Mapping the cancerspecific EORTC QLQBR23 onto the preferencebased EuroQol5D instrument
Authors
Name  Affiliation  

Zoltan Voko 
Department of Health Policy & Health Economics, Institute of Economics, Faculty of Social Sciences, Eötvös Loránd UniversitySyreon Research Institute 

Renata Nemeth 
Department of Statistics, Faculty of Social Sciences, Eötvös Loránd University 

Magdolna Dank 
Department of Diagnostic Radiology and Oncotherapy, Semmelweis University 

Zsófia NagyErdei 
Novartis Ltd 

Zoltan Kalo 
Department of Health Policy & Health Economics, Institute of Economics, Faculty of Social Sciences, Eötvös Loránd UniversitySyreon Research Institute 

Lajos Geczi 
National Institute of Oncology 
Background: For costeffectiveness analysis quality of life weights estimated by preference based utility measures are needed. In many studies however, quality of life is estimated by instruments that cannot provide utility measures. The aim of the study was to derive a function which can map the EORTC QLQBR23 questionnaire onto the EuroQol5D (EQ5D) questionnaire in breast cancer patients.
Methods: A cross sectional study was performed in Hungary in 615 breast cancer patients with different states of the disease. Quality of life was measured by both EORTC QLQBR23 and EuroQol5D. Ordinary stepwise backward leastsquares regression was used to develop a mapping function. Adjusted R2, Akaike’s Information Criterion (AIC) and root mean square error (RMSE) were used to assess model performance. The robustness of the models was tested by 10fold crossvalidation and bootstrapping.
Results: The “best fitting” model contained 26 BR23 item levels as predictors selected in a stepwise backward procedure. However, this model showed considerable variability in the selection of predictors. A model, which performed only marginally worse than the “best fitting model” (adjusted R2 0.44, RMSE: 0.216, AIC:85.8) and contained the BR23 items was much more stable, therefore we considered it as the best mapping function.
Conclusions: The expected value of EQ5D can be reasonably well predicted based on the results of EORTC QLQBR23 in patients with breast cancer. Its applicability, however, for prediction on the individual level is limited.Background
Patient reported outcomes considered important by the researchers, physicians and patients, as well. Therefore, in many research projects not only outcome events, health states are assessed, but the quality of life of patients, too. Quality of life is an important measure in health economic analyses, too. When costeffectiveness of interventions is compared, the incremental cost corresponding to incremental health gain is estimated. In these analyses health gain is measured by quality adjusted life years (QALYs). To obtain a valid estimate of QALY, one needs a preference based utility measure of quality of life. In many instances ample of data is available on the quality of life of patients with different health states, but usually measured by disease specific instruments which are not capable to provide utility measures. In these cases mapping should be considered as the secondbest solution. The advantage of mapping is that it enables outcomes data collected in a study to be used in economic evaluation, even if the main source trial or study did not include a preference based measure [1]. The aim of this study was to develop a function which can map the EORTC QLQBR23 questionnaire onto the EuroQol5D (EQ5D) questionnaire [2,3].
Methods
Participants, setting
The study was performed in 12 centers specialized in the care of cancer patients in Hungary. The data collection was completed in 11.200906.2010. Women were selected according to the treatment modalities. Quotas according to these modalities were given to the centers, and they enrolled the patients consecutively. The primary objective of the study was to estimate the quality of life of patients in different stages of breast cancer. This report presents the results related to the secondary objective, which was mapping EORTC QLQBR23 onto EQ5D. The study was approved by the institutional ethical boards and by the National Ethical Board for Medical Research.
Instruments
All patients were asked to fillin the EORTC QLQBR23 and the EQ5D questionnaires. The questionnaires were selfadministered, but help was provided by the study personals upon request. EQ5D consists of the EQ5D descriptive system and the EQ visual analogue scale [2]. We used the former for the analysis. QLQBR23 is the breast cancer supplement module of the EORTC QLQC30 questionnaire [3].
The EQ5D descriptive system comprises 5 dimensions: mobility, selfcare, usual activities, pain/discomfort and anxiety/depression. Each dimension has 3 levels: no problems, some problems, extreme problems. The respondent indicates which statement in each of the 5 dimensions describes her/his state the most appropriately. A total of 243 possible health states can be defined this way. Utility values were attached to these states in our analysis by the time tradeoff (TTO) valuation technique from a UK study [4].
