A longitudinal model for disease progression was developed and applied to multiple sclerosis

Modeling and simulation for prediction of multiple sclerosis progression

In light of extensive work that has created a wide range of techniques for predicting the course of multiple sclerosis (MS) disease, this paper attempts to provide an overview of these approaches and put forth an alternative way to predict the disease progression. For this purpose, the existing methods for estimating and predicting the course of the disease have been categorized into clinical, radiological, biological, and computational or artificial intelligence-based markers. Weighing the weaknesses and strengths of these prognostic groups is a profound method that is yet in need and works directly at the level of diseased connectivity. Therefore, we propose using the computational models in combination with established connectomes as a predictive tool for MS disease trajectories. The fundamental conduction-based Hodgkin-Huxley model emerged as promising from examining these studies. The advantage of the Hodgkin-Huxley model is that certain properties of connectomes, such as neuronal connection weights, spatial distances, and adjustments of signal transmission rates, can be taken into account. It is precisely these properties that are particularly altered in MS and that have strong implications for processing, transmission, and interactions of neuronal signaling patterns. The Hodgkin-Huxley (HH) equations as a point-neuron model are used for signal propagation inside a small network. The objective is to change the conduction parameter of the neuron model, replicate the changes in myelin properties in MS and observe the dynamics of the signal propagation across the network. The model is initially validated for different lengths, conduction values, and connection weights through three nodal connections. Later, these individual factors are incorporated into a small network and simulated to mimic the condition of MS. The signal propagation pattern is observed after inducing changes in conduction parameters at certain nodes in the network and compared against a control model pattern obtained before the changes are applied to the network. The signal propagation pattern varies as expected by adapting to the input conditions. Similarly, when the model is applied to a connectome, the pattern changes could give an insight into disease progression. This approach has opened up a new path to explore the progression of the disease in MS. The work is in its preliminary state, but with a future vision to apply this method in a connectome, providing a better clinical tool.

Modelling Disease Progression of Multiple Sclerosis in a South Wales Cohort

OBJECTIVES

The objective of this study was to model multiple sclerosis (MS) disease progression and compare disease trajectories by sex, age of onset, and year of diagnosis.

STUDY DESIGN AND SETTING

Longitudinal EDSS scores (20,854 observations) were collected for 1,787 relapse-onset MS patients at MS clinics in South Wales and modelled using a multilevel model (MLM). The MLM adjusted for covariates (sex, age of onset, year of diagnosis, and disease-modifying treatments), and included interactions between baseline covariates and time variables.

RESULTS

The optimal model was truncated at 30 years after disease onset and excluded EDSS recorded within 3 months of relapse. As expected, older age of onset was associated with faster disease progression at 15 years (effect size (ES): 0.75; CI: 0.63, 0.86; p: <0.001) and female-sex progressed more slowly at 15 years (ES: -0.43; CI: -0.68, -0.18; p: <0.001). Patients diagnosed more recently (defined as 2007-2011 and >2011) progressed more slowly than those diagnosed historically (<2006); (ES: -0.46; CI: -0.75, -0.16; p: 0.006) and (ES: -0.95; CI: -1.20, -0.70; p: <0.001), respectively.

CONCLUSION

We present a novel model of MS outcomes, accounting for the non-linear trajectory of MS and effects of baseline covariates, validating well-known risk factors (sex and age of onset) associated with disease progression. Also, patients diagnosed more recently progressed more slowly than those diagnosed historically.

