Multivariate modeling of magnetic resonance biomarkers and clinical outcome measures for Duchenne muscular dystrophy clinical trials

Abstract

Although regulatory agencies encourage inclusion of imaging biomarkers in clinical trials for Duchenne muscular dystrophy (DMD), industry receives minimal guidance on how to use these biomarkers most beneficially in trials. This study aims to identify the optimal use of muscle fat fraction biomarkers in DMD clinical trials through a quantitative disease‐drug‐trial modeling and simulation approach. We simultaneously developed two multivariate models quantifying the longitudinal associations between 6‐minute walk distance (6MWD) and fat fraction measures from vastus lateralis and soleus muscles. We leveraged the longitudinal individual‐level data collected for 10 years through the ImagingDMD study. Age of the individuals at assessment was chosen as the time metric. After the longitudinal dynamic of each measure was modeled separately, the selected univariate models were combined using correlation parameters. Covariates, including baseline scores of the measures and steroid use, were assessed using the full model approach. The nonlinear mixed‐effects modeling was performed in Monolix. The final models showed reasonable precision of the parameter estimates. Simulation‐based diagnostics and fivefold cross‐validation further showed the model's adequacy. The multivariate models will guide drug developers on using fat fraction assessment most efficiently using available data, including the widely used 6MWD. The models will provide valuable information about how individual characteristics alter disease trajectories. We will extend the multivariate models to incorporate trial design parameters and hypothetical drug effects to inform better clinical trial designs through simulation, which will facilitate the design of clinical trials that are both more inclusive and more conclusive using fat fraction biomarkers.

Study Highlights.

• WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

Duchenne muscular dystrophy (DMD) is a phenotypically heterogeneous rare pediatric disease. Drug development for DMD has accelerated during the past decade but continues to face significant challenges in endpoint and cohort selection. Significant correlations have been found between 6MWD, the current primary endpoint, and muscle fat fraction measures.

• WHAT QUESTION DID THIS STUDY ADDRESS?

Although regulatory agencies encourage the inclusion of imaging biomarkers in DMD clinical trials, the pharmaceutical industry receives minimal guidance on how to use these biomarkers most beneficially in trials.

• WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

We developed multivariate models quantifying the longitudinal associations between 6MWD and fat fraction measures from vastus lateralis and soleus muscles.

• HOW MIGHT THIS CHANGE DRUG DISCOVERY, DEVELOPMENT, AND/OR THERAPEUTICS?

The multivariate models will guide drug developers on how to use fat fraction most efficiently using available data, including 6MWD. The models will provide valuable information about how individual characteristics alter disease trajectories, which will facilitate the design of clinical trials that are both more inclusive and more conclusive using fat fraction biomarkers.

INTRODUCTION

Duchenne muscular dystrophy (DMD) is a phenotypically heterogeneous pediatric disease affecting 1.38 per 10,000 males. ¹ Affected individuals experience progressive muscle weakness and disability, with death typically occurring as a result of cardiac and respiratory failure in early adulthood. ¹ Drug development for DMD has accelerated during the past decade but continues to face significant challenges in both endpoint and cohort selection. Numerous phase II or III clinical trials have failed to detect significant differences in the primary endpoint (often a 6‐minute walk distance, also referred to as 6MWD), even in trials of therapies that eventually received conditional marketing approval. ² Sources of variability associated with the heterogeneity of the disease are insufficiently understood and lead to large sample size requirements, a condition that is hard to meet in rare diseases. ³

There is currently no cure for DMD and only one fully approved therapy (deflazacort [Emflaza®]), a corticosteroid. However, a large number of potential therapies (>30) are in clinical development, and although five therapies have received conditional marketing approval from either the U.S. Food and Drug Administration (FDA) (eteplirsen [Exondys 51®], golodirsen [Vyondys 53®], casimersen [Amondys 45®], viltolarsen [Viltepso®]) or the European Medicines Agency (EMA) (ataluren [Translarna®]), phase III clinical trials of these and other drugs have been inconclusive and controversial. ⁴ More appropriately designed trial protocols are needed to overcome the high rate of inconclusive and failed trials, which convincingly determine whether a therapy is effective.

Developing robust clinical trials in DMD is challenging because the disease is progressive and rare. ³ , ⁵ , ⁶ First, given that DMD is a progressive disease, it is critical to develop endpoints or biomarkers that cover the entire disease continuum. With endpoints that are only appropriate at some disease stages (e.g., ambulatory physical function tests), it is difficult to ascertain whether a drug is effective across other stages of the disease. In addition, individuals who are likely to transition between disease stages are often excluded from clinical trials. Second, because DMD is a rare disease affecting children, the number of individuals available to enter trials is limited. This limitation is further compounded by the number of concurrent trials being run. Finally, clinical trials in DMD often focus on a narrow range of individuals defined by age and functional ability to reduce heterogeneity and improve statistical power as well as select patients in whom the sensitivity of available clinical endpoints is presumed to be optimized. Collectively, these limitations and strategies result in the exclusion of a large segment of the DMD population from clinical trials, denying them the opportunity to share the burdens and benefits of trial participation and potentially reducing the generalizability of study results. A poll of industry representative attendees at the 2018 Parent Project Muscular Dystrophy annual meeting found that participant recruitment was the top barrier to conducting clinical trials in this population. ⁷

The FDA has explicitly encouraged the inclusion of imaging biomarkers, which can detect disease progression noninvasively and nonvolitionally. In addition, these biomarkers can be acquired across a large spectrum of disease stages in clinical trials for DMD. ⁸ , ⁹ Quantitative magnetic resonance imaging (qMR) biomarkers have proven to be sensitive to the progressive decline in muscle health, predictive of future changes in function, and able to detect therapeutic effects of investigational drugs. ⁵ , ¹⁰ , ¹¹ , ¹² This has resulted in the rapid inclusion of qMR biomarkers as primary or secondary endpoints in numerous clinical trials in DMD. The ImagingDMD study (NCT01484678) has captured the natural history of qMR biomarkers and functional endpoints over 10 years in a large DMD cohort (n = 180, ages 3–22 years, 1–9 years follow‐up).