The QLQBR23 functional and symptom scores are constructed following EORTC scoring rules. The questionnaire contains 20 fourlevel questions in five multiitem domains: systemic therapy side effects, arm symptoms, breast symptoms, body image and sexual functioning; and in addition, three single items to assess sexual enjoyment, upset by hair loss and future perspective. The primary result of the scale is the domain specific mean raw scores. These raw scores are then linearly transformed to the final scores of 0100 scales. Larger values correspond to better quality of life for functional domains (body image, future perspective, sexual functioning, sexual enjoyment), and worse quality of life for symptomatic domains (systemic therapy side effects, arm symptoms, breast symptoms, upset by hair loss) [5].
The questionnaire includes a few filter questions. If the answer to the filter question BR4 (“Have you lost any hair?”) was ’Not at all’, then the upset by hair loss score (BRHL) which is a singleitem measure calculated from BR5 (“Were you upset by the loss of your hair?”), was set to 0, its minimum. This recoding was in accordance with the EORTC Scoring Manual.
We used the same technique for the sexual enjoyment score (BRSEE): the score was set to 0 if the filter item BR15 (“To what extent were you sexually active?”) was “Not at all”. The latter recoding is not mentioned in the EORTC Scoring Manual but the technique we used was a straightforward extension of the technique applied for the other screening question. In this way we got valid, interpretable hair loss and sexual enjoyment scores even if the patient had not lost her hair and was not sexually active.
An overall BR23 score (OBR23) was calculated as the sum of the 8 scores. In the calculation of OBR23 the symptom scores were calculated in a reversed way to have the same direction as the functional scores (greater value corresponds to better quality of life). The EORTC Scoring Manual does not recommend using such a global score to measure quality of life, however, from pure statistical considerations, it could be worth using the overall score as predictor in the first simplest regression model serving as a point of reference for more complex models.
Analysis
OLS regression models
The essence of our approach was to explore the relationship between the two instruments by ordinary leastsquares (OLS) regression analyses.
We built four regression models using EORTC QLQBR23 questions aggregated to different extent as predictors. In each model the dependent variable was the EQ5D index (the utility value). The individual EQ5D dimensions were not attempted to be predicted separately, as previous studies showed it to be a less efficient or equally efficient procedure in terms of prediction [6,7].
The predictors of the models were refined step by step, always using a lower level of data aggregation. In the first model the predictor was the calculated QLQBR23 overall score. In the next model the predictors were the eight QLQBR23 scores. Next the predictors were the 23 QLQBR23 items (questions), separately. These models require the assumption that the predictors are measured by an interval scale, i.e. the same difference in a predictor has the same effect on the utility value regardless of the actual value of the predictor. For example in the model with the QLQBR23 scores as predictors if a score changes from 20 to 30 it has the same effect on the utility values as changing from 50 to 60 since the difference in the scores is 10. In the next more complex model the four levels of the items were entered as categorical predictors, not assuming this linear trend for the items of a question. Thus, in this case the number of the independent variables was three times the number of questions (because each item has four levels, one of which was the reference category).
If the full models fitted reasonably well, then we looked for more parsimonious models by running stepwise backward regression. We started with the full model and set the removal criterion to p= 0.1 and the reentry criterion to p=0.05. This means that if a predictor was not significant at the level of 0.1 then it was removed from the model but could reenter if its significance reached 0.05 after removing other predictors.
OLS regression assumptions were examined by the following methods:
 VIF index was used to test collinearity. Some of the problematic (VIF>10) predictors were removed.
 Nonlinearity in any of the predictors was checked with the help of augmented partial residual plots.
 Normality assumption for regression residuals was checked with plotting the quantiles of the regression residuals against the quantiles of standard normal distribution (QQ plot).
 The assumption of the homoscedasticity of the residuals was visually checked with plotting predicted values against standardized residuals since known statistical tests for homoscedasticity are very sensitive to violation of the normality assumption hence they cannot be used if normality assumption fails.
