Guidance has been published on NH modelling for rare diseases [9,10,11,12]. This details the requirement to construct a statistical analysis plan, pool data from multiple sources, make use of specific patient registry databases where available and have patient and clinical involvement in defining health states and mapping clinical outcomes to these states. This study followed the published guidance and any assumptions made in the construction of the NHM are explained and justified.

2.1 Health States

Health states were based on previously identified health states; health states which make sense to clinicians, patients and caregivers; and health states which can be defined using outcomes commonly collected in clinical trials and real-world practice.

2.1.1 Determining Previously Identified Health States and Outcomes Captured in Previous Clinical Trials

A targeted literature review (TLR) of previous NH studies and functional scales used in DMD was performed in MEDLINE. In the interest of expediency, and as there was no plan to undertake formal quantitative analysis from the findings, a TLR was considered a sufficient and pragmatic solution to providing an overview of published NH data.

The TLR identified existing health state definitions, key milestones in disease progression and the outcomes captured in clinical trials. The results of this review are presented in Supplementary Material 2 (see ESM). Following the review, a set of preliminary health states was determined which could be defined using outcomes commonly collected in clinical trials and real-world practice. These health states depicted the common ‘ambulatory’ model first described by Bushby et al. in the 2010 DMD Guidelines (early/late ambulatory/non-ambulatory) [13].

2.1.2 Expert Input

Health states were presented for stakeholder input to determine whether they reflected clinical experience, and step-changes in patient care and health-related quality of life. Stakeholder input included an advisory board meeting, follow-up questions with two neuromuscular specialists and validation of final health states with a group of clinical experts. The advisory board comprised the two neuromuscular specialists who provided follow-up input, one nurse, one patient advocate and three mothers of individuals with DMD, all from the UK. The advisory board also included three representatives from Duchenne UK and Project HERCULES contributors (including the University of Leicester and Source Health Economics). The final set of health states, developed with stakeholder input, were shared with 20 UK-based clinicians for validation; 14 clinicians did not provide a response, whilst six provided feedback confirming face validity of the states presented.

2.1.3 Final Health State Definitions

Figure 1 presents the final health states, which includes three phases: ambulatory, transfer and non-ambulatory; and permitted transitions.

Fig. 1

Model structure. HTMF hand-to-mouth function, vent. ventilation

Health states capture the progression of disease within each phase. This includes the loss of ambulatory function, the loss of the ability to stand and weight bear, and the progressive loss of upper body and respiratory function in non-ambulatory patients.

These health states reflect states that clinicians, patients and caregivers felt captured the natural history of DMD, and were defined using measures used in clinical practice.

The key addition to this model, compared with NHMs previously described in the literature, is the inclusion of the transfer state. This state was identified by patients and caregivers as a key stage in the progression of DMD due to its impact on quality of life, care support requirements and cost. Patients in the transfer state are no longer able to walk but can support their own weight to facilitate transfers, for example between wheelchair and toilet. Once this ability is lost, additional resources are required to transfer patients and the burden on caregivers increases.

Table 1 presents the health state definitions, which were informed by expert clinical input. A degree of pragmatism was required to define the identified health states using available clinical data. In particular, clinical opinion was required to estimate the forced vital capacity percent predicted (FVC%) associated with night-time and full-time ventilation. The rationale for each stage and the definitions used are presented in Supplementary Material 3 (see ESM).

Table 1 Health state definitions

The model splits after state 4, where patients start ventilation and lose hand-to-mouth function (HTMF), as there is no consistent order in which these events occur.

The inclusion of states for, or state definitions including, scoliosis and cardiomyopathy was considered. However, the reporting of data for these diagnoses in the primary data source, the Critical Path Institute (C-Path) Duchenne Regulatory Science Consortium (D-RSC), was poor. In addition, these sequelae do not represent discrete heath states, but are present in patients within several of the health states defined. The onset of scoliosis often occurs at the onset of loss of ambulation [14]. Most patients develop cardiomyopathic features between the ages of 10 and 15 years [15]. As such, future estimation of costs and utilities for economic evaluation using the health states in the NHM should capture these morbidities, for example, by assuming the proportion of patients in each state that may experience them and adjusting quality of life and resource use accordingly.

2.2 Data2.2.1 Critical Path Institute Duchenne Regulatory Science Consortium

The primary data source informing the NHM is the C-Path D-RSC database. The D-RSC database comprises patient-level multinational clinical data for DMD shared with D-RSC by the original data custodians. The dataset used includes anonymised individual patient data (IPD) from 11 international data sources, including NH studies, placebo arms of clinical trials and registry data (further details are provided in Supplementary Material 4, see ESM). The dataset included the following variables (among others): type of functional test performed, age when the test was performed, test score, race, mutation status and steroid use. Of note, there was not a standard set of common variables collected in clinical studies and registries in DMD; as such, the variables available varied between data sources.

Table 2 presents the number (%) of transitions observed from one state to another in the D-RSC dataset; that is, how many patients were observed in state X at one point in their follow-up and then state Y at the next. Transitions from health state 1 represented the largest percentage of transitions observed (3164 [70.8%]); observations in health states 1 and 2 (early and late ambulatory patients) comprised 81.3% of observed transitions. The greatest number of ‘transitions’ observed was in patients remaining in state 1 (the early ambulatory state; 67.4% of observed transitions).