The qMR biomarkers are noninvasive and nonvolitional and can be reliably and robustly measured across a wide age range (3 years to adulthood) in both ambulatory and nonambulatory individuals. These measures, which primarily quantify intramuscular fat accumulation, have been demonstrated to be sensitive to disease progression and drug effects as well. ¹³ , ¹⁴ In addition, they have been shown to be closely related to functional performance and predictive of future functional declines, ⁹ , ¹¹ , ¹³ , ¹⁴ , ¹⁵ demonstrating their promise as biomarkers for DMD.

Although the FDA and EMA explicitly encourage the inclusion of imaging biomarkers in clinical trials for DMD, ⁸ , ¹⁶ drug developers need more guidance on how to use these biomarkers most beneficially in trials. This study aimed to develop models to facilitate the use of qMR biomarkers for efficacy evaluation studies of potential therapies in DMD. We developed two multivariate models using a nonlinear mixed‐effect modeling approach that captures longitudinal changes of both the qMR biomarkers (i.e., magnetic resonance [MR] spectroscopy [MRS] fat fraction measures from the vastus lateralis [VL] and soleus [SOL], also referred to as FFVL and FFSOL, respectively) and a functional endpoint (i.e., 6MWD) simultaneously. We leveraged the comprehensive ImagingDMD data to develop the multivariate models, which will facilitate the design of clinical trials that are both more inclusive and more conclusive using qMR biomarkers.

METHODS

Existing data from ImagingDMD study

The ImagingDMD study used a multicenter (three sites: University of Florida, Oregon Health & Science University, and the Children's Hospital of Philadelphia), prospective, longitudinal study design to measure the progressive fat infiltration in the lower extremity muscles of a large DMD cohort. ¹⁵ , ¹⁷ Sequences and procedures were standardized across sites, and qMR measures demonstrated excellent day‐to‐day and between‐site reproducibility. ¹⁸ Annual qMR and functional measures were performed in 180 DMD participants with 1–9 years of follow‐up (mean follow‐up = 3.8 ± 2.6 years; n = 105 > 4 years), comprising the most comprehensive qMR study in muscle to date. Participant ages ranged from 3 to 22 years, and both ambulatory and nonambulatory individuals were included. Only males participated because DMD is an X‐linked genetic disorder, and females with a DMD phenotype are extremely rare. Primary MR measures included muscle fat fraction measured using MRS in the SOL and VL muscles. ¹⁴ , ¹⁸ , ¹⁹ ImagingDMD participants also provided extensive medication and medical history information by parent report. At each visit, weight and height were recorded, and ambulatory participants completed a standardized battery of functional evaluations typically used in clinical trials, including the 6‐minute walk test and timed supine to stand, 4‐stair climb, and 10‐meter walk/run tests. ⁵ , ¹⁷ All data were checked for quality by experts in the relevant field (MR and functional evaluation) before being included in a final data set.

Data exclusion and formatting

Individuals were excluded from the study data set if they were taking experimental therapeutics, such as dystrophin restoration therapies; if they were nonambulatory at baseline; or if, based on their mutation, they were likely to have nonzero dystrophin expression (e.g., exon 45–47 deletion, consistent with milder Becker muscular dystrophy). Subjects who were ambulatory after 15 years old were further excluded because of the presumed less severe disease progression, thus potentially defined outside of the scope of DMD. Missing values for individual measurements may result from a participant's failure to comply with task instructions or from inadequate data quality for magnetic resonance imaging (MRI) and MRS measures. Missing measures resulting from a participant's inability to perform a task as a result of disease progression were treated as censored and addressed using the likelihood‐based M4 method. ²⁰ , ²¹ For subjects with missing baseline values for the dependent variables, we used the first visit where all dependent variables have values and we defined it as the derived baseline. Finally, we excluded individuals who were nonambulatory at their derived baseline visits. This is because our model is fit‐for‐purpose, informing clinical trials with a target population for individuals with DMD 4 years of age or older who are ambulatory at their baseline visit. Participants were considered ambulatory if they were able to complete the 10‐meter walk/run in 45 s or less without assistance.

Time metric, dependent variables, and covariates

Age of the individuals at assessment was chosen as the time metric, consistent with our previously published DMD modeling work. ³ , ²² This is because the qMR biomarkers and physical functional endpoint are age‐dependent variables affected by DMD progression. The functional endpoints are also affected by developmental progress.

As dependent variables, 6MWD and MRS fat fraction measures from each lower extremity region (i.e., VL from thigh and SOL from calf) were used. The 6MWD is a functional test measure of the distance an individual can walk in 6 min. The MRS spectra were acquired from the belly of each muscle. The area under the fat and water peaks were measured, and the ratio fat over the sum of fat and water was calculated to obtain the fat fraction. ¹⁸ Figure 1 presents the natural history of a single individual's disease progression.

FIGURE 1.

