Parameter estimation for multistage clonal expansion models from cancer incidence data: A practical identifiability analysis

Assessing potential insights of an imperfect testing strategy: Parameter estimation and practical identifiability using early COVID-19 data in India

A deterministic model with testing of infected individuals has been proposed to investigate the potential consequences of the impact of testing strategy. The model exhibits global dynamics concerning the disease-free and a unique endemic equilibrium depending on the basic reproduction number when the recruitment of infected individuals is zero; otherwise, the model does not have a disease-free equilibrium, and disease never dies out in the community. Model parameters have been estimated using the maximum likelihood method with respect to the data of early COVID-19 outbreak in India. The practical identifiability analysis shows that the model parameters are estimated uniquely. The consequences of the testing rate for the weekly new cases of early COVID-19 data in India tell that if the testing rate is increased by 20% and 30% from its baseline value, the weekly new cases at the peak are decreased by 37.63% and 52.90%; and it also delayed the peak time by four and fourteen weeks, respectively. Similar findings are obtained for the testing efficacy that if it is increased by 12.67% from its baseline value, the weekly new cases at the peak are decreased by 59.05% and delayed the peak by 15 weeks. Therefore, a higher testing rate and efficacy reduce the disease burden by tumbling the new cases, representing a real scenario. It is also obtained that the testing rate and efficacy reduce the epidemic's severity by increasing the final size of the susceptible population. The testing rate is found more significant if testing efficacy is high. Global sensitivity analysis using partial rank correlation coefficients (PRCCs) and Latin hypercube sampling (LHS) determine the key parameters that must be targeted to worsen/contain the epidemic.

Autoimmune alleles at the major histocompatibility locus modify melanoma susceptibility

Autoimmunity and cancer represent two different aspects of immune dysfunction. Autoimmunity is characterized by breakdowns in immune self-tolerance, while impaired immune surveillance can allow for tumorigenesis. The class I major histocompatibility complex (MHC-I), which displays derivatives of the cellular peptidome for immune surveillance by CD8+ T cells, serves as a common genetic link between these conditions. As melanoma-specific CD8+ T cells have been shown to target melanocyte-specific peptide antigens more often than melanoma-specific antigens, we investigated whether vitiligo- and psoriasis-predisposing MHC-I alleles conferred a melanoma-protective effect. In individuals with cutaneous melanoma from both The Cancer Genome Atlas (n = 451) and an independent validation set (n = 586), MHC-I autoimmune-allele carrier status was significantly associated with a later age of melanoma diagnosis. Furthermore, MHC-I autoimmune-allele carriers were significantly associated with decreased risk of developing melanoma in the Million Veteran Program (OR = 0.962, p = 0.024). Existing melanoma polygenic risk scores (PRSs) did not predict autoimmune-allele carrier status, suggesting these alleles provide orthogonal risk-relevant information. Mechanisms of autoimmune protection were neither associated with improved melanoma-driver mutation association nor improved gene-level conserved antigen presentation relative to common alleles. However, autoimmune alleles showed higher affinity relative to common alleles for particular windows of melanocyte-conserved antigens and loss of heterozygosity of autoimmune alleles caused the greatest reduction in presentation for several conserved antigens across individuals with loss of HLA alleles. Overall, this study presents evidence that MHC-I autoimmune-risk alleles modulate melanoma risk unaccounted for by current PRSs.

Mechanistic inference of the metabolic rates underlying [Formula: see text]C breath test curves

Carbon stable isotope breath tests offer new opportunities to better understand gastrointestinal function in health and disease. However, it is often not clear how to isolate information about a gastrointestinal or metabolic process of interest from a breath test curve, and it is generally unknown how well summary statistics from empirical curve fitting correlate with underlying biological rates. We developed a framework that can be used to make mechanistic inference about the metabolic rates underlying a 13C breath test curve, and we applied it to a pilot study of 13C-sucrose breath test in 20 healthy adults. Starting from a standard conceptual model of sucrose metabolism, we determined the structural and practical identifiability of the model, using algebra and profile likelihoods, respectively, and we used these results to develop a reduced, identifiable model as a function of a gamma-distributed process; a slower, rate-limiting process; and a scaling term related to the fraction of the substrate that is exhaled as opposed to sequestered or excreted through urine. We demonstrated how the identifiable model parameters impacted curve dynamics and how these parameters correlated with commonly used breath test summary measures. Our work develops a better understanding of how the underlying biological processes impact different aspect of 13C breath test curves, enhancing the clinical and research potential of these 13C breath tests.