Two sample Mendelian Randomisation using an outcome from a multilevel model of disease progression

Identifying factors that are causes of disease progression, especially in neurodegenerative diseases, is of considerable interest. Disease progression can be described as a trajectory of outcome over time-for example, a linear trajectory having both an intercept (severity at time zero) and a slope (rate of change). A technique for identifying causal relationships between one exposure and one outcome in observational data whilst avoiding bias due to confounding is two sample Mendelian Randomisation (2SMR). We consider a multivariate approach to 2SMR using a multilevel model for disease progression to estimate the causal effect an exposure has on the intercept and slope. We carry out a simulation study comparing a naïve univariate 2SMR approach to a multivariate 2SMR approach with one exposure that effects both the intercept and slope of an outcome that changes linearly with time since diagnosis. The simulation study results, across six different scenarios, for both approaches were similar with no evidence against a non-zero bias and appropriate coverage of the 95% confidence intervals (for intercept 93.4-96.2% and the slope 94.5-96.0%). The multivariate approach gives a better joint coverage of both the intercept and slope effects. We also apply our method to two Parkinson's cohorts to examine the effect body mass index has on disease progression. There was no strong evidence that BMI affects disease progression, however the confidence intervals for both intercept and slope were wide.

Enlarged choroid plexus related to cortical atrophy in multiple sclerosis

OBJECTIVES

To investigate the correlation between choroid plexus volume and whole brain morphology in patients with multiple sclerosis (MS) and neuromyelitis optica spectrum disorder (NMOSD).

METHODS

Fifty-one patients with MS, 42 patients with NMOSD, and 56 healthy controls (HC) were recruited. The morphological changes in choroid plexus and whole brain tissue were compared between three groups and the correlations between choroid plexus volume and brain atrophy were further investigated. The longitudinal alterations of brain morphology in 25 MS and 20 NMOSD patients were compared.

RESULTS

Compared to the HC group, the choroid plexus volumes were increased in the MS group (p < 0.001) but not in the NMOSD group (p > 0.05). Compared to the HC group, the MS group showed reduced cortex thickness, deep gray matter volume, and increased ventricle system volume, and the NMOSD group showed increased third ventricle volume (all p < 0.05, false discovery rate corrected). In the MS group, there were widespread correlations between enlarged choroid plexus volume and reduced cerebral cortex thickness (p < 0.05, r = -0.292~-0.538, false discovery rate corrected). The interval time was not significantly different between the MS (median: 1.37 years) and NMOSD group (median: 1.25 years) (p > 0.05). In MS, compared with the baseline, the right hippocampus and nucleus accumbens volumes were decreased in long follow-up, and bilateral lateral ventricle volumes were increased both in short and long follow-up (all p < 0.05, false discovery rate corrected).

CONCLUSIONS

The enlarged choroid plexus related to reduced cortical thickness and progressive local brain atrophy are shown in MS patients, but not obvious in NMOSD patients.

KEY POINTS

• MS and NMOSD have different altered patterns in choroid plexus volume and brain atrophy. • The enlarged choroid plexus related to brain atrophy is shown in MS patients, but not obvious in NMOSD patients. • Progressive local brain atrophy is shown in MS patients, but not obvious in NMOSD patients.

Longitudinal analysis of disability outcomes among young people with MS

BACKGROUND

The age of onset of MS appears to influence the course of disease progression and people with younger age of onset might have a different disability trajectory.

OBJECTIVES

To identify longitudinal patterns of disability progression, as measured by changes in the Multiple Sclerosis Functional Composite (MSFC), of young people in MS drug trials and to estimate the extent to which disability progression differ in two age groups (≤25 years and 26 - 35 years).

METHODS

Data from the Multiple Sclerosis Outcomes Assessment Consortium (MSOAC) was used. Longitudinal patterns on the MSFC were identified using group-based trajectory models (GBTM). For difference between the expected and observed proportions of people with pediatric-onset MS chi-square statistic was used. Linear mixed models were used to estimate the average change in performance over time, age and sex.

RESULTS

GBTM results showed little variability in performance over time. Mixed modeling showed that the younger group performed better for gait speed, dexterity, and cognition. Men performed poorer on dexterity and cognition. Distribution of people with pediatric-onset MS differed from expected on dexterity, cognition, and the EDSS.

CONCLUSIONS

The combined use of trajectory models and linear mixed models provided rich information about the variability in function over time.