Magnetic resonance (MR) spectra and images from a single subject capturing 4 years of disease progression. In these transaxial images and spectra, red indicates muscle water, and green indicates fat. MR spectroscopy fat fraction is measured from a single voxel, shown as the white rectangles in top images, and quantifies the ratio of the peak areas of fat (green) to the sum of peak areas of fat (green) and water (red).

Clinically relevant candidate covariates were identified in the data set, which can be collected at a clinical trial screening visit, with a focus on age, steroid use status, and scores measured at the first visit. To avoid duplicated effects of age as a covariate and the time metric, we formatted the data set to allow the baseline scores of the measures to vary by young versus old baseline age (cutoff: 7 years old ²³ ) and removed age from the covariate list.

Multivariate disease progression model development

Nonlinear mixed‐effects models were used for the multivariate disease progression models. Models were fit using the stochastic approximation expectation maximization algorithm in Monolix (Version 2021R1). After the longitudinal dynamics of each measure were modeled separately, the selected univariate models were combined using correlation parameters. Covariates were then added to the selected multivariate models.

For the structural model component that describes average changes of each dependent variable over age, several mathematical functions were considered, including linear, quadratic, sigmoid E_max and I_max functions, and the product of the Chapman‐Richards growth function and sigmoid I_max function. ²² The parameters of the structural functions, which determine the shape of the graphs, were chosen considering that the functional endpoint measure 6MWD decreases and the qMR biomarker fat fractions increase, respectively, as the disease progresses (Figure 2a–d).

FIGURE 2.

Longitudinal correlations between dependent variables and correlations among covariates of 118 individuals with Duchenne muscular dystrophy who were ambulatory at derived baseline visits. (a) Observed individual trajectories of 6MWD and FFVL versus age at assessments. (b) Observed individual trajectories of 6MWD and FFSOL versus age at assessments. (c) 6MWD versus FFVL (the Pearson correlation coefficient, r = −0.81). (d) 6MWD versus FFSOL (the Pearson correlation coefficient, r = −0.76). (e) Estimated correlations among continuous covariates. (f) Distribution of baseline measures per subgroup. Sample size: nonsteroid use and young = 10 subjects, nonsteroid use and old = 8 subjects, steroid users and young = 27 subjects, and steroid users and old = 73 subjects. 6MWD, 6‐minute walk distance (m); BS6MWD, baseline 6‐minute walk distance; BSFFSOL, baseline fat fraction measure from the soleus muscle; BSFFVL, baseline fat fraction measure from the vastus lateralis muscle; FFSOL, fat fraction measure from the soleus muscle; FFVL, fat fraction measure from the vastus lateralis muscle.

Variability around the structural model was quantified via two levels of random effects (sources of variability): between‐subject variability (BSV) and residual variability (RV). A logit‐normal distribution (Equation 1) was specified for parameters constrained within $\left(0,1\right)$. Otherwise, an exponential model (Equation 2) was used to characterize the BSV for non‐negative parameters.

$$\begin{array}{c}\text{logit}\left({\theta }_i\right)=\log \left(\frac{{\theta }_i}{1-{\theta }_i}\right)\sim \mathcal{N}\left(\text{logit}\left(\overline{\theta }\right),,,{\mathrm{\omega }}_{\theta }^2\right)\hfill \\ ⟺\text{logit}\left({\theta }_i\right)=\text{logit}\left(\overline{\theta }\right)+{\eta }_i,\text{where}{\eta }_i\sim \mathcal{N}\left(0,,,{\mathrm{\omega }}_{\theta }^2\right).\hfill \end{array}$$ (1)

$$\begin{array}{c}\ln \left({\theta }_i\right)\sim \mathcal{N}\left(\ln \left(\overline{\theta }\right),,,{\mathrm{\omega }}_{\theta }^2\right)⟺\ln \left({\theta }_i\right)=\ln \left(\overline{\theta }\right)+{\eta }_i\hfill \\ ⟺{\theta }_i=\overline{\theta }·{\mathrm{e}}^{{\eta }_i},\text{where}{\eta }_i\sim \mathcal{N}\left(0,,,{\mathrm{\omega }}_{\theta }^2\right).\hfill \end{array}$$ (2)

In Equations (1) and (2), ${\theta }_i$ is a model parameter for the ith individual, $\overline{\theta }$ is the typical (mean) population value, and ${\eta }_i$ is a normally distributed random variable with a mean of zero and variance ${\mathrm{\omega }}_{\theta }^2$. The RV was quantified by a separate error term that follows a mean zero normal distribution. Additive, proportional, and combined error models were considered. When the shrinkage of the variable is higher than 90% for a parameter, the random effect was removed from the parameter. Standard errors were estimated using a variance–covariance matrix computed from the negative of the second derivative of the log‐likelihood.

Inclusion of covariates were selected using the full model approach, along with assessments of the clinical importance of the effects. The power model used continuous covariates normalized with their median values and exponential functions of categorical covariates (Equation 3).

$$\begin{array}{c}{\theta }_{\mathit{ij}}={\overline{\theta }}_j·{\prod }_{k=1}{\left({\mathrm{C}}_{k,i}/{\mathrm{C}}_{k,\mathrm{ref}}\right)}^{{\beta }_{j,k}}·{\prod }_{k=1}{\left({\mathrm{e}}^{{\beta }_{j,a}}\right)}^{0\text{or}1}·{\mathrm{e}}^{{\eta }_{\mathit{ij}}},\hfill \end{array}$$ (3)

where ${\theta }_{\mathit{ij}}$ is the jth parameter for the ith individual, ${\overline{\theta }}_j$ is the typical (mean) population value of the jth parameter, ${\eta }_{\mathit{ij}}$ is a normally distributed random variable with mean zero and variance ${\mathrm{\omega }}_{\theta }^2$, ${\mathrm{C}}_{k,i}$ is the kth continuous covariate for the ith individual, ${\mathrm{C}}_{k,\mathrm{ref}}$ is the median value of the kth continuous covariate, and ${\beta }_{j,k}$ and ${\beta }_{j,a}$ are the exponents for the kth continuous and ath categorical covariate effects, respectively.