Table 2 Transitions observed in the D-RSC dataset (%)

Of the 4467 observed transitions in the dataset, there were 54 (1.2%) backwards transitions, suggesting an improvement in function. Based on the small number of backwards transitions observed and clinical advice, it was deemed reasonable to assume a progressive NHM in which no backwards transitions can occur. As such, where backwards transitions were observed for an individual in the D-RSC dataset, their health state was assumed to remain unchanged.

There were very few transitions observed into or out of state 3 (the new ‘transfer’ state). There were no data pertaining to transitions into state 4 (the first non-ambulatory state) or out of state 4 into states 5 and 6, as no patients were observed in state 4 in the D-RSC dataset. This could be because in order to be assigned to states 3 or 4, a NSAA score (of 1 or 0, respectively) must be recorded, but if the patients are classed by clinicians as non-ambulatory, then the NSAA is unlikely to have been conducted.

2.2.2 Elicitation Exercise

Due to the paucity of data pertaining to health states 3, 4, 5 and 6 in the dataset, an elicitation approach was used to inform transition intensities. This included an initial pilot, in which information was elicited from four clinicians and four caregivers involved in the Project HERCULES collaboration. This was followed by an online survey of Duchenne UK stakeholders, with 20 responses from DMD parents, caregivers and practitioners (separate to the 20 UK-based clinicians who validated the final set of health states).

Using a questionnaire, respondents were asked to describe the average age at which patients enter and exit health states. From the responses received, the mean age and standard deviation (SD) for entering and exiting the states was estimated. These data were then used to simulate IPD from which transition intensities could be estimated [16]. Where some transitions were observed in the D-RSC dataset, the simulated IPD were used to augment rather than replace these data.

Using the elicitation approach, the estimated mean (SD) age at which patients transition into states 3, 4, 5 and 6 was estimated to be 11.8 (4.2), 14.3 (4.5), 19.5 (5.6) and 19.3 (6.4) years, respectively. Please see Supplementary Material 5 for more information and a copy of the survey used.

2.2.3 Mortality

No mortality data were available from the D-RSC dataset. A systematic literature review (SLR) and meta-analysis was therefore performed to identify published mortality data in DMD [17]. Kaplan Meier (KM) curves from 14 studies were digitised and IPD reconstructed via a frequently used algorithm, details of which are presented by Guyot et al. [18]. This is a commonly used technique for obtaining IPD from published studies that makes use of the fact that event times can be determined from the step-function of a KM curve. The digitised mortality data contained 2283 patients and 1050 deaths across the 14 studies. The total follow-up time was 40,274 patient years; the oldest patient in the dataset was aged 44 years. Mortality rates were determined from a parametric survival model assuming a piecewise constant hazard function. This included all 14 studies, and controlled for birth cohort (before 1970, 1970–1990 and after 1990).

Previous studies have observed improvements in survival since 1990 among individuals with DMD who are ventilated [17, 19, 20]. The authors observed this trend in the studies identified, with lower rates of mortality by age estimated in studies published since 1990. Therefore, mortality rates from the birth cohort after 1990 were used in the base-case analysis. The sub-set of patients born after 1990 included 943 patients, of whom 251 had died. Estimated median survival and reported statistics were consistent with the original studies. This validated the IPD reconstruction and estimation of mortality rates which were used in the NHM. Full methods and results of the meta-analysis are reported in Broomfield et al. [17].

2.3 Estimating Transition Intensities

Once the structure of the NHM (health states) had been agreed and data identified, transition intensities were estimated via the following six steps: (1) the mean age of patients observed in each state in the D-RSC dataset was estimated. (2) To estimate the mortality rate for each state, a piecewise constant hazard function was fitted to the mortality data, with cut points determined by the mean age in each state. (3) The initial values of a transition intensity matrix were specified using the estimated mortality rates and setting transition intensities for all transient states to 0.1 (initial transition intensities of 0.01 and 1 were also considered). (4) A multistate model was fitted in R using the msm package using the specified transition intensity matrix and fixing mortality rates at their initial values. (5) A new transition intensity matrix was then defined using the transition intensities estimated in Step 4 and mortality rates estimated in Step 2. (6) Steps 4 and 5 were then repeated using the newly defined transition intensity matrix until the model converged. Convergence was defined as transition rates being equal to 4 decimal places. An exponential distribution (i.e. constant transition intensities) was used to fit the multistate model for transitions up to health states defined by the requirement for full-time ventilation. A piecewise exponential distribution was assumed for transitions from full-time ventilation states to death. Initial consideration of the exponential distribution for all transitions led to an implausibly long length of stay in the full-time ventilation states. This was due to the long tails associated with the exponential distribution and a fixed mortality rate. Use of the piecewise exponential facilitated implementation of an increased rate of mortality after age 30 years in the full-time ventilation states. Age 30 years was selected as a mid-point in the follow up, approximately corresponding to the median survival of patients in the mortality dataset and in the published literature [17, 20].

2.4 Sensitivity Analysis

To explore areas of uncertainty, a set of scenario analyses were performed (Table 3). The NHM was generated with the transfer state (NHM A) and without (NHM B) in a scenario analysis to assess uncertainty associated with transitions into and out of the newly identified transfer state, where data were informed by the elicitation exercise.

Table 3 Scenario analyses