Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

A four-hit mechanism is sufficient for meningioma development

PURPOSE

Meningiomas are central nervous system tumors whose incidence increases with age. Benign meningioma pathogenesis involves germline or somatic mutation of target genes, such as NF2, leading to clonal expansion. We used an established cancer epidemiology model to investigate the number of rate-limiting steps sufficient for benign meningioma development.

METHODS

Incidence data was obtained from the Surveillance, Epidemiology and End Results Program (SEER) for nonmalignant meningioma from 2004 to 2020. Age-adjusted incidence rates per 100,000 person-years were divided into 5-year bands. This was repeated for vestibular schwannomas as a negative control. The Armitage-Doll methodology was applied. Mathematical solutions correcting for volatile tumor microenvironments were applied to fit higher-order models using polynomial regression when appropriate. A 75:25 training:test split was utilized for validation.

RESULTS

222,509 cases of benign meningiomas were identified. We noted strong linear relationships between log-transformed incidence and age across the cohort and multiple subpopulations: male, white, black, Hispanic, Asian/Pacific Islander, and American Indian subpopulations all demonstrated R2 = 0.99. Slopes were between 3.1 and 3.4, suggesting a four-step process for benign meningioma development. Female patients exhibited nonlinear deviations, but the corrected model demonstrated R2 = 0.99 with a four-hit pathway. This model performed robustly on test data with R2 = 0.99. Vestibular schwannomas demonstrated a slope of 2.1 with R2 = 0.99, suggesting a separate three-step process.

CONCLUSION

Four mutations are uniquely required for the development of benign meningiomas. Correcting for volatile tumor microenvironments reliably accounted for nonlinear deviations in behavior. Further studies are warranted to elucidate genomic findings suggestive of key mutations in this pathway.

MS-CPFI: A model-agnostic Counterfactual Perturbation Feature Importance algorithm for interpreting black-box Multi-State models

Multi-state processes (Webster, 2019) are commonly used to model the complex clinical evolution of diseases where patients progress through different states. In recent years, machine learning and deep learning algorithms have been proposed to improve the accuracy of these models' predictions (Wang et al., 2019). However, acceptability by patients and clinicians, as well as for regulatory compliance, require interpretability of these algorithms's predictions. Existing methods, such as the Permutation Feature Importance algorithm, have been adapted for interpreting predictions in black-box models for 2-state processes (corresponding to survival analysis). For generalizing these methods to multi-state models, we introduce a novel model-agnostic interpretability algorithm called Multi-State Counterfactual Perturbation Feature Importance (MS-CPFI) that computes feature importance scores for each transition of a general multi-state model, including survival, competing-risks, and illness-death models. MS-CPFI uses a new counterfactual perturbation method that allows interpreting feature effects while capturing the non-linear effects and potentially capturing time-dependent effects. Experimental results on simulations show that MS-CPFI increases model interpretability in the case of non-linear effects. Additionally, results on a real-world dataset for patients with breast cancer confirm that MS-CPFI can detect clinically important features and provide information on the disease progression by displaying features that are protective factors versus features that are risk factors for each stage of the disease. Overall, MS-CPFI is a promising model-agnostic interpretability algorithm for multi-state models, which can improve the interpretability of machine learning and deep learning algorithms in healthcare.

How much disease risk is due to old age and established risk factors?

Improved healthcare is leading to older populations and increasing numbers of individuals experiencing multiple diseases, possibly concurrently (multimorbidity). This article asks whether the observed number of new diseases is more than expected based on age and established risk factors alone, assuming that disease risk is unchanged by prior or pre-existing disease. This is accomplished by designing a new epidemiological approach, where the expected number of disease types are estimated for individuals without prior disease, by combining individual risk predictions with a "Poisson-Binomial" model to estimate the expected number of new diseases and its confidence interval. For 123 diseases in men and 99 diseases in women, the expected number of new diseases based on age and established risk factors was approximately 2 / 3 of that observed, with the observed number of new diseases approximately 1.5 times that predicted. The differences could not be explained by natural statistical variation, and provide a rigorous statistical demonstration of lower disease risk for individuals without any previous disease. The multiple of 1.5 was sufficiently consistent across different diseases to prevent its use for classification of disease types, but there were differences for subgroups such as smokers with high body mass index, and for some classes of disease (as defined by the International Classification of Diseases, version 10). The results suggest that empirical modeling might allow reliable predictions of future hospital admissions, and confirm the value of conventional epidemiological approaches that study disease risk in healthy individuals. The implications and future possibilities of this new approach are discussed.

Forecasting prevalence and mortality of Alzheimer's disease using the partitioning models

OBJECTIVES

Health forecasting is an important aspect of ensuring that the health system can effectively respond to the changing epidemiological environment. Common models for forecasting Alzheimer's disease and related dementias (AD/ADRD) are based on simplifying methodological assumptions, applied to limited population subgroups, or do not allow analysis of medical interventions. This study uses 5 %-Medicare data (1991-2017) to identify, partition, and forecast age-adjusted prevalence and incidence-based mortality of AD as well as their causal components.

METHODS

The core underlying methodology is the partitioning analysis that calculates the relative impact each component has on the overall trend as well as intertemporal changes in the strength and direction of these impacts. B-spline functions estimated for all parameters of partitioning models represent the basis for projections of these parameters in future.

RESULTS

Prevalence of AD is predicted to be stable between 2017 and 2028 primarily due to a decline in the prevalence of pre-AD-diagnosis stroke. Mortality, on the other hand, is predicted to increase. In all cases the resulting patterns come from a trade-off of two disadvantageous processes: increased incidence and disimproved survival. Analysis of health interventions demonstrates that the projected burden of AD differs significantly and leads to alternative policy implications.