Model evaluation and validation

Model selection was guided by the Akaike information criterion (AIC), Bayesian information criterion (BIC), objective function value (OFV) for nested models, ²⁴ convergence of the minimization criteria including a successful covariance step, reasonable precision of the parameter estimates, ²⁵ goodness‐of‐fit plots, visual predictive check plots, ²⁶ and the physiological plausibility of parameter estimates.

We performed fivefold cross‐validation. Individuals were randomly divided into fivefolds while maintaining a balanced variation in dependent variables and covariates. For each iteration, onefold (i.e., 20% of the total) was held for simulation‐based diagnostic purpose, and the model parameters were estimates using the remaining fourfolds (i.e., 80% of the total).

Simulation

Simulations were conducted to demonstrate the utility of the proposed multivariate models. To generate clinically meaningful results, covariate profiles (the individual characteristics that can be collected at screening visits) were randomly selected from the observed profiles of individuals with DMD. Prediction intervals for each individual were computed, and the variance included the BSV, the RV, and parameter uncertainty.

Software

Model building was done using Monolix (Version 2021R1). Simulations were conducted in R (Version 4.2.2) using R packages lixoftConnectors (Versions 2021R1 and 2019R2) and RsSimulx (Version 2.0.2). Data formatting and visualization were also performed in R.

RESULTS

Data summary

The data set included a total of 118 individuals with DMD from 5 to 20 years of age with a total of 567 observations for each dependent variable, that is, 6MWD, FFVL, and FFSOL. Figure 3 describes details for each step of the data exclusion. A total of 14 individuals were removed from the analysis because of their ambulatory status after 15 years old. A total of 15 individuals were further removed because of missing observations. In addition, two individuals were excluded because they were already nonambulatory at the derived baseline.

FIGURE 3.

Data exclusion. DMD, Duchenne muscular dystrophy.

Univariate models

For the structural models, the sigmoid I_max (Equation 4) and E_max (Equation 5) functions best captured the longitudinal dynamics of 6MWD and both fat fraction biomarkers (i.e., FFVL and FFSOL), respectively.

(4)

(5)

where $6{\mathrm{MWD,}}_i$ and ${\mathrm{FF,}}_i$ are the measures for individual $i$, $\mathrm{S}{0}_{6\mathrm{MWD},i}$ and $\mathrm{S}{0}_{\mathrm{FF},i}$ represent 6MWD and fat fraction scores, respectively, when Age $=0$ for individual $i$, and the $\mathrm{S}0$ parameters can also be clinically interpreted as the extrapolated values when age is around 5 years by considering the shape of the function trajectories. ${\mathrm{DP}}_{\max ,6\mathrm{MWD},i}$ represents the maximum fractional decrease in 6MWD for individual $i$, ${\mathrm{DPT}}_{50,6\mathrm{MWD},i}$ represents the age at which 6MWD is half of its maximum decrease for individual $i$, ${\mathrm{DP}}_{\max ,\mathrm{FF},i}$ represents the maximum increase in fat fraction for individual $i$, ${\mathrm{DPT}}_{50,\mathrm{FF},i}$ represents the age at which the fat fraction is half of its maximum increase for individual $i$, and ${\mathrm{\gamma }}_{,6\mathrm{MWD},i}$ and ${\mathrm{\gamma }}_{,\mathrm{FF},i}$ are the Hill coefficients for individual $i$. The comparison of the AIC and BIC values of the tested structural models is summarized in Tables S1–S3.

The models were further fine‐tuned. For 6MWD, random effects on the parameter ${\mathrm{DP}}_{\max ,6\mathrm{MWD},i}$ were removed and fixed as 1 because the relative standard error was near 0 with a high shrinkage (i.e., 98.6%). The proportional error model was selected according to the lower OFV value compared with those for additive and combined error models. Adding a correlation parameter between ${\mathrm{DPT}}_{50,6\mathrm{MWD},i}$ and $\mathrm{S}{0}_{6\mathrm{MWD},i}$ improved the model evaluation criteria values. For both FFVL and FFSOL, the combined error model was selected. Although the coefficient of the additive part in the combined error model was small (i.e., 0.01 = ~1.5% of the maximal changes), adding the term improved the model evaluation criteria values, including lower OFV values of ~50 in FFVL and ~65 in FFSOL. No significant correlations were found among the model parameters in the fat fraction univariate models.

Multivariate models

To quantify the association between 6MWD and each fat fraction biomarker, the correlations of the random‐effect parameters between the selected univariate models were explored. In addition to the correlation parameter between ${\mathrm{DPT}}_{50,6\mathrm{MWD},i}$ and $\mathrm{S}{0}_{6\mathrm{MWD},i}$ in the 6MWD univariate model, adding a correlation with each of the fat fraction model parameters (i.e., ${\mathrm{DP}}_{\max ,\mathrm{FF},i}$, ${\mathrm{DPT}}_{50,\mathrm{FF},i}$, ${\mathrm{\gamma }}_{,\mathrm{FF},i}$, and $\mathrm{S}0{,}_{\mathrm{FF},i}$) was examined. The addition of ${\mathrm{DPT}}_{50,\mathrm{FF},i}$ resulted in the lowest AIC and BIC values among the explored connections that gave reasonable precisions. Table S4 presents the multivariate base model parameter estimates, including the correlation parameters connecting the 6MWD and each fat fraction measure.

