may thus respond differently on the QLQC30 functional scale scores [8]. In contrast, as was previously shown by Doble et al. disease severity is more likely to drive EQ5D estimation based on QLQC30, and less by the cancer type [5]. Moreover, several studies developed conditionspecific instruments, such as the EORTC QLUC10D to derive healthrelated quality of life utilities, which might be more sensitive to diseasespecific effects and in theory be preferred over EQ5D. However, one can question whether these conditionspecific instruments outperform EQ5D [22,23,24]. Finally, with the emergence of novel treatment strategies in cancer treatment, such as immunotherapy, one could hypothesize a different value of QLQC30 functional scale or symptom scores, which could affect mapping outcomes.
Nevertheless, we pursued a better fitting algorithm for the mCRC patient population. All developed models demonstrated improved utility prediction ability with nonsignificant differences between observed and predicted utilities, although we acknowledge that the performance of the models developed in this study are not tested in a truly external dataset (as the models taken from the literature). Importantly, with the commonly used statistical methods to develop mapping algorithm, we did not succeed in the development of a better performing mapping algorithm. In case a mapping algorithm would be selected from our study, we would suggest the use of the RE model based on QLQC30 functional scale scores (model 1). This model provided the benefit of utility prediction for incomplete QLQC30 questionnaires (for which functional scale scores could be calculated), while retaining a good performance if tested on incomplete QLQC30 questionnaires. QLQC30 outcome conversion into EQ5D3L based utilities (Dutch tariff) could therefore be performed with the following algorithm, developed on functional scale scores (model 1):
The main purpose of mapping algorithms is to convert disease specific quality of life data into utilities for the purpose of costeffectiveness research, if utilities cannot directly be derived from the dataset. We investigated the influence of a mapping algorithm on a costeffectiveness model evaluating CB maintenance treatment compared to observation in mCRC patients. We demonstrated that the use of mappings results in comparable outcomes when used in a costeffectiveness model. The newly developed algorithm slightly underperformed compared to the previously developed algorithm by Longworth et al. (ICER differences between in CEA using observed utilities and mapping: â‚¬1765/QALY gained for the Longworth et al. mapping and â‚¬5094 /QALY gained for the preferred model 1 in this study). An ICER difference of â‚¬10,140/QALY gained was seen if compared to the Versteegh et al. mapping. Disparities were explained by small differences in incremental QALY estimation between treatment arms. The algorithm by Versteegh et al. and Longworth et al. slightly overestimated the utilities in both study arms; while the preferred model algorithm (model 1) overestimated the utilities in the observation arm and underestimated the utilities in the CB maintenance arm. Nevertheless, the Longworth algorithm outperformed our preferred model algorithm in this costeffectiveness model. In a model with more pronounced utility differences, the impact of the chosen mapping algorithm might be different due to case mix effects. The good performance of the Longworth algorithm in this study is remarkable, as this algorithm had not been developed on colon cancer patients, and was estimated on an entirely different sample. Hence, its good performance, especially relative to the withinsample validation of the algorithm we developed, shows the usefulness of this flexible algorithm. Its performance raises the question if similarity of symptoms and severity of symptoms between the development sample and the application sample might not be of greater importance than type of cancer or tumor. While this study seems to suggest that indeed tumor type is less relevant, such a statement must be made with caution: many mapping algorithms, including the one by Versteegh et al., use only a selection of items of the QLQC30. As a consequence, out of sample prediction in patients with other cancer types with specific symptoms not captured by the included items might be complicated.