DISCUSSION

We developed a forecasting model of AD/ADRD risks that involves rigorous mathematical models and incorporation of the dynamics of important determinative risk factors for AD/ADRD risk. The applications of such models for analyses of interventions would allow for predicting future burden of AD/ADRD conditional on a specific treatment regime.

Sporadic, late-onset, and multistage diseases

Multistage disease processes are often characterized by a linear relationship between the log of incidence rates and the log of age. Examples include sequences of somatic mutations, that can cause cancer, and have recently been linked with a range of non-malignant diseases. Using a Weibull distribution to model diseases that occur through an ordered sequence of stages, and another model where stages can occur in any order, we characterized the age-related onset of disease in UK Biobank data. Despite their different underlying assumptions, both models accurately described the incidence of over 450 diseases, demonstrating that multistage disease processes cannot be inferred from this data alone. The parametric models provided unique insights into age-related disease, that conventional studies of relative risks cannot. The rate at which disease risk increases with age was used to distinguish between "sporadic" diseases, with an initially low and slowly increasing risk, and "late-onset" diseases whose negligible risk when young rapidly increases with age. "Relative aging rates" were introduced to quantify how risk factors modify age-related risk, finding the effective age-at-risk of sporadic diseases is strongly modified by common risk factors. Relative aging rates are ideal for risk-stratification, allowing the identification of ages with equivalent-risk in groups with different exposures. Most importantly, our results suggest that a substantial burden of sporadic diseases can be substantially delayed or avoided by early lifestyle interventions.

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Background

It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events.

Methods

Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence.

Results

We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age.

Conclusions

This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells.

A Multi-Step Model of Parkinson's Disease Pathogenesis

BACKGROUND

Parkinson's disease (PD) may result from the combined effect of multiple etiological factors. The relationship between disease incidence and age, as demonstrated in the cancer literature, can be used to model a multistep pathogenic process, potentially affording unique insights into disease development.

OBJECTIVES

We tested whether the observed incidence of PD is consistent with a multistep process, estimated the number of steps required and whether this varies with age, and examined drivers of sex differences in PD incidence.

METHODS

Our validated probabilistic modeling process, based on medication prescribing, generated nationwide age- and sex-adjusted PD incidence data spanning 2006-2017. Models of log(incidence) versus log(age) were compared using Bayes factors, to estimate (1) if a linear relationship was present (indicative of a multistep process); (2) the relationship's slope (one less than number of steps); (3) whether slope was lower at younger ages; and (4) whether slope or y-intercept varied with sex.

RESULTS

Across >15,000 incident cases of PD, there was a clear linear relationship between log(age) and log(incidence). Evidence was strongest for a model with an initial slope of 5.2 [3.8, 6.4], an inflexion point at age 45, and beyond this a slope of 6.8 [6.4, 7.2]. There was evidence for the intercept varying by sex, but no evidence for slope being sex-dependent.

CONCLUSIONS

The age-specific incidence of PD is consistent with a process that develops in multiple, discrete steps - on average six before age 45 and eight after. The model supports theories emphasizing the primacy of environmental factors in driving sex differences in PD incidence. © 2021 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

Analysis of Time Trends in Alzheimer's Disease and Related Dementias Using Partitioning Approach

BACKGROUND

Understanding the dynamics of epidemiologic trends in Alzheimer's disease (AD) and related dementias (ADRD) and their epidemiologic causes is vital to providing important insights into reducing the burden associated with these conditions.

OBJECTIVE

To model the time trends in age-adjusted AD/ADRD prevalence and incidence-based mortality (IBM), and identify the main causes of the changes in these measures over time in terms of interpretable epidemiologic quantities.

METHODS

Trend decomposition was applied to a 5%sample of Medicare beneficiaries between 1991 and 2017.

RESULTS

Prevalence of AD was increasing between 1992 and 2011 and declining thereafter, while IBM increased over the study period with a significant slowdown in its rate of growth from 2011 onwards. For ADRD, prevalence and IBM increased through 2014 prior to taking a downwards turn. The primary determinant responsible for declines in prevalence and IBM was the deceleration in the increase and eventual decrease in incidence rates though changes in relative survival began to affect the overall trends in prevalence/IBM in a noticeable manner after 2008. Other components showed only minor effects.

CONCLUSION

The prevalence and IBM of ADRD is expected to continue to decrease. The directions of these trends for AD are not clear because AD incidence, the main contributing component, is decreasing but at a decreasing rate suggesting a possible reversal. Furthermore, emerging treatments may contribute through their effects on survival. Improving ascertainment of AD played an important role in trends of AD/ADRD over the 1991-2009/10 period but this effect has exhausted itself by 2017.

Likelihood function for estimating parameters in multistate disease process with Laplace-transformation-based transition probabilities

Multistate statistical models are often used to characterize the complex multi-compartment progression of the disease such as cancer. However, the derivation of multistate transition kernels is often involved with the intractable convolution that requires intensive computation. Moreover, the estimation of parameters pertaining to transition kernel requires the individualized time-stamped history data while the traditional likelihood function forms are constructed. In this paper, we came up with a novel likelihood function derived from Laplace transformation-based transition probabilities in conjunction with Expectation-Maximization algorithm to estimate parameters. The proposed method was applied to two large population-based screening data with only aggregated count data without relying on individual time-stamped history data.