Introducing combined covariates into the model

Table 1 summarizes the final model parameter estimates after the covariate analysis quantifying BSV. The steroid use was shown to delay ~10% of the age at which 6MWD is half of its maximum decrease. The steroid use was also found to delay ~10% of the age at FFSOL is half of its maximum increase. It should be noted that the covariate effects of steroid use were estimated simultaneously with other covariates. Thus, the correlations among the covariates should be considered in interpreting the magnitudes of the parameter estimates (Figure 2e,f).

TABLE 1.

Parameter estimates of the final multivariate models quantifying the associations between 6MWD and FFVL and FFSOL.

	6MWD + FFVL	6MWD + FFSOL
Fixed effects
$\mathrm{TV}\_{\mathrm{DP}}_{\max ,6\mathrm{MWD}}$	1 (Fixed, N/A)	1 (Fixed, N/A)
$\mathrm{TV}\_{\mathrm{DPT}}_{50,6\mathrm{MWD}}$	11.73 (4.35)	10.96 (5.31)
$\mathrm{\beta }\_\text{STERUSE}\_{\mathrm{DPT}}_{50,6\mathrm{MWD}}$	0.09 (49.8)	0.13 (41.1)
$\mathrm{\beta }\_\text{BSFFOld}\_{\mathrm{DPT}}_{50,6\mathrm{MWD}}$	−0.05 (53.3)	–
$\mathrm{\beta }\_\text{BSFFYoung}\_{\mathrm{DPT}}_{50,6\mathrm{MWD}}$	−0.14 (23.4)	−0.09 (61.9)
$\mathrm{\beta }\_\mathrm{BS}6\text{MWDOld}\_{\mathrm{DPT}}_{50,6\mathrm{MWD}}$	–	0.09 (54.4)
$\mathrm{TV}\_\mathrm{\gamma }{,}_{6\mathrm{MWD}}$	53.7 (10.5)	52.92 (10.3)
$\mathrm{\beta }\_\text{BSFFOld}\_\mathrm{\gamma }{,}_{6\mathrm{MWD}}$	0.28 (40.9)	–
$\mathrm{TV}\_\mathrm{S}0{,}_{6\mathrm{MWD}}$	354.02 (0.955)	355.4 (1.05)
$\mathrm{\beta }\_\text{BSFFOld}\_\mathrm{S}0{,}_{6\mathrm{MWD}}$	−0.04 (41.1)	–
$\mathrm{\beta }\_\mathrm{BS}6\text{MWDOld}\_\mathrm{S}0{,}_{6\mathrm{MWD}}$	0.63 (8.14)	0.68 (7.57)
$\mathrm{\beta }\_\mathrm{BS}6\text{MWDYoung}\_\mathrm{S}0{,}_{6\mathrm{MWD}}$	0.89 (11.1)	0.9 (15.1)
$\mathrm{TV}\_{\mathrm{DP}}_{\max ,\mathrm{FF}}$	0.72 (4.62)	0.49 (7.6)
$\mathrm{\beta }\_\mathrm{BS}6\text{MWDYoung}\_{\mathrm{DP}}_{\max ,\mathrm{FF}}$	–	−1.32 (81.4)
$\mathrm{TV}\_{\mathrm{DPT}}_{50,\mathrm{FF}}$	11.59 (2.29)	12.16 (4.72)
$\mathrm{\beta }\_\text{STERUSE}\_{\mathrm{DPT}}_{50,\mathrm{FF}}$	–	0.14 (34.1)
$\mathrm{\beta }\_\text{BSFFOld}\_{\mathrm{DPT}}_{50,\mathrm{FF}}$	−0.12 (20.6)	−0.07 (34.7)
$\mathrm{\beta }\_\text{BSFFYoung}\_{\mathrm{DPT}}_{50,\mathrm{FF}}$	−0.17 (25.3)	−0.16 (29.3)
$\mathrm{\beta }\_\mathrm{BS}6\text{MWDYoung}\_{\mathrm{DPT}}_{50,\mathrm{FF}}$	0.2 (129)	–
$\mathrm{TV}\_{\mathrm{\gamma }}_{,\mathrm{FF}}$	7.62 (6.72)	6.87 (5.25)
$\mathrm{\beta }\_\text{BSFFYoung}\_\mathrm{\gamma }{,}_{\mathrm{FF}}$	−0.32 (30.9)	–
$\mathrm{\beta }\_\mathrm{BS}6\text{MWDYoung}\_\mathrm{\gamma }{,}_{\mathrm{FF}}$	−0.99 (69.3)	–
$\mathrm{\beta }\_\mathrm{BS}6\text{MWDOld}\_\mathrm{\gamma }{,}_{\mathrm{FF}}$	–	−0.68 (28.5)
$\mathrm{TV}\_\mathrm{S}0{,}_{\mathrm{FF}}$	0.032 (9.04)	0.06 (3.46)
$\mathrm{\beta }\_\text{BSFFOld}\_\mathrm{S}0{,}_{\mathrm{FF}}$	–	1.08 (5.29)
$\mathrm{\beta }\_\text{BSFFYoung}\_\mathrm{S}0{,}_{\mathrm{FF}}$	–	0.99 (4.98)
Standard deviation of the random effects
$\mathrm{\omega }\_{\mathrm{DPT}}_{50,6\mathrm{MWD}}$	0.17 (10.9)	0.15 (10.8)
$\mathrm{\omega }\_\mathrm{\gamma }{,}_{6\mathrm{MWD}}$	0.51 (19.4)	0.45 (19.7)
$\mathrm{\omega }\_\mathrm{S}0{,}_{6\mathrm{MWD}}$	0.06 (15.3)	0.06 (14.6)
$\mathrm{\omega }\_{\mathrm{DP}}_{\max ,\mathrm{FF}}$	0.61 (18.7)	0.5 (15.1)
$\mathrm{\omega }\_{\mathrm{DPT}}_{50,\mathrm{FF}}$	0.17 (9.6)	0.13 (15.6)
$\mathrm{\omega }\_{\mathrm{\gamma }}_{,\mathrm{FF}}$	0.36 (13.8)	0.24 (13.5)
$\mathrm{\omega }\_\mathrm{S}0{,}_{\mathrm{FF}}$	0.4 (21.3)	0.08 (34.8)
Correlations
$\text{Corr\_}{\mathrm{DPT}}_{50,6\mathrm{MWD}}\_{\mathrm{DPT}}_{50,\mathrm{FF}}$	0.81 (8.21)	0.9 (9.46)
$\text{Corr\_}\mathrm{S}0{,}_{6\mathrm{MWD}}\_{\mathrm{DPT}}_{50,\mathrm{FF}}$	0.54 (28.7)	0.43 (52.5)
$\text{Corr\_}\mathrm{S}0{,}_{6\mathrm{MWD}}\_{\mathrm{DPT}}_{50,6\mathrm{MWD}}$	0.57 (28.8)	0.58 (28.6)
Error model parameters
$\text{Prop}\_6\mathrm{MWD}$	0.11 (4.77)	0.12 (5.3)
$\mathrm{Add}\_\mathrm{FF}$	0.01 (26.3)	0.01 (21.6)
$\text{Prop}\_\mathrm{FF}$	0.12 (9.53)	0.1 (12.4)

