Mapping function from FACTB to EQ5D5 L using multiple modelling approaches: data from breast cancer patients in China
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Abstract
Background
The Functional Assessment of Cancer TherapyBreast (FACTB) is the most commonly used scale for assessing quality of life in patients with breast cancer. The lack of preferencebased measures limits the costutility of breast cancer in China. The goal of this study was to explore whether a mapping function can be established from the FACTB to the EQ5D5 L when the EQ5D healthutility index is not available.
Methods
A crosssectional survey of adults with breast cancer was conducted in China. All patients included in the study completed the EQ5D5 L and the diseasespecific FACTB questionnaire, and demographic and clinical data were also collected. The Chinese tariff value was used to calculate the EQ5D5 L utility scores. Five models were evaluated using three different modelling approaches: the ordinary least squares (OLS) model, the Tobit model and the twopart model (TPM). Total scores, domain scores, squared terms and interaction terms were introduced into models. The goodness of fit, signs of the estimated coefficients, and normality of prediction errors of the model were also assessed. The normality of the prediction error is determined by calculating the root mean squared error (RMSE), the mean absolute deviation (MAD), and the mean absolute error (MAE). Akaike information criteria (AIC) and Bayes information criteria (BIC) were also used to assess models and predictive performances. The OLS model was followed by simple linear equating to avoid regression to the mean.
Results
The performance of the models was improved after the introduction of the squared terms and the interaction terms. The OLS model, including the squared terms and the interaction terms, performed best for mapping the EQ5D5 L. The explanatory power of the OLS model was 70.0%. The AIC and BIC of this model were the smallest (AIC = 705.106, BIC = 643.601). The RMSE, MAD and MAE of the OLS model, Tobit model and TPM were similar. The MAE values of the 5fold crossvalidation of the multiple models in this study were 0.07155~0.08509; meanwhile, the MAE of the TPM was the smallest, followed by that of the OLS model. The OLS regression proved to be the most accurate for the mean, and linearly equated scores were much closer to observed scores.
Conclusions
This study establishes a mapping algorithm based on the Chinese population to estimate the EQ5D5 L index of the FACTB and confirms that OLS models have higher explanatory power and that TPMs have lower prediction error. Given the accuracy of the mean prediction and the simplicity of the model, we recommend using the OLS model. The algorithm can be used to calculate EQ5D scores when EQ5D data are not directly collected in a study.
Keywords
Mapping Health utility Breast cancer EQ5D5 L FACTB Quality of lifeAbbreviations
 AIC
Akaike information criteria
 BCS
Additional concerns for breast cancer
 BIC
Bayes information criteria
 CLAD
Censored least absolute deviations
 EQ5D
EuroQol5 dimension
 EWB
Emotional wellbeing
 FACTB
Functional Assessment of Cancer Therapy – Breast
 FWB
Functional wellbeing
 MAD
Mean absolute deviation
 MAE
Mean absolute error
 OLS
Ordinary leastsquare
 PWB
Physical wellbeing
 QALYs
Qualityadjusted life years
 RMSE
Root mean squared error
 SWB
Social/family wellbeing
 TPM
Twopart model
Background
Breast cancer has a devastating effect on global population health, accounting for 0.52 million annual deaths [1]. In China, the morbidity rate of breast cancer significantly outweighs that of other cancers, although the survival rate of breast cancer patients has dramatically increased with the development of clinical practice and disease management [2]. As survival rates have improved, healthrelated quality of life has gained significant attention recently, since the vast majority of survivors suffer from a loss of functions, including arm activity, sexual activity, and sleep quality [3, 4, 5]. At the same time, the growing number of survivors and the comprehensive application of advanced medical technology are increasing the burden of the disease on society [6], which calls for an economic reevaluation, such as a costutility analysis.