Assessment of goodnessoffit
Goodnessoffit and predictive power were measured with the root mean square error (RMSE), the adjusted R^{2} indices and Akaike’s Information Criterion (AIC). AIC is an informationtheoretical model selection criteria with the advantage of applicability to nonnested models. Lower AIC values indicate a better model. The range of the predicted EQ5D values is also reported since OLS models struggle to produce EQ5D indices that are negative or equal to 1.
Internal validity
Judging the internal validity of the results is of primary importance when predictive models are built. Since no external dataset is available, withinsample validation was carried out with the help of replication techniques. Two tests were conducted. Firstly, stability of the model coefficients is of interest since the relatively large number of predictors may lead to an overparametrised model. Stability, tendencytooverfitting was tested using kfold crossvalidation. Secondly, stepwise backward selections were validated with refitting the stepwisebackward model in 200 independent bootstrap samples of the same size as the original model had, using simple random sampling with replacement. The validity, robustness of the selection is described in terms of what percent of the replications retrieve each of the predictors selected in the original model.
The whole analysis was conducted by the software package STATA 10.0 [8].
Results
615 women with breast cancer participated in the study. Table 1 shows the major characteristics of the study population. Patients were roughly equally distributed in the treatment modalities defined study groups as planned. Seventy percent of the tumors were in stage T2 or in T1, approximately 60% had lymph node metastasis and 40% had distant metastasis.
Table 1. Characteristics of the study population
Characteristics  N (%) 
age (years) 50 5160 6170 >70 
144 (23.4) 188 (30.5) 177 (28.7) 107 (17.4) 
T1 stage^{*} T2 stage T3 stage T4 stage 
152 (30.4) 196 (39.2) 50 (10.0) 102 (20.4) 
Lymph node metastasis  373 (61.6) 
Distant metastasis  231 (38.1) 
Adjuvant chemotherapy  76 (12.3) 
Adjuvant radiotherapy  85 (13.8) 
Adjuvant hormone therapy  93 (15.1) 
Adjuvant targeted therapy  83 (13.5) 
Palliative chemotherapy  87 (14.1) 
Palliative radiotherapy  80 (13.0) 
Palliative hormone therapy  93 (15.1) 
Palliative targeted therapy  74 (12.0) 
* only 500 patients had tumour (T) classification at the time of questioning
Skip errors and missing data
55 patients should have skipped BR16 but answered it; their answers were recoded to missing. Similarly, 50 patients should have skipped BR5 but answered it; their answers were also recoded to missing.
The number of patients with missing data for one or more questions varied between 0.5% and 8% by score.
Table 2 presents the summary results of the calculated QLQBR23 scores and EQ5D index. As figure 1 shows, the distribution of the EQ5D index was heavily skewed with 22% of the indices equal to 1, 89% of the indices above 0.5 and 5% below 0.
Table 2. Summary statistics of QLQBR23 scores and EQ5D index
N  Mean  SD  Median  
BRBI (Body Image)  615  73.62  25.05  83.33 
BRFU (Future Perspective)  613  42.03  33.01  33.33 
BRSEF (Sexual Functioning)  536  13.77  21.48  0.00 
BRSEE (Sexual Enjoyment)  481  13.65  25.92  0.00 
BRST (Systematic Therapy Side Effects)  614  22.97  16.10  19.05 
BRBS (Breast Symptoms)  615  17.02  18.48  16.67 
BRAS (Arm Symptoms)  615  24.95  23.30  22.22 
BRHL (Upset by Hairloss)  595  19.16  32.29  0.00 
OBR23 (Overall BR23 score)  466  454.70  113.50  462.70 
EQ5D  614  0.70  0.29  0.73 
SD: standard deviation
Fulfilment of the model assumptions
Normal quantile plots seemed to indicate that normality assumption did not hold for any of the OLS models. Residual distributions had high kurtosis and were leftskewed basically due to the leftskewness of the EQ5D distribution. Technically, violation of normality affects the confidence intervals of the parameter estimates and hence the validity of the hypothesis tests, but does not affect the parameter estimates themselves. The confidence intervals of the parameters, however, should be interpreted with caution. Also, residuals were proved to be heteroscedastic in each case, hence regression models and backward selection procedures were run with HuberWhite sandwich estimate of the variance.
