01032015  Uitgave 3/2015 Open Access
Mapping FACTP to EQ5D in a large crosssectional study of metastatic castrationresistant prostate cancer patients
 Tijdschrift:
 Quality of Life Research > Uitgave 3/2015
Introduction
Prostate cancer is the most common cancer in Europe among men [
1]. In 2012, there were 417,000 new cases of prostate cancer in Europe, representing 12.1 % of all new cancers [
1]. The economic burden associated with this high incidence is substantial. For example, the combined cost of direct healthcare, informal care and productivity loss associated with prostate cancer was estimated at €7,848 million in the European Union, in 2009 [
2].
Despite 80–90 % of metastatic prostate cancer patients responding to androgen deprivation therapy [
3], progression to castrationresistant disease occurs in most patients after 2–3 years, with a subsequent survival time of 24–48 months [
4]. The healthrelated quality of life (HRQoL) of patients with prostate cancer declines substantially toward the end of life [
5]. Therefore, treatment of metastatic castrationresistant prostate cancer (mCRPC) is mainly palliative, with the aim of prolonging survival, relieving symptoms and improving HRQoL. The European Association of Urology guidelines recommend docetaxel as firstline chemotherapy, together with corticosteroids, for the treatment of symptomatic mCRPC [
6]. Bisphosphonates are prescribed for the management of metastatic bone disease (present in >90 % of patients with mCRPC [
7]) to prevent skeletalrelated events and improve symptom control [
6]. Radionuclides, radiotherapy and analgesics may also be considered for the management of bone pain [
6].
Costefficacy is important in the technical evaluation of new therapies by reimbursement agencies. Generic preference instruments, such as the EuroQol5D (EQ5D) [
8], can aid decision makers in resource allocation. These instruments generate health state utilities that can be used to compare qualityadjusted life years gained for interventions across different patient groups and diseases. However, measurements of HRQoL in clinical trials often use diseasespecific instruments that address outcomes important to a particular patient population, thus limiting their usefulness in costutility analyses. One solution is to derive validated algorithms that map scores from diseasespecific HRQoL instruments onto generic preference instruments. This approach has been accepted by bodies such as the UK’s National Institute for Health and Care Excellence, who specifically require EQ5D utility values as part of health technology assessment submissions [
9].
In line with such requirements, an increasing number of strategies for mapping diseasespecific responses to preferencebased instruments have been published. A database held at the Health Economics Research Centre, Oxford University, lists ninety studies of statistical mapping to predict EQ5D utilities [
10]. However, only one of these focused on mCRPC. Furthermore, 17 % of models were based on less than 200 observations and 39 % of studies used ordinary least squares (OLS) regression as the single statistical tool.
The mCRPC study included in the database demonstrated the feasibility of mapping the functional assessment of cancer therapyprostate (FACTP) questionnaire, which specifically measures the HRQoL of prostate cancer patients, to EQ5D scores [
11]. However, application of the algorithm to an external data set was found to yield mean EQ5D values greater than 1 [
12], and the algorithm requires a correction applicable to a truncated linear model [
13].
Therefore, a requirement remains for the development of a mapping function that adequately predicts EQ5D utility values based on responses to FACTP. In this article, we describe the construction of a prediction model using data obtained from a large, crosssectional, observational study in patients with mCRPC. Furthermore, we assess the performance of four regression models to predict EQ5D utility values from responses to the FACTP questionnaire. In addition to OLS, Tobit, median and Gamma regression models were included to account for ceiling effects and to anticipate any violations of normality and homoscedasticity.
Methods
Study sample and data collection
Data were derived from a crosssectional, observational study conducted in six countries: Belgium, France, Germany, Sweden, the Netherlands and the UK. The study enrolled male patients aged ≥18 years presenting with mCRPC at 47 specialist prostate cancer centers during a 10month recruitment period. Consecutive patients who visited the clinic during regular followup visits were invited to participate. Patients were eligible for inclusion in the study if they had a histologically or cytologically confirmed diagnosis of adenocarcinoma of the prostate; prostate cancer progression documented by prostatespecific antigen according to Prostate Cancer Working Group 2 (PCWG2) criteria or radiographic progression, and disease progression despite surgical or medical castration [a testosterone level of <50 ng/dL (<1.735 nM) was required if testosterone levels were routinely measured]. Exclusion criteria included participation in any investigational drug study or any expanded access program during the observation period. Patients’ HRQoL was assessed at the inclusion visit by utilizing the EQ5D and FACTP questionnaires.