A scoping review of causal methods enabling predictions under hypothetical interventions

BACKGROUND

The methods with which prediction models are usually developed mean that neither the parameters nor the predictions should be interpreted causally. For many applications, this is perfectly acceptable. However, when prediction models are used to support decision making, there is often a need for predicting outcomes under hypothetical interventions.

AIMS

We aimed to identify published methods for developing and validating prediction models that enable risk estimation of outcomes under hypothetical interventions, utilizing causal inference. We aimed to identify the main methodological approaches, their underlying assumptions, targeted estimands, and potential pitfalls and challenges with using the method. Finally, we aimed to highlight unresolved methodological challenges.

METHODS

We systematically reviewed literature published by December 2019, considering papers in the health domain that used causal considerations to enable prediction models to be used for predictions under hypothetical interventions. We included both methodologies proposed in statistical/machine learning literature and methodologies used in applied studies.

RESULTS

We identified 4919 papers through database searches and a further 115 papers through manual searches. Of these, 87 papers were retained for full-text screening, of which 13 were selected for inclusion. We found papers from both the statistical and the machine learning literature. Most of the identified methods for causal inference from observational data were based on marginal structural models and g-estimation.

CONCLUSIONS

There exist two broad methodological approaches for allowing prediction under hypothetical intervention into clinical prediction models: (1) enriching prediction models derived from observational studies with estimated causal effects from clinical trials and meta-analyses and (2) estimating prediction models and causal effects directly from observational data. These methods require extending to dynamic treatment regimes, and consideration of multiple interventions to operationalise a clinical decision support system. Techniques for validating 'causal prediction models' are still in their infancy.

Model-based prediction of CD4 cells counts in HIV-infected adults on antiretroviral therapy in Northwest Ethiopia: A flexible mixed effects approach

Background

CD4 cell counts is widely used as a biomarker for treatment progression when studying the efficacy of drugs to treat HIV-infected patients. In the past, it had been also used in determining eligibility to initiate antiretroviral therapy. The main aim of this was to model the evolution of CD4 counts over time and use this model for an early prediction of subject-specific time to cross a pre-specified CD4 threshold.

Methods

Hospital based retrospective cohort study of HIV-infected patients was conducted from January 2009 to December 2014 at University of Gondar hospital, Northwest Ethiopia. Fractional polynomial random effect model is used to model the evolution of CD4 counts over time in response to treatment and to estimate the individual probability to be above a pre-selected CD4 threshold. Human subject research approval for this study was received from University of Gondar Research Ethics Committee and the medical director of the hospital.

Results

A total of 1347 patients were included in the analysis presented in this paper. The cohort contributed a total of 236.58 per 100 person-years of follow-up. Later the data were divided into two periods: the first is the estimation period in which the parameters of the model are estimated and the second is the prediction period. Based on the parameters from the estimation period, model based prediction for the time to cross a threshold was estimated. The correlations between observed and predicted values of CD4 levels in the estimation period were 0.977 and 0.982 for Neverapine and Efavirenz containing regimens, respectively; while the correlation between the observed and predicted CD4 counts in the prediction period are 0.742 and 0.805 for NVP and EFV, respectively.

Conclusions

The model enables us to estimate a subject-specific expected time to cross a CD4 threshold and to estimate a subject-specific probability to have CD4 count above a pre-specified threshold at each time point. By predicting long-term outcomes of CD4 count of the patients one can advise patient about the potential ART benefits that accrue in the long-term.

Assessing the long-term effectiveness of interferon-beta and glatiramer acetate in multiple sclerosis: final 10-year results from the UK multiple sclerosis risk-sharing scheme

BACKGROUND

Because multiple sclerosis (MS) is a chronic disease causing disability over decades, it is crucial to know if the short-term effects of disease-modifying therapies reported in randomised controlled trials reduce long-term disability. This 10-year prospective observational study of disability outcomes (Expanded Disability Status Scale (EDSS) and utility) was set up, in conjunction with a risk-sharing agreement between payers and producers, to investigate this issue.