Overall QLQBR23 score (OBR23) regression
Because of missing QLQBR23 items, the overall OBR23 could be computed only in 466 patients. The mean EQ5D value of these patients and of those with missing overall QLQBR23 was not significantly different. The overall EQ5D index was missing in only 2 cases. The model used 465 observations.
The explanatory and predictive power of the model was very poor, with adjusted R^{2} of 0.195; RMSE of 0.262 and AIC of 75.75. The highest EQ5D value could appear at almost any level of OBR23, and observations around the mean OBR23 score had very large variance of the EQ5D value.
QLQBR23 component scores regression
Next we regressed EQ5D on the 8 QLQBR23 scores separately. The model used 465 observations. The variance inflation factor (VIF) did not show high collinearity for any of the eight BR23 scores. The OLS regression still did not have very impressive goodnessoffit statistics with adjusted R^{2}, RMSE and AIC equal to 0.298, 0.245 and 19.528, respectively. Three out of eight scores (body image, sexual enjoyment and breast symptoms) were not significant at the 0.05 level. Symptom scores are expected to have a negative effect on EQ5D, i.e. the smaller the score the better the quality of life, whereas functional scores are expected to have a positive effect on EQ5D. Among the predictors upset by hair loss score and sexual enjoyment score had the reverse, wrong sign.
QLQBR23 component items regression
By regressing EQ5D on all BR23 items separately, analysis of VIF suggested collinearity between BR15 and BR16 (Sexual Functioning and Sexual Enjoyment). We have chosen to drop BR16 considering that its derivation is slightly arbitrary (see definition of scores above). Overall, the model resulted in an improved goodnessoffit with adjusted R^{2} of 0.4430, RMSE of 0.2157 and AIC of 85.837 (Table 3). A relatively large number of predictors were nonsignificant. The sign of the parameter estimates were as expected with the exception of BR04 (“Have you lost any hair?”), BR11 (“Did you find it difficult to look at yourself naked?”) and BR18 (“Did you have a swollen arm or hand?”).
The stepwise backward selection left 9 items in the model, namely: BR1, BR4, BR6, BR11, BR13, BR14, BR18, BR19, BR20. Fitting this model using 516 observations yields adjusted R^{2} equal to 0.4391 and RMSE equal to 0.2141. Compared to the full model, AIC dropped notably from 85.837 to 116.5737. Again, the same predictors (BR04, BR11 and BR18) had regression coefficients with the reverse sign than expected.
Table 3. Coefficients of the full model with QLQBR23 component items as predictors
Coefficient  Pvalue  95% CI  
br01  0.053  0.006  0.090  0.015 
br02  0.004  0.843  0.033  0.040 
br03  0.005  0.796  0.042  0.032 
br04  0.013  0.416  0.018  0.043 
br05^{*}  0.011  0.599  0.029  0.050 
br06  0.131  0.000  0.169  0.093 
br07  0.017  0.182  0.008  0.041 
br08  0.017  0.311  0.050  0.016 
br09  0.016  0.421  0.054  0.023 
br10  0.030  0.158  0.012  0.071 
br11  0.025  0.120  0.006  0.056 
br12  0.024  0.119  0.053  0.006 
br13  0.041  0.001  0.065  0.016 
br14  0.089  0.001  0.038  0.140 
br15  0.038  0.155  0.091  0.015 
br17  0.021  0.233  0.055  0.013 
br18  0.032  0.035  0.002  0.062 
br19  0.063  0.001  0.100  0.025 
br20  0.021  0.355  0.066  0.024 
br21  0.014  0.552  0.032  0.060 
br22  0.010  0.605  0.050  0.029 
br23  0.000  0.993  0.035  0.034 
Constant  1.134  0.000  1.017  1.252 
CI: confidence interval
* set to 1 if BR04 is ‘Not at all’
QLQBR23 component item levels regression
The previous model required the assumption of interval scale QLQBR23 items. The assumption could be eliminated by creating a dummy variable for each level of the items. After omitting BR16 because of collinearity with BR15 (see above), this approach resulted in 22×3 = 66 dummy predictors. Compared to the previous model, a large deterioration in goodnessoffit could be observed, with an adjusted R^{2} of 0.4619, a RMSE of 0.21194 and an AIC of 62.83772. On the other hand, this was the first model to predict negative EQ5D values.