Study instruments
FACTP is a questionnaire that has been validated to estimate HRQoL in men with prostate cancer [
14]. The tool comprises the 27item FACTGeneral (FACTG) questionnaire, which measures HRQoL in cancer patients, and a 12item prostate cancer subscale, designed to measure prostate cancerspecific HRQoL. The FACTP is scored by adding the subscales of the FACTG plus the prostate cancer subscale to yield a comprehensive HRQoL score.
The EQ5D comprises five domains, which measure general health status: mobility, selfcare, usual activities, pain/discomfort and anxiety/depression. In this study, the ‘3l,’ rather than the ‘5l’ version of the tool was used, which subdivides each domain into three, rather than five levels. The EQ5D provides a simple descriptive profile and a single utility index of health status and is widely used in health economic analyses [
8].
Model specifications—statistical analysis
Utility values were derived from EQ5D profiles based on a UKspecific EQ5D value set. The mapping exercise was conducted using responses from patients from multiple countries, and UK preference weights were applied.
The predictive validity of the five FACTP subscales, patient demographics, comorbidities and prior chemotherapy for utility values was tested using four different regression models: (1) OLS regression was used to construct linear prediction models of EQ5D, describing differences in mean EQ5D as a function of mean patient characteristics; (2) median regression was used to describe differences in median health status; (3) generalized linear models (GLM) with log link and Gamma family predicting EQ5D disutility (where disutility = 1—utility), which allows for skewed distribution of utility values and prevents prediction of utilities >1; (4) the Tobit model, also called a censored regression model, designed to estimate linear relationships between variables when there is either left censoring or right censoring in the dependent variable.
Model validation and predictive ability
A prediction model usually performs better with the data that were used in its development. Therefore, it is critical to evaluate how well the model works with other data sets. Similar to Wu et al. [
11], we estimated the crossvalidation
R
^{2} as the primary indicator of prediction model performance. Tenfold crossvalidation techniques were employed to derive goodness of fit statistics. To calculate the crossvalidation model performance indicators, the study sample was first divided into 10 equally sized groups. Each group was used successively to test each model, and the remaining 90 % of the sample were used to fit the prediction model. The resulting estimated prediction model was then used to estimate the performance of the original 10 % of the sample. Finally, the estimated error terms were pooled to estimate the overall performance of the model. Additionally, the root mean square error and the mean absolute deviation were generated.
Predictive ability was assessed by comparing observed and predicted EQ5D scores for three patient subgroups that were defined according to the chemotherapy status of patients at study inclusion: chemotherapynaïve, undergoing chemotherapy and previously treated with chemotherapy.
Results
Patient characteristics
The study included 699 patients. Questionnaire response rates were high, and complete FACTP and EQ5D questionnaires were available for 602 (86 %) patients. The response rates were not related to any of the baseline characteristics. The baseline characteristics of this population are shown in Table
1. Patient characteristics were generally similar across countries and between chemotherapy status subgroups, except for mean years since prostate cancer diagnosis (7.0, 4.9 and 4.8 years for the postchemotherapy, chemotherapynaïve and undergoing chemotherapy groups, respectively) and mean time since mCRPC diagnosis (1.6, 0.7 and 0.9 years, correspondingly), which were higher in patients who had received chemotherapy previously. In the postchemotherapy group, the median time since the end of chemotherapy was 3.7 months, and in those undergoing chemotherapy, the median time since initiation of treatment was in 4.6 months.
Table 1
Patient characteristics at time of inclusion
Number of patients analyzed,
n (%)