METHODS

The outcomes of the UK treated patients were compared with a modelled untreated control based on the British Columbia MS data set to assess the long-term effectiveness of these treatments. Two complementary analysis models were used: a multilevel model (MLM) and a continuous Markov model.

RESULTS

4862 patients with MS were eligible for the primary analysis (mean and median follow-up times 8.7 and 10 years). EDSS worsening was reduced by 28% (MLM), 7% (Markov) and 24% time-adjusted Markov in the total cohort, and by 31% (MLM) and 14% (Markov) for relapsing remitting patients. The utility worsening was reduced by 23%-24% in the total cohort and by 24%-31% in the RR patients depending on the model used. All sensitivity analyses showed a treatment effect. There was a 4-year (CI 2.7 to 5.3) delay to EDSS 6.0. An apparent waning of treatment effect with time was seen. Subgroup analyses suggested better treatment effects in those treated earlier and with lower EDSS scores.

CONCLUSIONS

This study supports a beneficial effect on long-term disability with first-line MS disease-modifying treatments, which is clinically meaningful. However the waning effect noted requires further study.

Using marginal structural models to adjust for treatment drop-in when developing clinical prediction models

Clinical prediction models (CPMs) can inform decision making about treatment initiation, which requires predicted risks assuming no treatment is given. However, this is challenging since CPMs are usually derived using data sets where patients received treatment, often initiated postbaseline as "treatment drop-ins." This study proposes the use of marginal structural models (MSMs) to adjust for treatment drop-in. We illustrate the use of MSMs in the CPM framework through simulation studies that represent randomized controlled trials and real-world observational data and the example of statin initiation for cardiovascular disease prevention. The simulations include a binary treatment and a covariate, each recorded at two timepoints and having a prognostic effect on a binary outcome. The bias in predicted risk was examined in a model ignoring treatment, a model fitted on treatment-naïve patients (at baseline), a model including baseline treatment, and the MSM. In all simulation scenarios, all models except the MSM underestimated the risk of outcome given absence of treatment. These results were supported in the statin initiation example, which showed that ignoring statin initiation postbaseline resulted in models that significantly underestimated the risk of a cardiovascular disease event occurring within 10 years. Consequently, CPMs that do not acknowledge treatment drop-in can lead to underallocation of treatment. In conclusion, when developing CPMs to predict treatment-naïve risk, researchers should consider using MSMs to adjust for treatment drop-in, and also seek to exploit the ability of MSMs to allow estimation of individual treatment effects.

Assessment of Biochemical and Densitometric Markers of Calcium-Phosphate Metabolism in the Groups of Patients with Multiple Sclerosis Selected due to the Serum Level of Vitamin D3

Background

In addition to the widely known effect of vitamin D₃ (vitD₃) on the skeleton, its role in the regulation of the immune response was also confirmed.

Aim

The assessment of biochemical and densitometric markers of calcium-phosphate metabolism in the groups of patients with relapsing-remitting multiple sclerosis (RRMS) selected due to the serum level of vitamin D₃.

Methods

The concentrations of biochemical markers and indices of lumbar spine bone densitometry (DXA) were determined in 82 patients divided into vitamin D₃ deficiency (VitDd), insufficiency (VitDi), and normal vitamin D₃ level (VitDn) subgroups.

Results

The highest level of the parathyroid hormone (PTH) and the highest prevalence of hypophosphatemia and osteopenia were demonstrated in VitDd group compared to VitDi and VitDn. However, in VitDd, VitDi, and VitDn subgroups no significant differences were observed in the levels of alkaline phosphatase (ALP) and ionized calcium (Ca²⁺) and in DXA indices. A negative correlation was observed between the level of vitamin D₃ and the Expanded Disability Status Scale (EDSS) in the whole MS group. The subgroups were significantly different with respect to the EDSS scores and the frequency of complaints related to walking according to the EQ-5D.