Note: The numbers represent the parameter values, and the numbers in the parentheses represent relative standard errors in percentages.

Abbreviations: 6MWD, 6‐minute walk distance; BS6MWDYoung and BS6MWDOld, baseline 6‐minute walk distance for young and old individuals (cutoff: 7 years old at baseline), respectively; BSFFYoung and BSFFOld, baseline fat fraction values for young and old individuals (cutoff: 7 years old at baseline), respectively; DP_max,6MWD, maximum fractional decrease in 6MWD; DP_max,FF, maximum increase in fat fraction; DPT_50,6MWD, age at which 6MWD is half of its maximum decrease; DPT_50,FF, age at which fat fraction is half of its maximum increase; FFSOL, fat fraction measure from the soleus muscle; FFVL, fat fraction measure from the vastus lateralis muscle; TV, typical value; N/A, not applicable; STERUSE, steroid use status at baseline; γ,_6MWD and γ,_FF, Hill coefficients.

Heterogeneities in the BSVs of the parameters ${\mathrm{DPT}}_{50,6\mathrm{MWD}}$ and ${\mathrm{DPT}}_{50,\mathrm{FF}}$ were also explained by the baseline measures of 6MWD and fat fractions, whose effects vary by age group. The negative exponent $\mathrm{\beta }$ values in Table 1 show that with higher fat fraction baseline values, we observe lower values of ${\mathrm{DPT}}_{50,6\mathrm{MWD}}$ and ${\mathrm{DPT}}_{50,\mathrm{FF}}$, which indicates faster disease progression. On the other hand, the positive exponents associated with 6MWD on ${\mathrm{DPT}}_{50,6\mathrm{MWD}}$ and ${\mathrm{DPT}}_{50,\mathrm{FF}}$ indicated that with higher 6MWD baseline scores, we see higher values of these parameters, which indicates slower disease progression.

Baseline scores were collected at different ages (i.e., 5–13 years old). Using the baseline scores scattered over the entire age range, the BSVs of the parameters $\mathrm{S}0{,}_{6\mathrm{MWD}}$ and $\mathrm{S}0{,}_{\mathrm{FF}}$ were explained. Although we prioritized adding baseline fat fraction scores on $\mathrm{S}0{,}_{6\mathrm{MWD}}$ first and vice versa, their own baseline scores were chosen as the significant covariates, except baseline FFVL scores in the old group on $\mathrm{S}0{,}_{6\mathrm{MWD}}$. $\mathrm{S}0{,}_{6\mathrm{MWD}}$ has a positive correlation with the baseline scores of 6MWD, whereas it has a negative correlation with the baseline scores of the fat fraction. Likewise, $\mathrm{S}0{,}_{\mathrm{FF}}$ has a positive correlation with the baseline scores of fat fraction and a negative correlation with the baseline scores of 6MWD. After adding covariates, the standard deviations (i.e., $\mathrm{\omega }$) of the random effects of $\mathrm{S}{0}_{6\mathrm{MWD}}$ were reduced from 0.14 to 0.06 in both multivariate models, and the $\mathrm{\omega }$ values of $\mathrm{S}0{,}_{\mathrm{FF}}$ were reduced from 0.56 to 0.4 in FFVL and from 0.65 to 0.08 in FFSOL (cf. Table S4, Table 1).