Total

602 (100)

Germany

272 (45.2)

France

94 (15.6)

Netherlands

89 (14.8)

UK

79 (13.1)

Belgium

45 (7.5)

Sweden

23 (3.8)

Mean age, years (SD)

72.1 (7.9)

Mean time since prostate cancer diagnosis, years (SD)

5.4 (4.4)

Mean time since initiation of androgen deprivation therapy, years (SD)

4.1 (3.5)

Mean time since failure of androgen deprivation therapy, years/diagnosis of mCRPC (SD)

1.0 (1.6)

Treatment status at inclusion,
n (%)


Chemotherapynaïve

236 (39)

Undergoing chemotherapy

223 (37)

Postchemotherapy

143 (24)

Comorbidity at inclusion,
n (%)


Cardiovascular disease

266 (44.2)

Endocrine/metabolic disease

111 (18.4)

Genitourinary disease

88 (14.6)

Renal disease

42 (7)

Gastrointestinal disease

61 (10.1)

Other

219 (36.7)

No comorbidity reported

114 (18.9)

Gleason score at initial diagnosis


≤ 5

29 (4.8)

6

51 (8.5)

7

150 (24.9)

8

125 (20.8)

9

129 (21.4)

10

12 (2)

Missing

106 (17.6)

Observed mean values for the EQ5D utility, FACTP and the five dimensions of the FACTP are presented in Table
2. For all patients, the mean FACTP and EQ5D utility scores were 104 and 0.66, respectively.
Table 2
Mean (SE) FACTP and EQ5D values
Treatment status

N

PWB

SWB

EWB

FWB

PCS

Total FACTP

EQ5D utility


Chemotherapynaïve

236

21.9 (0.4)

20.7 (0.4)

16.6 (0.3)

17.6 (0.4)

30.1 (0.6)

106.9 (1.6)

0.70 (0.02)

Undergoing chemotherapy

223

20.3 (0.3)

20.9 (0.3)

17.2 (0.3)

15.9 (0.4)

30.1 (0.5)

104.5 (1.4)

0.66 (0.02)

Postchemotherapy

143

18.8 (0.5)

20.2 (0.5)

16.0 (0.4)

15.4 (0.5)

28.3 (0.7)

98.6 (1.8)

0.60 (0.03)

All patients

602

20.6 (0.2)

20.6 (0.2)

16.7 (0.2)

16.5 (0.3)

29.7 (0.3)

104.0 (0.9)

0.66 (0.01)

Model selection
All FACTP subscales were included individually in the regression model, together with binary comorbidity variables and treatment status (Table
1). Squared terms were entered into each model to allow for nonlinear relationships with utility measures. All variables that were significant at the 0.05 level were retained in the final model.
The OLS model included most covariates of all models and included all FACTP subscales and age, with quadratic terms for emotional wellbeing (EWB), functional wellbeing (FWB) and age. Covariates that did not reach statistical significance were left out of the final model [social wellbeing (SWB) in the median regression model; SWB, EWB and FWB
^{2} in the Gamma model; and FWB
^{2} in the Tobit model].
The crossvalidation results for all prediction models are presented in Table
3. The OLS, median and Tobit models performed equally well and explained 61.2 % of the variation in the EQ5D index, while the Gammabased model explained slightly less variation (59.8 %). OLS regression generated a slightly lower root mean square error, while the mean absolute deviation between observed and predicted values was lowest for the OLS and median regression models.
Table 3
Crossvalidation results by statistical model
Model

R
^{2}

Mean absolute deviation

Root mean square error


OLS

0.612

0.148

0.198

Median regression

0.612

0.148

0.201

Gamma

0.598

0.157

0.201

Tobit

0.612

0.149

0.201

Table
4 presents the correlation values between observed and estimated utility values for the different models. The high correlations between estimated values for OLS, median and Tobit regression illustrate that estimates were very similar across the different statistical models.
Table 4
Matrix of correlations between observed and estimated utility values, by statistical model
Observed

OLS

Median

Gamma

Tobit



Observed

1.000

0.789

0.789

0.775

0.790

OLS

1.000

0.993

0.960

0.996


Median regression

1.000

0.965

0.991


Gamma

1.000

0.968


Tobit

1.000

Table
5 shows parameter estimates for the OLS model. All FACTP scales were found to be significantly predictive with the physical wellbeing (PWB) (coefficient = 0.022,
p < 0.0001) and FWB (coefficient = 0.026,
p < 0.0001) subscales having the highest explanatory value. Nonlinear relationships were observed between age and both the EWB and FWB domains, and this was accounted for by adding a squared term in the regression model. Comorbidities and prior chemotherapy did not add explanatory value.
Table 5
Parameter estimates for the OLS model
Estimate