Conclusions

It is necessary to assess calcium-phosphate metabolism and supplementation of vitamin D₃ in RRMS patients. The higher the clinical stage of the disease assessed with the EDSS, the lower the level of vitamin D₃ in blood serum. Subjectively reported complaints related to difficulties with walking were reflected in the EDSS in VitDd patients.

Modelling disease progression in relapsing-remitting onset multiple sclerosis using multilevel models applied to longitudinal data from two natural history cohorts and one treated cohort

BACKGROUND

The ability to better predict disease progression represents a major unmet need in multiple sclerosis (MS), and would help to inform therapeutic and management choices.

OBJECTIVES

To develop multilevel models using longitudinal data on disease progression in patients with relapsing-remitting MS (RRMS) or secondary-progressive MS (SPMS); and to use these models to estimate the association of disease-modifying therapy (DMT) with progression.

DESIGN

Secondary analysis of three MS cohorts.

SETTING

Two natural history cohorts: University of Wales Multiple Sclerosis (UoWMS) cohort, UK, and British Columbia Multiple Sclerosis (BCMS) cohort, Canada. One observational DMT-treated cohort: UK MS risk-sharing scheme (RSS).

PARTICIPANTS

The UoWMS database has > 2000 MS patients and the BCMS database (as of 2009) has > 5900 MS patients. All participants who had definite MS (RRMS/SPMS), who reached the criteria set out by the Association of British Neurologists (ABN) for eligibility for DMT [i.e. age ≥ 18 years, Expanded Disability Status Scale (EDSS) score of ≤ 6.5, occurrence of two or more relapses in the previous 2 years] and who had at least two repeated outcome measures were included: 404 patients for the UoWMS cohort and 978 patients for the BCMS cohort. Through the UK MS RSS scheme, 5583 DMT-treated patients were recruited, with the analysis sample being the 4137 who had RRMS and were eligible and treated at baseline, with at least one valid EDSS score post baseline.

MAIN OUTCOME MEASURES

EDSS score observations post ABN eligibility.

METHODS

We used multilevel models in the development cohort (UoWMS) to develop a model for EDSS score with time since ABN eligibility, allowing for covariates and appropriate transformation of outcome and/or time. These methods were then applied to the BCMS cohort to obtain a 'natural history' model for changes in the EDSS score with time. We then used this natural history model to predict the trajectories of EDSS score in treated patients in the UK MS RSS database. Differences between the progression predicted by the natural history model and the progression observed at 6 years' follow-up for the UK MS RSS cohort were used as indicators of the effectiveness of the DMTs. Previously developed utility scores were assigned to each EDSS score, and differences in utility also examined.

RESULTS

The model best fitting the UoWMS data showed a non-linear increase in EDSS score over time since ABN eligibility. This model fitted the BCMS cohort data well, with similar coefficients, and the BCMS model predicted EDSS score in UoWMS data with little evidence of bias. Using the natural history model predicts EDSS score in a treated cohort (UK MS RSS) higher than that observed [by 0.59 points (95% confidence interval 0.54 to 0.64 points)] at 6 years post treatment.

LIMITATIONS

Only two natural history cohorts were compared, limiting generalisability. The comparison of a treated cohort with untreated cohorts is observational, thus limiting conclusions about causality.

CONCLUSIONS

EDSS score progression in two natural history cohorts of MS patients showed a similar pattern. Progression in the natural history cohorts was slightly faster than EDSS score progression in the DMT-treated cohort, up to 6 years post treatment.

FUTURE WORK

Long-term follow-up of randomised controlled trials is needed to replicate these findings and examine duration of any treatment effect.

FUNDING DETAILS

The National Institute for Health Research Health Technology Assessment programme.

Does Testing More Frequently Shorten the Time to Detect Disease Progression?