Modeling age-specific incidence of colon cancer via niche competition

Cancer development is a multistep process often starting with a single cell in which a number of epigenetic and genetic alterations have accumulated thus transforming it into a tumor cell. The progeny of such a single benign tumor cell expands in the tissue and can at some point progress to malignant tumor cells until a detectable tumor is formed. The dynamics from the early phase of a single cell to a detectable tumor with billions of tumor cells are complex and still not fully resolved, not even for the well-known prototype of multistage carcinogenesis, the adenoma-adenocarcinoma sequence of colorectal cancer. Mathematical models of such carcinogenesis are frequently tested and calibrated based on reported age-specific incidence rates of cancer, but they usually require calibration of four or more parameters due to the wide range of processes these models aim to reflect. We present a cell-based model, which focuses on the competition between wild-type and tumor cells in colonic crypts, with which we are able reproduce epidemiological incidence rates of colon cancer. Additionally, the fraction of cancerous tumors with precancerous lesions predicted by the model agree with clinical estimates. The correspondence between model and reported data suggests that the fate of tumor development is majorly determined by the early phase of tumor growth and progression long before a tumor becomes detectable. Due to the focus on the early phase of tumor development, the model has only a single fit parameter, the time scale set by an effective replacement rate of stem cells in the crypt. We find this effective rate to be considerable smaller than the actual replacement rate, which implies that the time scale is limited by the processes succeeding clonal conversion of crypts.

Cancer development is a multistep process often starting with a single cell turning into a tumor cell whose progeny growths via clonal expansion into a macroscopic tumor with billions of cells. While experimental insight exists on the cellular scale and cancer registries provide statistics on detectable tumors, the complex dynamics leading from the microscopic cellular scale to a macroscopic tumor is still not fully resolved. Models of cancer biology are commonly used to explain incidence rates but usually require the fit of several biological parameters due to the complexity of the incorporated processes. We employ a cell-based model based on the competition in colonic crypts, to reproduce epidemiological age-specific incidence rates of colon cancer. Due to the focus on the early stage of tumor development, only the time scale in the model has to be calibrated. The agreement between theoretical prediction and epidemiological observation suggests that the fate of tumor development is dominated by the early phase of tumor development long before a tumor becomes detectable.

Parameter estimation and uncertainty quantification using information geometry

In this work, we: (i) review likelihood-based inference for parameter estimation and the construction of confidence regions; and (ii) explore the use of techniques from information geometry, including geodesic curves and Riemann scalar curvature, to supplement typical techniques for uncertainty quantification, such as Bayesian methods, profile likelihood, asymptotic analysis and bootstrapping. These techniques from information geometry provide data-independent insights into uncertainty and identifiability, and can be used to inform data collection decisions. All code used in this work to implement the inference and information geometry techniques is available on GitHub.

Estimation of Breast Cancer Overdiagnosis in a U.S. Breast Screening Cohort

BACKGROUND

Mammography screening can lead to overdiagnosis-that is, screen-detected breast cancer that would not have caused symptoms or signs in the remaining lifetime. There is no consensus about the frequency of breast cancer overdiagnosis.

OBJECTIVE

To estimate the rate of breast cancer overdiagnosis in contemporary mammography practice accounting for the detection of nonprogressive cancer.

DESIGN

Bayesian inference of the natural history of breast cancer using individual screening and diagnosis records, allowing for nonprogressive preclinical cancer. Combination of fitted natural history model with life-table data to predict the rate of overdiagnosis among screen-detected cancer under biennial screening.

SETTING

Breast Cancer Surveillance Consortium (BCSC) facilities.

PARTICIPANTS

Women aged 50 to 74 years at first mammography screen between 2000 and 2018.

MEASUREMENTS

Screening mammograms and screen-detected or interval breast cancer.

RESULTS

The cohort included 35 986 women, 82 677 mammograms, and 718 breast cancer diagnoses. Among all preclinical cancer cases, 4.5% (95% uncertainty interval [UI], 0.1% to 14.8%) were estimated to be nonprogressive. In a program of biennial screening from age 50 to 74 years, 15.4% (UI, 9.4% to 26.5%) of screen-detected cancer cases were estimated to be overdiagnosed, with 6.1% (UI, 0.2% to 20.1%) due to detecting indolent preclinical cancer and 9.3% (UI, 5.5% to 13.5%) due to detecting progressive preclinical cancer in women who would have died of an unrelated cause before clinical diagnosis.

LIMITATIONS

Exclusion of women with first mammography screen outside BCSC.

CONCLUSION

On the basis of an authoritative U.S. population data set, the analysis projected that among biennially screened women aged 50 to 74 years, about 1 in 7 cases of screen-detected cancer is overdiagnosed. This information clarifies the risk for breast cancer overdiagnosis in contemporary screening practice and should facilitate shared and informed decision making about mammography screening.

PRIMARY FUNDING SOURCE

National Cancer Institute.

Identifiability analysis for stochastic differential equation models in systems biology

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

Testing structural identifiability by a simple scaling method

Successful mathematical modeling of biological processes relies on the expertise of the modeler to capture the essential mechanisms in the process at hand and on the ability to extract useful information from empirical data. A model is said to be structurally unidentifiable, if different quantitative sets of parameters provide the same observable outcome. This is typical (but not exclusive) of partially observed problems in which only a few variables can be experimentally measured. Most of the available methods to test the structural identifiability of a model are either too complex mathematically for the general practitioner to be applied, or require involved calculations or numerical computation for complex non-linear models. In this work, we present a new analytical method to test structural identifiability of models based on ordinary differential equations, based on the invariance of the equations under the scaling transformation of its parameters. The method is based on rigorous mathematical results but it is easy and quick to apply, even to test the identifiability of sophisticated highly non-linear models. We illustrate our method by example and compare its performance with other existing methods in the literature.