Since no collinearity was detected between the dummies by VIF analysis, we fitted OLS regression with stepwise backward selection starting from the full model of 66 dummy predictors, out of which 26 predictors were left. The model was fitted using 492 observations and yielded largely improved goodnessoffit with adjusted R^{2}, RMSE and AIC of 0.4936, 0.20587 132.7386, respectively.
Summary of model results
Table 4 summarizes the results of goodnessoffit for the above models. In terms of explained variance, predictive fit and AIC, the model with BR23 item levels a predictors and stepwise selection performed the best. Predicted EQ5D range should be judged comparing to the range of the observed data which is (0.594; 1). Table 4 shows that only three models gave negative predictions, but two of them predicted values significantly above 1, as well.
When deciding which model is the recommended mapping function, results of internal validity tests were also taken into account.
Table 4. Summary results of goodnessoffit
Predictor(s)  Selection  N  Adjusted R^{2}  RMSE  AIC  Predicted EQ5D range 
Overall BR23 score  Full  465  0.195  0.262  75.750  0.34; 1.00 
BR23 scores  Full  465  0.298  0.245  19.528  0.24; 1.15 
BR23 items  Full  470  0.443  0.216  85.837  0.02; 1.05 
BR23 items  Stepwise backward  516  0.439  0.214  116.574  0.05; 1.06 
BR23 item levels  Full  470  0.462  0.212  62.838  0.21; 1.18 
BR23 item levels  Stepwise backward  492  0.494  0.206  132.739  0.21;1.21 
RMSE: root mean squares error, AIC: Akaike’s Information Criterion
Internal validity, recommended mapping function
In order to test the stability of the stepwise backward selection processwhich yielded it, a bootstrap procedure with 200 replications was applied. 14 of the 26 predictors were retrieved less than 70% of the time, and 7 of them were retrieved less than 50% of the time.
The model with BR23 items as predictors and stepwise selection was the second best model according to AIC. Its bootstrap test showed a similar picture: 4 of the 9 predictors were retrieved less than 70% of the time, and 2 of them were retrieved less than 50% of the time.
The results above seem to indicate strong variability in the selection procedures. This hangs a question mark on the applicability of the two models with stepwise selection. The full models with BR23 items and with item levels as predictors were the best models among the remained ones. The latter was better according to AIC and RMSE, while adjusted R^{2} preferred the first one. Predictive validity of these two models was tested using 10fold crossvalidation. According to the results, the average increase in RMSE by going from training set predictions to validation set predictions was of significant size (0.025) in case of the model with BR23 item levels as predictors, while it was very small (0.002) in case of the other model.
After all, we favour the full model with BR23 items as predictors for two reasons. Firstly, it performed only marginally worse than the “best fitting” model. Secondly, it was more robust than the others.
Discussion
Our results showed that the expected value of a preference based quality of life measure (EQ5D) can be reasonably well predicted based on the results of a disease specific quality of life instrument (EORTC QLQBR23) in patients with breast cancer. Disease specific instruments generally have the advantage that they are tailored to those aspects of quality of life that are mostly affected by the specific disease, thus they are usually more sensitive to changes in quality of life of patients with the specific disease than the generic instruments. Therefore, these questionnaires are widely used in studies on outcomes in patients with a specific disease. With the use of the mapping function developed in this study it is possible to translate the results of existing and future studies in which the QLQBR23 questionnaire is used to the utility scale of EQ5D, and use these estimates in economic analyses.
There are many studies reporting mapping between EORTC QLQC30 onto EQ5D; most of them applied OLS regression [912]. Concerning the heavily skewed sample distribution of EQ5D, the same pattern was reported by Crott and Briggs in a sample of female patients with locally advanced breast cancer with good baseline health status. The ceiling effect (skewness toward 1 /perfect health/) and the lack of data from the lower region of the scale (below zero) of EQ5D is often problematic when building a mapping model regressing EQ5D overall score on any nonpreference based instruments [9]. Therefore, the predictive power of the mapping models can be characterized by how much they are capable of giving predicted scores equalling 1 or below 0. Our recommended function performed well in this respect. Nevertheless, OLS has limitations in general to give good predictions in the extreme regions when the outcome variable is so much skewed as EQ5D index is. A potential statistical alternative could be censored least absolute deviations (CLAD) regression, which has not been widely applied, but showed a better performance than OLS in a study of mapping SF12 onto EQ5D [13]. However, it is not selfevident that CLAD performs better than OLS when a disease specific instrument is mapped onto EQ5D. In a recent publication OLS performed better than CLAD in mapping Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) onto EQ5D [14]. A study was published recently, in which EORTC QLQ30 and EORTC QLQBR23 questionnaires were mapped onto EQ5D [15]. EORTC30 performed better than EORTC QLQBR23. In our view, the results of this study need to be interpreted cautiously, because the authors used only the component scores but not the component items as predictors. Our analysis showed that a mapping function with the component items as independent variables had a much better performance.