Standard error

95 % confidence level

p value



Intercept

−1.7306

0.458

−2.6283

−0.833

0.0002

Age

0.0384

0.0129

0.0132

0.0636

0.0028

Age
^{2}

−0.0003

0.0001

−0.0005

−0.0001

0.002

PWB

0.0222

0.0023

0.0176

0.0267

<0.0001

SWB

−0.005

0.0017

−0.0082

−0.0017

0.0026

EWB

0.027

0.0097

0.008

0.046

0.0054

EWB
^{2}

−0.0007

0.0003

−0.0013

−0.0001

0.0179

FWB

0.0263

0.0064

0.0137

0.0389

<0.0001

FWB
^{2}

−0.0005

0.0002

−0.0009

−0.0001

0.009

PCS

0.008

0.0016

0.0048

0.0111

<0.0001

Figure
1 shows the scatterplot of observed versus the OLSpredicted values. The predicted utility value exceeded one for a limited number of patients (
n = 12, 2 %). The highest predicted value was 1.05.
×
Predictive ability assessment
Figure
2 shows the mean observed and estimated utility values as predicted by the four regression models according to treatment status at inclusion. Figure
3 represents a similar graph, stratified by number of years since mCRPC diagnosis. Both graphs suggest that the OLS model provides the best fit for the observed utility values for each of the subgroups. As shown in Table
6, a similar fit between observed and OLSpredicted utility was observed at the country level.
Table 6
Mean observed and estimated utility values, by country
Country

Patients (
n)