Extensive generic nonpreferencebased questionnaires were administered in a prior study to measure healthrelated quality of life; these questionnaires included the SF36 [7], the EORTC [8], the QLQC30 [9], the IBCSG, the WHOQOL BREF, and the FACTB. For breast cancer patients, the chief among these is the FACTB, which can most accurately measure quality of life [10]. Nonpreferencebased questionnaires are not appropriate for a costutility analysis, since their results cannot derive qualityadjusted life years (QALYs) directly. The QALY is a widely used measure of health improvement that is used to guide healthcare resource allocation decisions [11]. Therefore, preferencebased measures are highly recommended in healtheconomic evaluations, such as the EQ5D and SF6D, for these measures can directly assess health utility [12, 13].
Although generic preferencebased measures, especially the EQ5D, are highly recommended, they are usually excluded in clinical trials [14]. A recent systematic review of breast cancer health utility values in China found that all three studies of health economics models in China cited measurements of breast cancer patients in the UK or Hong Kong, China [15]. The lack of health utility values limits the development of health economics research. One potential solution is to perform a mapping function, mapping from nonpreferencebased to preferencebased measures. Although a mapping function would lose some information and increase uncertainty, it is currently the only solution for conducting a costutility analysis when straightforward health utility data are unavailable [16]. Therefore, it is of great significance to establish a health utility value mapping model for Chinese populations, which can broaden the sources of health utility values and provide important parameters for health economics evaluation.
Currently, there are 3 studies focusing on mapping from FACTB to EQ5D [16]. Two prior studies from Singapore performed mapping functions from FACTB to EQ5D5 L among breast cancer patients, and applied the utilityscoring systems, which were derived from data of British and Japanese patients [17, 18]. A study from the UK used the EQ5D3 L scale and UK tariffs [19]. However, the study pointed to disparities in utilityscoring systems among nations, owing to different utility weights [20]. Therefore, a utilityscoring system of one nation will not necessarily be applicable to other nations.
A prior study demonstrated that several sociodemographic and clinical factors are associated with the health utility of breast cancer patients [21, 22, 23], including age, gender, income, education, and treatment. It is unknown whether these factors could generalize to the overall Chinese population.
The present study will first develop three sophisticated mapping functions from the FACTB to the EQ5D5 L using three modelling algorithms, including the ordinary least squares (OLS) model, the Tobit model, and the twopart model (TPM). Second, this study will compare the predictability of the three models, and the resulting data will be used to select the most appropriate model for this purpose.
Method
Participants
The study included 446 breast cancer patients meeting the following criteria:1) diagnosed by pathology or clinical tests; 2) aged 18 or above; and 3) indicated no mental disorders, thus demonstrating full communicative capacity. Patients with severe chronic comorbidities, including cardiovascular and psychiatric disorders, were excluded from this study. All patients came from a tertiary oncology hospital in West China.
Informed consent from all participants was obtained prior to the study. Ethical permission was granted by the Ethics Committee, West China School of Medicine/West China Hospital, Sichuan University (approval number 2017–255).
Data source
Healthrelated quality of life data were sourced from two measures, namely, the FACTB and the EQ5D5 L. Demographic data came from field investigation, while clinical data were obtained from electronic medical records. Data were collected in the period from November 2017 to May 2018. Data was collected by the research team. To ensure data qualification, a data collection manual was prepared and the interviewers were trained strictly prior to data collection.
Independent variables
Healthrelated quality of life from the FACTB
The FACTB contains 37 questions along five dimensions: physical wellbeing (PWB), social/family wellbeing (SWB), emotional wellbeing (EWB), functional wellbeing (FWB), and additional concerns about breast cancer (BCS) [24]. The values for each question range from 0 to 4, and final scores are anchored on a scale of 0 to 148, where 148 represents the highest quality of life. There are 7 items for physical wellbeing (PWB), 7 items for social/family wellbeing (SWB), 6 items for emotional wellbeing (EWB), 7 items for functional wellbeing (FWB), and 10 items for additional concerns about breast cancer (BCS). The total scores for each dimension are as follows: PWB, 28; SWB, 28; EWB, 24; FWB, 28; and BCS, 40. The validity and reliability of the FACTB in the Chinese version were confirmed [25].
