Data
The data used for study come from the DS3 Score Study (NCT01136304) that followed 166 eligible patients 18 years and older from four investigative sites in the US and one in Canada; 33 patients were never treated and will be subjects for a future study. Here, we utilized data from the 133 treated patients for whom sufficient data were available to calculate baseline DS3 scores [
12]. DS3 scores were calculated for these patients annually from initiation of treatment for an average (standard deviation) of 13.3 (6.1) years. Initially, 57 (42.9%) patients received alglucerase, 73 (54.9%) imiglucerase, 2 (1.5%) velaglucerase, and 1 (0.8%) miglustat. At last follow-up, 105 (78.9%) patients were receiving ERT (71 imiglucerase, 33 velaglucerase, and 1 taliglucerase) and 12 (9.0%) were receiving SRT (6 miglustat and 6 eliglustat); treatment was unknown or had been interrupted in the remainder of patients. ERT was used in 99% of the treated patient-years. All ERT products were assumed to have biosimilar efficacy and therefore interchangeable.
Health states
We used the DS3 for GD1 to guide the development of health states [
11,
12]. The DS3 has been validated for GD1 patients at least 18 years old and was designed to capture the heterogeneous and dynamic aspects of the disease, especially skeletal complications that clinicians consider important when assessing disease severity. The DS3 was developed to serve as a standardized instrument to measure GD1 symptoms and severity (burden of disease) and to classify cohorts in GD1 clinical studies. The DS3 has three domains that include bone disease/skeletal, hematologic, and visceral symptoms. Each domain is measured by three or more assessment items scored by a physician. Content, face, criterion, discriminant, construct, and feasibility validity were deemed high by global GD1 experts and physicians treating patients with GD1 [
11]. The DS3 is highly correlated with other severity measures, such as the Clinical Global Impression (CGI) scale, the CGI-Severity (CGI-S), and the Zimran Severity Score Index [
13,
14]. Summary information on scoring the DS3 is available in Additional file
1: Appendix 1.
The nine mutually exclusive (alive) health states are based on GD1 severity categories defined by the total DS3 score category (mild, moderate, marked, and severe) and the presence or absence of bone pain (BP) or severe skeletal complications (SSC), which include lytic lesions, avascular necrosis, or fracture: (1) mild (0 ≤ DS3 ≤ 3.5) with no clinical symptoms of bone disease, (2) mild with BP, (3) mild with SSC, (4) moderate (3.5 < DS3 ≤ 6.5) without SSC, (5) moderate with SSC, (6) marked (6.5 < DS3 ≤ 9.5) without SSC, (7) marked with SSC, (8) severe (9.5 < DS3 ≤ 19) without SSC, and (9) severe with SSC. (This rank ordering was used in the ordinal regression analysis described below to derive transition probabilities.) Thus, each health state has two dimensions to best capture a treatment’s impact on hematologic and visceral symptoms and on bone disease and to create homogeneous groups of patients within each health state. Even though we do not conceptualize it as a health state, splenectomy status can still influence health outcomes in two ways: via its impact on the DS3 score, which defines the health state, and via its impact on health-state transition probabilities (as described below).
We estimated health state-specific utilities from patients enrolled in the DS3 Score Study for whom responses from the SF-36 (Version 1) questionnaire were available [
15]. DS3 and SF-36 data were not collected consistently or at fixed time intervals in the DS3 Score Study. As a result, only patient DS3 scores, and their corresponding health states, that could be matched to (the closest) SF-36 responses within a 90-day window around the DS3 score measurements were used to derive utilities. The original SF-36 measures were converted to the EuroQoL EQ-5D [
16] utilities for the United Kingdom (UK) population using the method developed by Brazier and Roberts (2004) [
17].