Mapped utility value



Observed

OLS predicted


Belgium

45

0.62

0.66

France

94

0.62

0.61

Germany

272

0.64

0.63

Netherlands

89

0.75

0.76

Sweden

23

0.78

0.72

UK

79

0.69

0.7

×
×
Discussion
We have developed an algorithm to map FACTP, a diseasespecific instrument, to EQ5D, a generic preference instrument, based on data collected from mCRPC patients. OLS was the bestperforming model. It explained 61.2 % of the variation in EQ5D values following tenfold crossvalidation and provided good concordance between actual and mapped EQ5D utility scores in predictive assessment.
A previous study demonstrated the feasibility of mapping FACTP to EQ5D scores [
11]. However, the equation cannot be used without correction [
13]. Furthermore, it has been reported that linear regressions may not always accurately predict the EQ5D distribution for high and low EQ5D values [
15,
16]. Our data tend to confirm this observation; the mapping formula tended to overpredict utility at the lower end of the scale (below 0.4; Fig.
1). Additionally, linear regression may not account for the bounded nature of the EQ5D, leading to implausible estimates outside of the possible range of values (1 to −0.594). We used a range of regression models to estimate EQ5D utility values. Tobit regression was included in our analyses to account for the ceiling effect, as it allows for censored dependent variables, and censored the predicted values at 1. However, the Tobit model operates poorly if assumptions of normality and homoscedasticity are violated [
17]. Median regression does not rely on these assumptions. However, it has been reported that median regression, while not explicitly dealing with censoring, is equivalent to censored least absolute deviation (used by other mapping studies) when censoring occurs in less than 50 % of the study sample [
18]. We also used a generalized linear model (Gamma regression) to account for any skewed distribution of utility values and prevent prediction of utilities >1.
Over the past decade, there has been an increase in the number of studies that have mapped diseasespecific responses to preferencebased instruments. In addition to the Oxford database [
10], a recent literature review identified ten studies that used mapping methods to determine utilities from two cancerspecific instruments (QLQC30 and FACT) [
19], of which only one study focused on mCRPC patients [
11].While statistical models differed across the ten studies, most employed an OLS method and did not conduct an outofsample validation. Most studies also used the statistical significance of the coefficients corresponding to different components of the HRQoL scale to determine which variables should be retained in the final model, with a parsimonious approach to final model selection. In doing so, most studies reported that OLS regression performed best, irrespective of its strict assumptions. All of the reviewed studies reported the models’ explanatory power in terms of R
^{2}, with a range of values between 0.417 and 0.909.
In our study, OLS regression performed equally well to the median and Tobit models in predicting utility scores, with an
R
^{2} (0.612) in the middle of the range reported by the recent literature review [
19]. In view of the relative simplicity of applying OLS regression formulae to other datasets, this was retained as our final model.
The patients included in this study provided FACTP and EQ5D data in line with those previously reported. For example, Sullivan et al. measured FACTP and EQ5D scores in 280 patients with a mean time from initial diagnosis of prostate cancer to diagnosis of mCRPC of 3.51 years and mean time from diagnosis of mCRPC to study entry of 1.5 years [
20]. FACTP prostate cancer subscale scores ranged from 27.3 to 30.7 and the EQ5D utility ranged from 0.527 to 0.750 across the seven countries included. These compare to a mean FACTP prostate cancer subscale of 29.7 and mean EQ5D utility of 0.66 in our study. In both studies, the FACTP scores and EQ5D utility index indicate the significant impact of prostate cancer on patients’ HRQoL.
The mapping exercise in our study was similar to that published previously by Wu et al. [
11]. Both studies used data from multinational studies and applied UK preference weights. Mean observed values for EQ5D and FACTP were very similar in both studies (EQ5D:0.66 and 0.64; FACTP: 104 and 105 for the present study and Wu et al., respectively). In addition to the OLS and median regression employed by Wu et al., we explored two additional statistical models. However, in both studies, OLS was retained as the bestperforming model. The estimates of the coefficients of the FACTP subscales based on the OLS model were in similar directions, with a high weight assigned to the PWB subscale in both studies. However, the larger sample size in this present study (
N = 602) compared with Wu et al. (
N = 280) may allow for the generation of more precise parameter estimates.
The limitations of our study include the derivation of utility values using the UKspecific EQ5D value set. Algorithms developed using countryspecific preference weights may account for differences in preferences arising from cultural influences, and value sets should be appropriate to the economic analysis required. The extent to which our algorithm can be generalized is strengthened by the multinational nature of the population that was used. However, further analysis is required to validate the algorithm in other populations.
Although regressionbased approaches are commonly used to map HRQol instruments, a recent publication by Fayers et al. (2014) suggests that such approaches may result in biased estimates as a result of regression to the mean [
20].
Diseasespecific instruments have been developed to address aspects of healthrelated outcomes that are important to specific patient populations and can overcome the limitation of generic instruments, which may lack the responsiveness to detect meaningful differences in HRQoL. However, some studies have found that OLS regression tends to overestimate the true value of EQ5D utilities for patients in poor health, while underestimating the true EQ5D utilities at the upper end of the scale [
16,
21–
23]. Such considerations reinforce the use of a preferencebased measure when assessing HRQoL in clinical trials. Nevertheless, our analysis provides an algorithm that can effectively translate FACTP scores to generic utility values.
This study has developed an algorithm for mapping EQ5D index scores from FACTP. The algorithm was found to have good predictive ability, with a high degree of correlation between observed and predictive EQ5Dbased utility scores in defined subgroups of patients with mCRPC. The algorithm provides an instrument for the calculation of appropriate preferencebased HRQoL scores for use in analyses of interventions for mCRPC when a generic measure is not available.
Acknowledgements
Funding for this study was provided by Janssen Pharmaceutica NV. We thank Paul Coyle (Senior Medical Writer) at Synergy Vision, UK, for the provision of editorial assistance, which was funded by Janssen Pharmaceutica NV.
Conflict of interest
None.
Ethical standard
The study was conducted in accordance with the principles of the Declaration of Helsinki, the International Conference on Harmonisation (ICH) and the Guidelines for Good Pharmacoepidemiology Practices (GPP), applicable regulatory requirements and sponsor policy. Each patient provided written informed consent. The data were collected and processed with adequate precautions to ensure confidentiality, and compliance with applicable data privacy protection laws and regulations
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