Clinical data
From electronic patient records, this study obtained clinical data, including morbidity status, clinical stages, clinical practice, and menopausal status.
Demographic determinants
Selfreported demographic determinants include patient age, education status, marriage, type of medical insurance, profession, and household income.
Dependent variable from EQ5D5 L
This study used the widely validated EQ5D5 L to measure health utility as a dependent variable [26]. The EQ5D5 L comprises five selfreported dimensions and the EQVAS. The selfreported dimensions are mobility, selfcare, usual activities, pain/discomfort, and anxiety/depression; each of these is measured along 5 levels of severity. To investigate the correlation between the FACTB and the EQ5D5 L, this study assigned the values of severity to range from 5 to 1, where 5 indicates that patients can perform activities in the dimension without difficulty. Additionally, the respondents agreed to complete the EQVAS test to measure their health status. Values of health status are anchored on a scale of 0 to 100, where 100 represents the best health status imaginable.
Data analysis
The value set of China was used to transfer overall scores from the EQ5D5 L to health utility [27].
The Wilcoxon test and the KruskalWallis H test were performed to screen potential demographic and clinical determinants of health utility. Only those of statistical significance were introduced into the modelling process. The skewness of the results from the EQ5D5 L and the FACTB was assessed.
The Spearman correlation coefficient was used to evaluate the correlation between the FACTB and the EQ5D5 L.
Three modelling algorithms, namely, the OLS model, the Tobit model, and the twopart model, were used to develop mapping functions from the FACTB to the EQ5D5 L.
OLS is commonly used in econometrics to estimate parameters by minimizing the sum of squared errors of data. Although it performs well in many fields of research, its predictability could be restricted by the scale of health utility, ranging from 0 to 1. The ceiling effects of health utility could also lead to skewed distribution and heteroscedasticity, which invalidates the normality assumption of OLS. Therefore, OLS is theoretically not the most appropriate model in mapping health utility [28]. However, OLS was concluded to be the best model in a prior study and was referred to by approximately 80% of publications conducting mapping functions with regard to health utility [17, 29, 30].
The Tobit model is an alternative that improves the ability to cope with ceiling effects. Another alternative is the censored least absolute deviations (CLAD), a medianbased method. However, most econometric models are based on the mean, which is a consideration that led this study not to include or evaluate CLAD [31].

Model 1:Overall score of the FACTB

Model 2: All domain scores on the FACTB

Model 3: Domain scores on the FACTB of statistical significance in model2

Model 4: Model3 + squared terms of statistical significance in model2

Model 5: Model 4 + interaction terms of statistical significance in model2
To compare the models, we considered their goodness of fit, applicability, and simplicity. Goodness of fit indicates the extent to which the model interprets the observed data. Mean absolute error (MAE), root mean square error (RMSE), mean absolute deviation (MAD), Akaike information criteria (AIC) and Bayes information criteria (BIC) were used as important indicators for model selection:lower MAE, RMSE, MAD, AIC and BIC represent better models. R^{2} was computed to measure the predictability of the OLS model. In the Tobit and TPM regression methods, the determination coefficient R^{2} is not clearly defined. Referring to the study by Cheung YB et al. [17] and comparing the results of the two studies, we calculated the square of the correlation coefficient (r) between the observed and predicted values of each model. Here, r^{2} is equivalent to R^{2} in OLS. To avoid overestimating r^{2} due to an increase in independent variables, we define the adjusted r^{2} as follows: 1 \( \frac{\left(n1\right)}{\left(np1\right)}\left(1{\mathrm{r}}^2\right) \). In this formula, n represents the sample size, and p is the number of parameters in the model. Finally, if the model shows similar MAE, RMSE, MAD, AIC, BIC and r^{2} values, applicability and model simplicity will be considered. Due to the lack of available external data in this study, 5fold crossvalidation was used to examine the stability and reliability of the model, and the result of the crossvalidation was measured using the MAE.