We assumed that health-state utilities depended on the DS3 severity category, bone pain, the presence of SSC, and patients’ age and sex at treatment initiation as follows:
$$ U= f\left( D, B, S, A, X\right), $$
where
U represents utility values,
D the DS3 severity (mild, moderate, marked, severe),
B the presence of bone pain,
S the presence of SSC,
A the age when the patient started treatment, and
X the patient’s sex. This equation was fitted with the generalized estimating equation method with a Gaussian error term and the identity link function, to account for multiple observations per patient, using data from the DS3 Score Study; heteroscedasticity-consistent (robust) standard errors were estimated. Utilities were calculated from the estimated regression coefficients and the values of
D,
B, and
S corresponding to each health state using the method of recycled predictions [
18]. The effect of bone pain was included when calculating utilities for health states that included SSC (see Additional file
2: Appendix 2).
Transitions between health states
Patients can remain in the same health state, transition to more or less severe health states, or die. We assumed that a patient’s probability of being in a particular health state, except for death, at a particular time depends on the health state in the previous period, the length of time the patient was receiving treatment, and other clinical characteristics as follows:
$$ {\mathrm{P}}_{\mathrm{r}}\left({H}_t\right)= f\left({H}_{t-1},{T}_t,,, D, S\right) $$
where
H is one the nine health states described above,
T is treatment duration (1, 2, or ≥ 3 years),
D is the starting DS3 category (mild, moderate, marked, or severe),
S is the patient’s splenectomy status, and
t indexes the time period. We included
T in the equation to capture the effect of disease stabilization over time [
19,
20].
This equation was fitted with the ordered logistic regression method using data from the DS3 Score Study; heteroscedasticity-consistent (robust) standard errors were estimated. Health states for the dependent variable were rank ordered based on the nine disease states described above. Although the assumption of proportional odds between categories of the dependent variable was not satisfied, it was not possible to use the less restrictive multinomial logistic or other more robust methods due to sparse data. Twenty-four annual health-state transition probability matrices were calculated from the estimated ordered logistic regression coefficients and all combinations of
T (3 levels)
D (4 levels), and
S (2 levels) using the method of recycled predictions [
18] (see Additional file
2: Appendix 2).
Model overview and analysis
We implemented our framework as a Markov state-transition model in Microsoft Excel® to simulate the experiences of cohorts of patients with GD1. The model includes nine health states based on DS3 Score Study severity categories as well as an absorbing state for death. Patients are assigned state-specific utilities for each health state. Except for death, patients can transition between health states, or remain in the same state, between each annual cycle. Although patients may have undergone splenectomy prior to starting the model, we assumed, in accordance with current clinical guidelines, that patients will not undergo a splenectomy once they start receiving treatment [
21]. Total undiscounted and discounted (3.5% per annum) quality-adjusted life years (QALYs) are calculated and a half-cycle correction is applied.
This model also includes death as an absorbing state. We estimated age-specific GD1 mortality probabilities from summary mortality data on patients enrolled in the International Collaborative Gaucher Group (ICGG) Gaucher Registry using a Gompertz survival function; the overall GD1 life expectancy at birth was 68 years (64 years for splenectomized patients and 72 years for nonsplenectomized patients) [
22]. Because the estimated mortality risks for ages 77 years and older were smaller than the corresponding mortality risks for the general UK population, we applied the maximum of the GD1-specific and the UK general population (
http://www.mortality.org) mortality risks for any given age to the patients in the model (see Additional file
2: Appendix 2).
To show how transition probabilities and utilities are used to predict long-term outcomes we focused on patients in the three most common health states observed in the DS3 Score Study data: mild with no clinical symptoms of bone disease (19%), moderate without SSC (28%), and marked with SSC (28%). The analyses were stratified by splenectomy status. Consistent with the characteristics of the patients enrolled in a recent clinical trial (ENGAGE), we assumed that 50% of the simulated cohort were women and all started treatment at 32 years of age [
23]. Total undiscounted and discounted (3.5% per annum) quality-adjusted life years (QALYs) are calculated and a half-cycle correction is applied.