PURPOSE

With the rise of smartphone devices to monitor health status remotely, it is tempting to conclude that sampling more often will provide a more sensitive means of detecting changes in health status earlier over time, when interventions may improve outcomes.

METHODS

The answer to this question is derived in the context of a model where observations are generated from a linear-trend model with independent as well as autocorrelated autoregressive-moving average, or ARMA(1,1), errors.

RESULTS

The results imply a cautionary message that an increase in the sampling frequency may not always lead to a faster detection of trend changes. The benefit of rapid successive observations depends on how observations, taken closely together in time, are correlated.

CONCLUSIONS

Shortening the observation period by half can be accomplished by increasing the number of independent observations to maintain the same power for detecting change over time. However, a strategy to detect progression of disease sooner by taking numerous closely spaced measurements over a shortened interval is limited by the degree of autocorrelation among adjacent observations. We provide a statistical model of disease progression that allows for autocorrelation among successive measurements, and obtain the power of detecting a linear change of specified magnitude when equal-spaced observations are taken over a given time interval.

TRANSLATIONAL RELEVANCE

New emerging technology for home monitoring of visual function will provide a means to monitor sensory status more frequently. The model proposed here takes into account how successive measurements are correlated, which impacts the number of measurements needed to detect a significant change in status.

Long-term disability trajectories in primary progressive MS patients: A latent class growth analysis

Background:

Several natural history studies on primary progressive multiple sclerosis (PPMS) patients detected a consistent heterogeneity in the rate of disability accumulation.

Objectives:

To identify subgroups of PPMS patients with similar longitudinal trajectories of Expanded Disability Status Scale (EDSS) over time.

Methods:

All PPMS patients collected within the MSBase registry, who had their first EDSS assessment within 5 years from onset, were included in the analysis. Longitudinal EDSS scores were modeled by a latent class mixed model (LCMM), using a nonlinear function of time from onset. LCMM is an advanced statistical approach that models heterogeneity between patients by classifying them into unobserved groups showing similar characteristics.

Results:

A total of 853 PPMS (51.7% females) from 24 countries with a mean age at onset of 42.4 years (standard deviation (SD): 10.8 years), a median baseline EDSS of 4 (interquartile range (IQR): 2.5–5.5), and 2.4 years of disease duration (SD: 1.5 years) were included. LCMM detected three different subgroups of patients with a mild ( n = 143; 16.8%), moderate ( n = 378; 44.3%), or severe ( n = 332; 38.9%) disability trajectory. The probability of reaching EDSS 6 at 10 years was 0%, 46.4%, and 81.9% respectively.

Conclusion:

Applying an LCMM modeling approach to long-term EDSS data, it is possible to identify groups of PPMS patients with different prognosis.

Explicit inclusion of treatment in prognostic modeling was recommended in observational and randomized settings

OBJECTIVES

To compare different methods to handle treatment when developing a prognostic model that aims to produce accurate probabilities of the outcome of individuals if left untreated.

STUDY DESIGN AND SETTING

Simulations were performed based on two normally distributed predictors, a binary outcome, and a binary treatment, mimicking a randomized trial or an observational study. Comparison was made between simply ignoring treatment (SIT), restricting the analytical data set to untreated individuals (AUT), inverse probability weighting (IPW), and explicit modeling of treatment (MT). Methods were compared in terms of predictive performance of the model and the proportion of incorrect treatment decisions.

RESULTS

Omitting a genuine predictor of the outcome from the prognostic model decreased model performance, in both an observational study and a randomized trial. In randomized trials, the proportion of incorrect treatment decisions was smaller when applying AUT or MT, compared to SIT and IPW. In observational studies, MT was superior to all other methods regarding the proportion of incorrect treatment decisions.

CONCLUSION

If a prognostic model aims to produce correct probabilities of the outcome in the absence of treatment, ignoring treatments that affect that outcome can lead to suboptimal model performance and incorrect treatment decisions. Explicitly, modeling treatment is recommended.