Observed and predicted EQ5D values were plotted to measure model performance.
We also performed nonparametric tests (MannWhitney U tests for two categories or KruskalWallistests for more than two categories) to examine differences in EQ5D5 L index scores from different models by demographic and clinical features. Simple linear equating was used to model OLS 5 to avoid regression to the mean. We used the following linking function that transforms the Xscores to have the same mean and standard deviation as the Yscores [35]:Y= \( {\upmu}_{\mathrm{Y}}+\left(\frac{\upsigma_{\mathrm{Y}}}{\upsigma_{\mathrm{X}}}\right)\left(\mathrm{X}{\upmu}_{\mathrm{X}}\right) \), where μ_{X} and μ_{Y} are the mean values of X and Y, and σ_{X} and σ_{Y} the standard deviations. The mean of the model OLS 5 was 0.857, and the variance was 0.161. Therefore , μ_{X} was 0.857 and σ_{X} was 0.161.
Data analyses were performed in Stata version 12.0(StatCorp, College Station, TX).
Results
Demographic and clinical characteristics of the study participants
Characteristic  Groups  N  % 

Age, year  <45  74  16.59 
45~54  215  48.21  
55~64  138  30.94  
≥65  19  4.26  
Nationality  Han nationality  438  98.21 
Minority  8  1.79  
Education level  Elementary and below  144  32.29 
Junior high school  150  33.63  
Senior high school  88  19.73  
Undergraduate or over  64  14.35  
Marital status  Single  7  1.57 
Married  411  92.15  
Divorced/separated  14  3.14  
Widowed  14  3.14  
Account location  Rural  220  49.33 
Urban  226  50.67  
Healthcare insurance  Urban employees  193  43.27 
Urban residents  54  12.11  
New rural cooperative scheme  177  29.69  
Other  22  4.93  
Occupation  Public sector employee  28  6.28 
Enterprise or company employee/worker  28  6.28  
Selfemployed  23  5.16  
Farmer/worker  123  27.58  
Unemployed  148  33.18  
Retiree  96  21.52  
Household income in 2017, Chinese Yuan  <30,000  234  52.47 
30,000~80,000  148  33.18  
80,000~ 150,000  45  10.09  
≥150,000  19  4.26  
Course of disease,month  ≤12  133  29.82 
13~36  147  32.96  
37~60  78  17.49  
≥61  88  19.73  
TNM stage  0  17  3.81 
I  72  16.14  
II  224  50.22  
III  99  22.20  
IV  34  7.62  
Hormone receptor (ER/PR)  Positive  306  68.61 
Negative  78  17.49  
Mixed  56  12.56  
Unkonwn/missing  6  1.35  
HER2  Positive  355  79.60 
Negative  81  18.16  
Unkonwn/missing  10  2.24  
Inpatient/Outpatient  Outpatient  376  84.30 
Inpatient  70  15.71  
Surgical therapy  Breast conserving surgery  101  22.65 
Modified radical surgery  331  74.22  
Unsurgical  14  3.14  
Chemotherapy  No  37  8.30 
Yes  409  91.70  
Radiotherapy  No  175  39.24 
Yes  271  60.76  
Targeted therapy  No  403  90.36 
Yes  43  9.16  
Endocrine therapy  No  139  31.17 
Yes  307  68.83  
Menopause  No  63  14.13 
Yes  383  85.87  
Disease state  Primary breast cancer within one year (state P)  125  28.03 
Primary and recurrent breast cancer for the second year and above (state S)  258  57.85  
Recurrent breast cancer within one year (state R)  20  4.48  
Metastatic cancer (state M)  43  9.64 
Description of EQ5D5 L and FACTB scale scores
Item  Mean  SD  Median  Maximum  Minimum  Flooring (%)  Ceiling (%) 

EQ5D  0.857  0.193  0.902  1  − 0.349  0  25.11 
FACTB  104.031  19.732  106  146  31  0  0 
Correlation between EQ5D5 L scale and FACTB scale scores
Dimension  PWB  SWB  EWB  FWB  BCS  FACTB total score 