The baseline FFVL scores in the older group were found to be associated with steeper longitudinal trajectories of 6MWD (i.e., $\mathrm{\gamma }{,}_{6\mathrm{MWD}}$); the higher baseline FFVL, the steeper ${\mathrm{\gamma }}_{,6\mathrm{MWD}}$. A high baseline 6MWD score decreased the steepness of longitudinal trajectories of fat fraction (i.e., $\mathrm{\gamma }{,}_{\mathrm{FF}}$) in the young group for VL muscle and in old group for SOL muscle. The BSV of ${\mathrm{DP}}_{\max ,\mathrm{FF}}$, one of the structural parameters for fat fraction in the SOL muscle, was further explained by the baseline 6MWD score in the younger group.

Model evaluation and validation

Model evaluations were performed during model development. We summarized representative model diagnostic plots in Figure 4 and Figure S1. The goodness‐of‐fit plots show that the predictions were in good agreement with the observed data, and the residuals were well distributed around zero (Figure 4a,b, Figure S1A,B). The visual predictive check plots present that the 90% confidence intervals of the median and 10th and 90th percentiles of the simulated profiles captured the corresponding longitudinal observed data adequately (Figure 4c,d, Figure S1C,D). The five sets of the multivariate model parameters estimated using the five‐fold validation approach were similar. Combining the univariate models into the multivariate models and adding covariates improved the prediction according to both visual and numerical criteria.

FIGURE 4.

Representative evaluation plots of the final multivariate model quantifying the associations between 6‐minute walk distance (6MWD) and fat fraction measure from the vastus lateralis muscle (FFVL). In the goodness‐of‐fit plots for 6MWD (a) and FFVL (b), observed data versus individual predictions are plotted in the left panel, conditional weighted residuals (CWRES) versus population predictions are plotted in the middle panel, and individual weighted residuals (IWRES) versus age are plotted in the right panel. The visual predictive check plots for 6MWD (c) and FFVL (d) show the median (red dashed curves) and 10th and 90th percentiles (lower and upper blue dashed curves, respectively) of the predicted profiles. The shaded areas indicate the 90% confidence intervals of each of the percentile curves. For 6MWD, the fraction of the below limit of quantification (BLQ) is plotted in the solid curve and the predicted median is plotted in the dashed line surrounded by the 90% prediction interval shown in the shaded area. The aqua color represents the censored (BLQ) data (when the data were missing because of the inability to perform the functional test to measure 6MWD).

Simulation

We selected 10 individuals with different characteristic profiles with respect to their baseline scores and steroid use to simulate the longitudinal trajectories of the measures using the final parameter estimates of the developed multivariate models linking 6MWD with FFVL (Figure 5a,b) and with FFSOL (Figure 5c,d). The covariate profiles are summarized in Table S5. Figure 5 presents the simulated profiles stratified by the categorical covariate, that is, steroid use, with the 20% intervals around the median. The prediction intervals summarized 500 simulated profiles, generated by 50 replicates of the 10 individuals. All figures in Figure 5 show slower and/or mild disease progression for the subgroup with steroid use.

FIGURE 5.

Representative simulation results. The shaded intervals represent 20% prediction intervals around the median of the 500 simulated profiles generated by 50 replicates of 10 individuals. The simulation outputs were stratified into two subgroups: steroid users versus nonusers. (a, b) The simulation was performed for all steroid users with higher baseline 6MWD measures compared with nonsteroid users. (c, d) The individuals' characteristics entered for simulation were mixed. These simulation results demonstrate that the developed models can predict the trajectories of each individual by accounting for the combined effects of the covariates as well as multiple sources of the variability. 6MWD, 6‐minute walk distance; FFSOL, fat fraction measure from the soleus muscle; FFVL, fat fraction measure from the vastus lateralis muscle.

It should be noted that the effects of the baseline scores are also accounted for in the simulated profiles. For example, the simulated 6MWD profiles of the two subgroups (i.e., with and without steroid use) are more separated in Figure 5a compared with Figure 5c in the early age range (<10 years old). This is because individuals with steroid use had higher baseline 6MWD scores compared with the nonsteroid use group in Figure 5a. In addition, individuals with steroid use had lower baseline 6MWD scores than individuals without steroid use in Figure 5c.

DISCUSSION

As the disease progresses, individuals with DMD experience a decrease in performance on functional tests and the replacement of muscle with fat. ²⁷ Significant correlations showing the opposing directions of the functional endpoint measures and fat fraction over the age at assessments have been quantified using statistical correlation analyses. ¹⁴ , ¹⁵ , ¹⁸ , ²⁸ , ²⁹ , ³⁰ , ³¹ Previous studies have shown that the recently introduced MR fat fraction biomarkers are promising surrogates for the functional tests that are frequently used as endpoints in clinical trials. In fact, the muscle fat fraction measures have been implemented in several clinical trials, including NCT01865084, NCT01803412, NCT02858362, NCT02420379, NCT02439216, NCT02310763, NCT01995032, and NCT02851797.

There is an opportunity for the use of the MR biomarkers as a proxy for functional endpoints, for example, by identifying the cohorts or inclusion criteria that will lead to an optimal balance of responsiveness to treatment and inclusion of as many patients as possible. These newly developed multivariate models that consist of structural, stochastic/statistical, and covariate components allow us to quantify not only the overall negative associations but also the longitudinal associations at each timepoint between 6MWD and fat fraction measures in two functionally important lower limb muscles, the VL (upper leg) and SOL (lower leg).

In addition, using the models, we can adequately predict the longitudinal trajectories of each variable, with baseline covariates that can be collected at a screening visit. In particular, the multivariate model can be used for quantitative predictions of the increases in fat fraction attributed to DMD progression using available data including the widely used 6MWD. Representative simulation results were shown (Figure 5). The effects of the individuals' characteristics that influence the model parameter estimates form a component of the generation of the predicted longitudinal trajectories of each variable of 6MWD, FFVL, and FFSOL. The model will provide valuable information about how individual characteristics alter disease trajectories.