Although we tested the robustness of our results by internal validation, it would be a particular interest to externally test the validation of the proposed function in a different series of breast cancer patients before the function is actually used to estimate utility values for economic analysis.
Our study has some limitations. The relatively large mean squares error and low R^{2} statistics indicate that the model cannot be used to predict EQ5D index of an individualpatient, just to predict the expected value of a group of patients based on their QLQBR23 results. This is generally true for any mapping function, nevertheless in quite a few mapping studies with other instruments higher explained variance was achieved [9].
We used only the specific QLQBR23 questionnaire without the general QLQC30 questionnaire. BR23 focuses on the specific aspects of breast cancer related to quality of life and does not directly assess the domains which are included in the EQ5D. This already theoretically limits the possibility to map it onto EQ5D. Nevertheless, our recommended model still maps QLQBR23 onto EQ5D reasonably well, showing that the specific functional and symptomatic items of QLQBR23 largely correlate with the aspects of quality of life assessed by EQ5D. The sign of all scores except for upset by hair loss and sexual enjoyment were consistent with EQ5D in the model with scores as predictors. When interpreting this result, one needs to consider that if someone did not experience hair loss, or did not have an active sexual life, then the answer to the question about upset by hair loss and to the question about sexual enjoyment were set to their minimum value (i.e. persons with poor quality of life but not experiencing hair loss and not having active sexual life had a low value of the upset by hair loss and of the sexual enjoyment score). Nevertheless, the behaviour of some predictors (BR23 items) was inconsistent (have the opposite sign than the expected) in the recommended final model, too. These were BR04 (“Have you lost any hair?”), BR11 (“Did you find it difficult to look at yourself naked?”) and BR18 (“Did you have a swollen arm or hand?”).
We used UK tariff valuation of EQ5D. Recent studies affirmed differences in healthrelated preferences between countries, indicating the necessity of the estimation of national tariffs [16, 17]. Unfortunately, Hungarian tariff values of EQ5D are not available. Similarly, preferences of patients with breast cancer might differ by countries, which may restrict the applicability of the mapping function we developed.
Conclusions
We developed a mapping function of QLQBR23 onto EQ5D which is capable to estimate the expected value of EQ5D utility value in a group of patients with breast cancer conditional on the answers given to QLQBR23 questionnaire.
Acknowledgements
We are grateful to the patients who participated in the study and the physicians and nurses in the centers who organized and performed the field work. We gratefully acknowledge financial support of Novartis Hungary and Sandoz Hungary. Participating centers (principal investigators): Department of Diagnostic Radiology and Oncotherapy, Semmelweis University, Budapest (Magdolna Dank); Department of Oncotherapy, University of Szeged, Faculty of Medicine, Szeged (László Thurzó); National Institute of Oncology, Budapest (Lajos Géczi); Department of Clinical Oncology, University of Debrecen, Debrecen (János Szántó); Uzsoki Street Hospital, Budapest (László Landherr); András Jósa County Hospital, Nyíregyháza (József Erfán); Lajos Markusovszky Hospital, Szombathely (András Csejtei); Zala County Hospital, Zalaegerszeg, (Ágnes Ruzsa); Pándy Kálmán Békés County Hospital, Gyula (Béla Pikó); 3rd Department of Internal Medicine, Semmelweis University, Budapest (Éva Katalin Tóth); BácsKiskun County Hospital, Kecskemét (Gábor Pajkos); BorsodAbaújZemplén County Hospital, Miskolc (László Tóth, László Marázi)
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