Mobility  0.463^{*}  0.264^{*}  0.316^{*}  0.386^{*}  0.332^{*}  0.424^{*} 
Selfcare  0.535^{*}  0.203^{*}  0.245^{*}  0.254^{*}  0.285^{*}  0.316^{*} 
Usual activities  0.432^{*}  0.334^{*}  0.360^{*}  0.405^{*}  0.418^{*}  0.483^{*} 
Pain/discomfort  0.469^{*}  0.272^{*}  0.416^{*}  0.305^{*}  0.425^{*}  0.465^{*} 
Anxiety/depression  0.488^{*}  0.378^{*}  0.643^{*}  0.428^{*}  0.533^{*}  0.627^{*} 
EQ5D5 Ltotal score  0.601^{*}  0.389^{*}  0.558^{*}  0.471^{*}  0.545^{*}  0.642^{*} 
Correlations between demographic and clinical characteristics and results from the EQ5D5 L were examined. Correlations between results from the EQ5D5 L and type of health insurance, clinical stage, TNM stage, admission, the practice of endocrine therapy, and morbidity status were statistically significant (P value less than 0.05). Age, minority status, education, marital status, registered location (Hukou), profession, household income, hormone receptor, HER2, surgical procedures, chemotherapy, radiotherapy, targeted therapy, and menopausal status were not found to be statistically significant.
Coefficient estimates of ordinary leastsquare regression
Variable  OLS1  OLS2  OLS3  OLS4  OLS5 

Constant  0.13583***  0.02434  0.03209  −0.73772***  − 0.9110*** 
FACTB total score  0.00693***  
PWB  0.02103***  0.02101***  0.05172***  0.05918***  
SWB  0.00118  
EWB  0.00368*  0.00400**  0.02837***  0.01932*  
FWB  0.00386***  0.00433***  0.01108**  0.02086***  
BCS  0.00722***  0.00728***  0.03138***  0.03505***  
Dimension squared  
PWB squared  −0.00088***  − 0.00030  
EWB squared  −0.00076***  − 0.00029  
FWB squared  −0.00017***  0.00006  
BCS squared  −0.00045***  0.00011  
Dimension interaction  
PWB × EWB  0.00006  
PWB × FWB  −0.00019  
PWB × BCS  −0.00111***  
EWB × FWB  −0.00019  
EWB × BCS  −0.00019  
FWB × BCS  −0.00036 
Coefficient estimates of Tobit and Twopart model using main effects with or without interaction terms
Variable  Tobit4  Tobit5  Twopart 4  Twopart 5  

Firstpart  Secondpart  Firstpart  Secondpart  
Constant  −0.60177***  − 0.77881***  0.00048  − 0.81605***  4.89e06  −1.02358*** 
FACTB total score  
PWB  0.04438***  0.05329***  0.62518**  0.05972***  0.76743  0.06598*** 
EWB  0.02293**  0.01407  
FWB  0.00821  0.01547  0.90802  0.02163***  0.89512  0.03590*** 
BCS  0.02609***  0.03107***  1.55562  0.04312***  1.78533  0.04396*** 
Dimension squared  
PWB squared  −0.00062***  − 0.00007  1.01569***  − 0.00106***  1.01664***  −0.00033 
EWB squared  −0.00057*  − 0.00023  
FWB squared  −0.00003  0.00013  1.00524  −0.00048***  1.00599*  −0.00019 
BCS squared  −0.00032*  0.00018  0.99500  −0.00069***  0.99905  −0.00015 
Dimension interaction  
PWB × EWB  0.00001  
PWB × FWB  −0.00013  1.00542  −0.00059*  
PWB × BCS  −0.00114***  0.98847  −0.00105***  
EWB × FWB  −0.00010  
EWB × BCS  −0.00005  
FWB × BCS  −0.00032  0.99508  −0.00042 
Summary of model performance for OLS, Tobit and TPM models
Model  Model 1  Model 2  Model 3  Model 4  Model 5 

OLS  
r^{2}  0.503  0.602  0.601  0.676  0.700 
Adjusted r^{2}  0.502  0.597  0.599  0.671  0.690 
RMSE  0.136  0.122  0.122  0.111  0.108 
MAD  0.106  0.112  0.112  0.103  0.101 
MAE  0.094  0.086  0.086  0.074  0.071 
AIC  − 511.486  −602.471  − 603.658  − 687.881  −705.106 
BIC  −503.286  −577.869  −583.157  − 650.979  −643.601 
Tobit model  