In our previously published disease progression models, which quantified five other functional endpoints of DMD (i.e., NorthStar Ambulatory Assessment, forced vital capacity, and the velocities of the following three timed functional tests: time to stand from supine, time to climb four stairs, and 10‐meter walk/run time), the multiplication of the Chapman‐Richards growth and sigmoid I_max functions was selected as the structural model for all the five endpoints. ²² , ³² , ³³ Compared with using only the I_max function, combining the Chapman‐Richards growth function improved the metric scores of the model evaluation criteria significantly. It also added the value of clinical interpretability as the growth function explained the increasing phase at young ages.

The structural function of the combined Chapman‐Richards growth and sigmoid I_max was also tested for 6MWD (Table S1). Its AIC and BIC values indicated that the combined function is the second‐best candidate model structure after the sigmoid I_max function. The differences in AIC and BIC between the two top model structures were less than 10. However, the precision of the empirical growth scaling parameter estimate in the combined function was too low (>150% relative standard error) and unstable to adequately quantify the increasing phase of the 6MWD functional score as a result of the few individuals (~5%) having increasing trajectories at younger ages. Given all these considerations, we decided to use the I_max function as the structural model of 6MWD.

We considered multiple covariates in developing the model. Corticosteroid use is a potent modifier of DMD disease progression, ⁶ , ⁹ significantly altering the curve in this multivariate analysis. Baseline subject characteristics (fat fraction, 6MWD, age group) were also included as covariates. Genetic covariates (genetic modifiers and primary genetic mutations) were considered but not included in the model. These have been shown to impact disease progression rate; however, the magnitude of the effect is disputed. ³⁴ , ³⁵ Including these features in the model presents obstacles that are insurmountable with the currently available data. Specifically, the most strongly protective modifiers and mutation groups (e.g., LTBP4 and mutations amenable to exon 8 skipping) are rare in both the DMD population and the study cohort. We also examined the impact of more common modifiers and mutation groups (i.e., SPP1 and mutations amenable to exon 51 skipping); these modifiers and mutations did not significantly alter the fat fraction curve. ³⁴

We will extend these multivariate disease progression models to a model‐based simulation tool that incorporates trial design parameters and assumed drug effects to better inform clinical trial designs. The model‐based tool will provide guidance on how to use the new MR biomarkers most beneficially in clinical trials using the widely used functional endpoint 6MWD. This will facilitate the design of clinical trials that are more inclusive and more conclusive using muscle fat fraction biomarkers. The tool will accelerate drug development by allowing users to simulate possible scenarios of a clinical trial before its actual execution, and hence it will inform trial designs by providing insights into key trial design aspects, including inclusion/exclusion criteria, trial duration, and sample sizes for clinical trials in DMD. ²² , ³⁶ , ³⁷ , ³⁸ As the clinical trial landscape in DMD continues to become more exciting and sophisticated, the development of quantitative model‐based clinical trial simulation tools will help maximize trial impact and minimize the trial burden for the DMD community.

AUTHOR CONTRIBUTIONS

S.K., R.J.W., M.J.D., A.M.B., R.B.‐O., T.N.M., W.D.R., and K.V. wrote the manuscript. S.K., R.J.W., M.J.D., W.D.R., and K.V. designed the research. S.K., R.J.W., J.F.M., D.Y.Y., W.T.T., and A.M.B. performed the research. S.K., R.J.W., M.J.D., J.F.M., D.Y.Y., W.T.T., A.M.B., D.J.C., V.A., G.A.W., W.D.R., and K.V. analyzed the data. S.K., J.F.M., D.Y.Y., W.T.T., and D.J.C. contributed new reagents/analytical tools.

FUNDING INFORMATION

Research reported in this publication was supported by the National Institutes of Health (NIH) National Center for Advancing Translational Sciences through grant number R21TR004006 and the University of Florida Clinical and Translational Science Institute, which is also supported in part by the NIH National Center for Advancing Translational Sciences under award number UL1TR001427. ImagingDMD’s data was supported by NIH grant R01AR056973. The author AMB was supported by a career development award during the conduct of this study (NIH K12 HD055929). Data acquisition and storage at Oregon Health & Science University were supported by shared instrument grants NIH S10OD021701 and NIH S10OD018224. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.

CONFLICT OF INTEREST STATEMENT

The authors declared no competing interests for this work.

Supporting information

Appendix S1

Appendix S2

Appendix S3

Kim S, Willcocks RJ, Daniels MJ, et al. Multivariate modeling of magnetic resonance biomarkers and clinical outcome measures for Duchenne muscular dystrophy clinical trials. CPT Pharmacometrics Syst Pharmacol. 2023;12:1437‐1449. doi: 10.1002/psp4.13021

DATA AVAILABILITY STATEMENT

In accordance with our informed consent form, researchers will be required to apply for access to the data set by submitting the following information, which will be reviewed by an Executive Committee: (i) researcher name(s) and institutional affiliation(s) and (ii) a brief proposal outlining how the data will be used. The request should be submitted to Dr. Krista Vandenborne, the Director of ImagingDMD (email contact: kvandenb@phhp.ufl.edu). If shared data are used in subsequent publications, the original funding source (AR056973) and the ImagingDMD network will need to be acknowledged and published methodology developed during the course of the study cited, as appropriate (https://imagingnmd.org/data‐sharing/).