A strength of this study was the use of multiple statistical methods which enabled us to evaluate and select the bestperforming algorithm, while also considering convenience in use. Furthermore, the analyses were conducted on a large population of patients, with a total of 1905 completed questionnaires. As previously mentioned, the algorithm by Versteegh et al. and the algorithm by Longworth et al. were not developed or validated in mCRC patient populations [6, 7]. Only, the algorithm by Marriott et al. was developed and tested in an mCRC patient population using a U.K. tariff for EQ5D3L [9]. Patients with different cancers types and stages of disease experience different symptoms and might thus respond differently on the QLQC30 domains functional scale scores. Thus, the most applicable algorithm in terms of cancer type and disease stage, should be applied for utility prediction, although it has previously been shown to be more dependent of disease severity than cancer type [5]. Of note, another colorectal cancer specific mapping algorithm estimating EQ5D5L values using a U.K. tariff was previously developed [25, 26]. However, this mapping algorithm could not be tested and validated with the EQ5D3L values in our dataset, as this would require an additional mapping of EQ5D3L to EQ5D5L and we consequently would not been able to separate performance of the mapping algorithm due to differences in utilities. Currently, the EQ5D5L questionnaire is increasingly being adopted in clinical trials as it is regarded more sensitive to health effects and reduce ceiling effects [27]. Further research on mapping of QLQC30 outcomes towards EQ5D5L is therefore necessary.
The mapping algorithm was developed using a single sample, in which completed questionnaires were assigned to one of five folds that functioned as holdout sample, which may be regarded as limitation of this study. Inevitably, the training and test datasets therefore contain comparable patients, who completed the quality of life questionnaires under similar circumstance. Preferably, validation of the developed algorithms should have occurred in another sample containing mCRC patient data on both the QLQC30 and the EQ5D3L questionnaires. Another limitation to this study, is the use of different timepoints. The regression algorithms accounted for the panel data structure where possible through the use of random effects models. However, it has previously been shown that colorectal cancer patients continue to report high quality of life during the course of their disease [28,29,30,31]. Nonetheless, significant and clinically relevant changes in quality of life occur in the palliative stage of the disease, especially in the last few months of life a decline in quality of life has been demonstrated [32]. Therefore, it may be hypothesized that this could also apply for different timepoints within a trial during which different dimensions of health are affected. The models developed in this study, are especially sensitive to this issue.
Conclusion
We have developed a QLQC30 to EQ5D3L mapping algorithm on a mCRC patient population with predicted utilities drawing close to the observed utilities. However, the mapping algorithm did not outperform existing mapping algorithms, especially compared with the response mapping algorithm by Longworth et al. Moreover, external validation of our preferred mapping algorithm remains desirable. The choice of mapping algorithm might only have a small impact on the predicted utility and costeffectiveness, as was illustrated in the case study. Nonetheless, for studies only including diseasespecific quality of life questionnaires, our results show that mapping is an adequate solution to obtain utility estimates for use in costeffectiveness analysis for mCRC patients, using either our newly developed mapping algorithm or one of the existing algorithms used in this study.
Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Abbreviations
 CAPOXB:

Capecitabine oxaliplatin bevacizumab
 CB:

Capecitabine bevacizumab
 DCCG:

Dutch Colorectal Cancer Group
 EORTC:

European Organisation for Research and Treatmen of Cancer
 HRQoL:

Healthrelated quality of life
 ICER:

Incremental costeffectiveness ratio
 QALY:

Quality adjusted life year
 mCRC:

Metastatic colorectal cancer
 OLS:

Ordinary least squares
 RE:

Random effects
 RMSE:

Root mean square error
 MAE:

Mean absolute error
 U.K.:

United Kingdom
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Funding
This research was not funded. The CAIRO3 study was supported by the Dutch Colorectal Cancer Group (DCCG). The DCCG received unrestricted scientific grants for data management and statistical analysis from the Commissie Klinische Studies of the Dutch Cancer Foundation, Roche and SanofiAventis.
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MF conception, design, analysis, interpretation of data, drafted manuscript, approved submitted manuscript and agree to be accountable regarding the manuscript. AdH analysis, interpretation of data, drafted manuscript, approved submitted manuscript and agree to be accountable regarding the manuscript. KD analysis, interpretation of data, drafted manuscript, approved submitted manuscript and agree to be accountable regarding the manuscript. CP substantively revised the manuscript, approved submitted manuscript and agree to be accountable regarding the manuscript. MK substantively revised the manuscript, approved submitted manuscript and agree to be accountable regarding the manuscript. CU substantively revised the manuscript, approved submitted manuscript and agree to be accountable regarding the manuscript. MV conception, design, interpretation of data, substantively revised the manuscript, approved submitted manuscript and agree to be accountable regarding the manuscript. MO conception, substantively revised the manuscript, approved submitted manuscript and agree to be accountable regarding the manuscript.
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Ethics approval and consent to participate
Previously collected quality of life questionnaires in the phase III randomized clinical trial, CAIRO3 study (NCT00442637) were used for this study. Informed consent was given by all patients prior to inclusion in the CAIRO3 study. Results of the CAIRO3 study have been reported elsewhere [11].
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Competing interests
Mira D. Franken declares no competing interests; Anne de Hond declares no competing interests; Koen Degeling declares no competing interests; Cornelis J.A. Punt is a principal investigator of the CAIRO3 study, a randomized controlledtrial sponsored by the Dutch Colorectal Cancer Group (DCCG); Miriam Koopman is a principal investigator of the CAIRO3 study; Carin A. Uylâ€“de Groot has received unrestricted research grants from Boehringer Ingelheim, Astellas, Celgene, Sanofi, JanssenCilag, Bayer, Amgen, Genzyme, Merck, Glycostem Therapeutics, Astra Zeneca, Roche; Matthijs M. Versteegh is a member of the EuroQoL research foundation which develops EQ5D; Martijn G.H. van Oijen has received unrestricted research funding from Amgen, Lilly, Merck, Nordic and Roche.
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Additional file 1.
Histogram of EQ5D3L based utilities of 1905 observations.
Additional file 2: Table 1.
Ordered logit regression (model 4) results for QLQC30 domain scores on EQ5D3L domain. Table 2. Ordered logit regression (model 4) results for QLQC30 domain scores on EQ5D3L domain. Table 3. Ordered logit regression (model 4) results for QLQC30 domain scores on EQ5D3L domain. Table 4. Separate equations subgroup approach (model 6) results for QLQC30 domain scores on EQ5D3L utility of i)â€‰<â€‰0.6, ii) â‰¥ 0.6 andâ€‰<â€‰1 and iii) 1. Table 5. Regression results (model 6) for EQ5D3L based utility values <â€‰0.6 on QLQC30 domain scores. Table 6. Regression results (model 6) for EQ5D3L based utility values â‰¥ 0.6 andâ€‰<â€‰1 on QLQC30 domain scores.
Additional file 3.
Patient characteristics for concurently collected EQ5D and partially incomplete QLQC30 questionnaires for which functional scale scores could still be calcuated.
Additional file 4: Figure 2.
Predicted EQ5D3L utility versus the observed utility for a) the RE model with QLQC30 domain scores (preferred model 1); b) the RE model with continuous QLQC30 questions (model 2); c) the RE model with QLQC30 dummy questions (model 3); d) the ordered logit model on the EQ5D3L domains (model 4); e) beta regerssion (model 5) and; f) the separate equations subgroup approach (model 6). Figure 3. Prediction error (observed â€“ predicted EQ5D3L uility) for a) the RE model with QLQC30 domain scores (preferred model 1); b) the RE model with continuous QLQC30 questions (model 2); c) the RE model with QLQC30 dummy questions (model 3); d) the ordered logit model on the EQ5D3L domains (model 4); e) beta regerssion(model 5) and; f) the separate equations subgroup approach (model 6).
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Franken, M.D., de Hond, A., Degeling, K. et al. Evaluation of the performance of algorithms mapping EORTC QLQC30 onto the EQ5D index in a metastatic colorectal cancer costeffectiveness model. Health Qual Life Outcomes 18, 240 (2020). https://doi.org/10.1186/s12955020014812
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DOI: https://doi.org/10.1186/s12955020014812
Keywords
 QLQC30
 EQ5D3L
 Quality of life
 Utility
 Mapping algorithm
 Colorectal cancer