r^{2}  0.575  0.648  0.647  0.680  0.694 
Adjusted r^{2}  0.574  0.644  0.645  0.676  0.687 
RMSE  0.127  0.115  0.115  0.109  0.107 
MAD  0.099  0.106  0.106  0.103  0.102 
MAE  0.084  0.078  0.078  0.073  0.072 
AIC  −131.380  − 196.891  −197.837  −216.597  − 220.060 
BIC  −119.079  − 168.189  − 173.235  − 175.594  −154.455 
Twopart model  
r^{2}  0.534  0.615  0.614  0.674  0.695 
Adjusted r^{2}  0.533  0.611  0.611  0.669  0.689 
RMSE  0.132  0.120  0.112  0.110  0.106 
MAD  0.110  0.113  0.114  0.102  0.099 
MAE  0.087  0.081  0.082  0.072  0.071 
AIC  − 341.450  −408.173  − 410.354  − 470.352  − 492.476 
BIC  − 333.877  − 385.306  − 395.109  −443.674  − 454.365 
From the perspective of r^{2}, the OLS model (0.503~0.700) had the largest r^{2}, in comparison to that of the TPM (0.534~0.695) and the Tobit model (0.575~0.694). In models 1–4, the r^{2} values of the OLS model and the TPM were slightly smaller than that of the Tobit model. However, it was significantly improved in model 5, exceeding that of the Tobit model. Independent variables varied among models 1–5. Model 2 generally performed better than model 1 within each domain with respect to the overall score, while model 2 performed consistently with model 3, which had fewer independent variables and was more concise. The introduction of squared terms and interaction terms in models 4 and 5 improved model performance. For the three indicators of RMSE, MAD, and MAE, the value of model 5 was the smallest. Compared with RMSE, MAD, MAE of OLS 5, Tobit 5 and TPM 5, the values of the three indicators were very similar. OLS 5 had the smallest AIC and BIC values. Thus, considering the simplicity of the model, the bestperforming model of the 15 models was TPM 5.
Descriptive summary of EQ5D5 L utility index derived from observed and predicted values of best fitting models
Model  Mean  SD  Minimum  P10  Median  P90  Maximum  Upper bound(%) 

Observed data  0.857  0.193  −0.348  0.642  0.902  1  1  0 
OLS4  0.857  0.158  −0.213  0.663  0.905  0.972  1.005  0.897 
OLS5  0.857  0.161  −0.267  0.685  0.909  0.962  0.988  0 
Tobit4  0.852  0.156  −0.157  0.648  0.902  0.963  0.985  0 
Tobit5  0.853  0.160  −0.212  0.674  0.906  0.962  0.979  0 
TPM4  0.857  0.156  −0.178  0.668  0.904  0.971  0.992  0 
TPM5  0.857  0.160  −0.305  0.685  0.906  0.964  0.986  0 
Outof sample 5fold crossvalidation of best fitting models
Model name  Mean absolute error 

OLS 4  0.07495 
OLS 5  0.07369 
Tobit 4  0.08509 
Tobit 5  0.08319 
TPM 4  0.07271 
TPM 5  0.07155 
Mean actual value and predicted value between different demographic and clinical characteristics patients in 3 best models
Characteristic  Groups  Actual value  Predicted value  Equated value  

OLS5  P  Tobit5  P  TPM5  P  OLS5  P  
Healthcare insurance  Urban employees  0.871  0.870  0.002  0.866  0.003  0.869  0.002  0.872  0.002 
Urban residents  0.912  0.907  0.904  0.908  0.916  
New rural cooperative scheme  0.825  0.826  0.822  0.827  0.820  
Other  0.857  0.869  0.863  0.867  0.871  
Course of disease, month  ≤12  0.809  0.821  <0.001  0.817  0.001  0.819  <0.001  0.814  <0.001 
13~36  0.887  0.883  0.879  0.882  0.888  
37~60  0.912  0.896  0.893  0.895  0.904  
≥61  0.831  0.833  0.829  0.836  0.828  
TNM stage  0  0.900  0.897  0.051  0.893  0.072  0.896  0.144  0.905  0.051 
I  0.899  0.892  0.888  0.890  0.899  
II  0.869  0.864  0.860  0.863  0.866  
III  0.844  0.835  0.831  0.835  0.831  
IV  0.701  0.776  0.775  0.791  0.760  
Inpatient/Outpatient  Outpatient  0.889  0.882  <0.001  0.878  <0.001  0.881  <0.001  0.887  <0.001 
Inpatient  0.685  0.723  0.720  0.726  0.696  
Endocrine therapy  No  0.810  0.820  0.001  0.817  0.003  0.821  0.002  0.813  0.001 
Yes  0.878  0.873  0.869  0.873  0.877  
Disease state  Primary breast cancer within one year (state P)  0.814  0.818  <0.001  0.814  <0.001  0.816  <0.001  0.811  <0.001 
Primary and recurrent breast cancer for the second year and above (state S)  0.904  0.893  0.888  0.892  0.900  
Recurrent breast cancer within one year (state R)  0.779  0.776  0.773  0.782  0.760  
Metastatic cancer (state M)  0.737  0.792  0.789  0.803  0.779 
Discussion
This study performed several mapping functions, mapping from values of the FACTB to the health utility of the EQ5D5 L. Three modelling approaches, namely, OLS, Tobit, and TPM, performed heterogeneously with respect to r^{2}. From the perspective of r^{2} and adjusted r^{2}, the OLS model is the largest in model 5. Three modelling approaches performed similarly in the RMSE, MAD and MAE in model 5. The AIC and BIC of model OLS 5 were the smallest, although the TPM achieved a slightly smaller MAE value than the OLS model at the 5fold crossvalidation. Considering the comprehensive performance and simplicity of the OLS model, OLS 5 was selected as the best model (r^{2} = 0.700, adjusted r^{2} = 0.690, RMSE = 0.108, MAD = 0.101, MAE = 0.071, AIC = 705.106, BIC = 643.601).
To the best of our knowledge, this is a pioneering study for conducting mapping functions based on data from breast cancer patients in China. Although extensive research has been conducted onhealth utility mapping functions, only three prior studies performed mapping functions for breast cancer patients [16]. One study used adjusted limited dependent variable mixture models (ALDVMMs) to establish mapping between the FACTB and the EQ5D3 L scales [19]. However, we chose a 5dimensional scale to avoid ceiling effects. The only two articles that used the EQ5D5 L scale were from the same study and were based on data from 238 Singaporean women [17, 18]. Five regression models mapping from the FACTB to the EQ5D5 L were conducted, which may or may not set the upper limit of health utility to 1 [17]. The OLS model, which had the best performance in the Singaporean study, performed better in this study with respect to goodness of fit(r^{2} = 0.497, adjusted r^{2} = 0.489, RMSE = 0.013, MAD = 0.091). Consistent with prior studies, the Tobit model presented lower predictability in our study [17].
Although the EQ5D5 L mitigated ceiling effects and floor effects, compared with the EQ5D3 L, the ceiling effects still existed for 25.11% of participants in the current study. The skewed distribution of EQ5D5 L values is presented in Fig. 1. The TPM was conducted separately for health utility values of 1 and other values to cope with data limitations, which was consistent with prior studies [36]. In Table 7, we also found that the TPM has a better predictive effect than the OLS model on larger values. However, Table 9 shows that the OLS regression had the most accurate means by different demographic and clinical characteristics, and the linear equated scores were more similar to the observed scores.
Correlation coefficients among domains of the EQ5D5 L and the FACTB were assessed in this study, and the correlation coefficients were statistically significant (P values less than 0.001). In the past, there were mapping studies to explore the correlation between scales [37, 38]; in the case of a conceptual overlap between the two tools, the mapping is more likely to succeed. It is notable that the values of SWB did not predict health utility from the EQ5D5 L in the OLS model, which may result from the lack of domains related to social function onthe EQ5D5 L. Similarly, SWB was not statistically significant in prior mapping studies of lung cancer, prostate cancer and breast cancer [17, 39, 40].
A systematic review reported that R^{2} for the mapping function from a specific questionnaire to a generic health utility measure usually ranged from 0.4 to 0.6 [28]. The introduction of squared terms and interaction terms could significantly increase R^{2} to 0.8, which suggested that the association was nonlinear [41, 42]. The introduction of squared terms and interaction terms in models 4 and 5 in our study improved model performance. The r^{2} of the model OLS 5 reached 0.700, which indicated good results. In addition, in contrast to prior studies [17], this study selected its value set in China instead of using a nonnative crosswalk project to convert the EQ5D3 L and the EQ5D5 L, thus leading to improved model performance.
Overall, the mapping functions performed well in this study. Although the predicted average health utility of the OLS models much closer to the observed values, OLS would overestimate poor health and underestimate higher health utility, which was consistent with prior studies [33, 43, 44]. To solve this problem, we used simple linear equating to avoid regression to the mean [35]. This method achieved similar results in previous mapping studies [18, 45]. As shown in Fig. 3, model OLS 5 had the closest predictive values to actual EQ5D5 L scores after a linear equivalent method was applied.
The present study suffers from several limitations. First, the study was based on a small sample size from a single hospital. Future studies should consider collecting data from larger sample sizes and from multiple treatment centres. Second, it is impossible to conduct crossvalidation for external validity in independent data sets. Therefore, although crossvalidation is considered to be “second best”, it was used in this study due to a lack of external data sources. Finally, the study only used three modelling approaches in mapping functions; many advanced technologies, including the threepart model and the probit mapping function based on Bayesian networks, could be potential alternative approaches to mapping functions.
Conclusion
Mapping is primarily used to obtain utility scores from diseasespecific nonpreference tools, allowing a large amount of existing survey data to be used for economic analysis. The use of mapping algorithms has facilitated the development of costutility research. To the best of the author’s knowledge, this study is the first to develop a mapping algorithm between the FACTB and the EQ5D5 L in the Chinese patient population and to adopt the recently developed EQ5D5 L tariff value based on Chinese population preferences. The best model for estimating the EQ5D5 L value includes the FACTB subscale scores. The addition of squared terms and interaction terms improves the predictability of the model. When using several algorithms developed by these data, we found that the prediction performance of the OLS model was better than that of the Tobit model and the TPM. It is hoped that this algorithm will help to develop costutility studies to evaluate breast cancer treatments in China’s healthcare environment.
Notes
Acknowledgements
Not applicable.
Authors’ contributions
All authors have contributed to design of the study, the acquisition of data, and the interpretation of the results. QY and XXY analyzed the data and involved in drafting the manuscript; WZ and HL were involved in revising the manuscript critically for important intellectual content. All authors have read and approved the final manuscript.
Funding
This study was supported by a project of Health Commission of Sichuan Province, China (number of study:18PJ224).
Ethics approval and consent to participate
The study obtained the approval by the Ethics Committee, West China school of Medicine/ West China Hospital, Sichuan University. Informed consent from all participants was obtained prior to the study.
Consent for publication
Not applicable. All results are reported as aggregated data.
Competing interests
The authors declare that they have no competing interests.
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