Mathematical modeling of female breast cancer in Japan

Cancer incidence rates are significantly different all over the world. Breast cancer is affected by many factors, the most important being genetics and lifestyle. The aim of this paper is to study the mutation mechanisms of breast cancer for Japanese women by fitting the incidence data of three high-quality population areas in Japan from 1985 to 2010. To achieve this goal, we have set up multi-stage models within the mathematical model of Moolgavkar, Venzon, and Knudson. Such models take both mutation rates and clonal expansion rates as parameters in each compartment into consideration. Based on our simulation outcomes, two to twelve driver mutations are sufficient in the pathway to female breast cancer in Japan. On the other hand, a previous study demonstrated that breast cancer in American women requires two to fourteen gene mutations to get a cancerous cell. Moreover, the 3-stage mathematical model is the optimal model as it fits clinical data very nicely for all affected cases of females in Japan and the US. The genetic instability has a prominent effect on the tumorigenesis of Japanese females caused by the first four driver mutations. The calculated results for Japanese women are compared with previous works for American women.

Case Studies of Gastric, Lung, and Oral Cancer Connect Etiologic Agent Prevalence to Cancer Incidence

Obtaining detailed individual-level data on both exposure and cancer outcomes is challenging, and it is difficult to understand and characterize how temporal aspects of exposures translate into cancer risk. We show that, in lieu of individual-level information, population-level data on cancer incidence and etiologic agent prevalence can be leveraged to investigate cancer mechanisms and to better characterize and predict cancer trends. We use mechanistic carcinogenesis models [multistage clonal expansion (MSCE) models] and data on smoking, Helicobacter pylori (H. pylori), and HPV infection prevalence to investigate trends of lung, gastric, and HPV-related oropharyngeal cancers. MSCE models are based on the initiation-promotion-malignant conversion paradigm and allow for interpretation of trends in terms of general biological mechanisms. We assumed the rates of initiation depend on the prevalence of the corresponding risk factors. We performed two types of analysis, using the agent prevalence and cancer incidence data to estimate the model parameters and using cancer incidence data to infer the etiologic agent prevalence as well as the model parameters. By including risk factor prevalence, MSCE models with as few as three parameters closely reproduced 40 years of age-specific cancer incidence data. We recovered trends of H. pylori prevalence in the United States and demonstrated that cohort effects can explain the observed bimodal, age-specific pattern of oral HPV prevalence in men. Our results demonstrate the potential for joint analyses of population-level cancer and risk factor data through mechanistic modeling. This approach can be a first step in systematically testing relationships between exposures and cancer risk when individual-level data is lacking.Significance: Analysis of trends in risk-factor prevalence and cancer incidence can shed light on cancer mechanisms and the way that carcinogen exposure through time shapes the risk of cancer at different ages.Graphical Abstract: http://cancerres.aacrjournals.org/content/canres/78/12/3386/F1.large.jpg Cancer Res; 78(12); 3386-96. ©2018 AACR.

What is the meaning of 'A compound is carcinogenic'?

Chemical Carcinogens are compounds which can cause cancer in humans and experimental animals. This property is attributed to many chemicals in the public discussion, resulting in a widespread perception of danger and threat. In contrast, a scientific analysis of the wide and non-critical use of the term 'carcinogenic' is warranted. First, it has to be clarified if the compound acts in a genotoxic or non-genotoxic manner. In the latter case, an ineffective (safe) threshold dose without cancer risk can be assumed. In addition, it needs to be investigated if the mode-of-action causing tumors in laboratory animals is relevant at all for humans. In case the compound is clearly directly genotoxic, an ineffective threshold dose cannot be assumed. However, also in this case it is evident that high doses of the compound are generally associated with a high cancer risk, low doses with a lower one. Based on dose-response data from animal experiments, quantification of the cancer risk is carried out by mathematical modeling. If the safety margin between the lowest carcinogenic dose in animals and the relevant level of exposure in humans exceeds 10,000, the degree of concern is classified as low. Cases, where the compound turns out to be genotoxic in one study or one test only but not in others or only in vitro but not in vivo, are particularly difficult to explain and cause controversial discussions. Also for indirectly genotoxic agents, an ineffective (threshold) dose must be assumed. The situation is aggravated by the use of doubtful epidemiological studies in humans such as in the case of glyphosate, where data from mixed exposure to various chemicals were used. If such considerations are mixed with pure hazard classifications such as 'probably carcinogenic in humans' ignoring dose-response behavior and mode-of-action, the misinformation and public confusion are complete. It appears more urgent but also more difficult than ever to return to a scientifically based perception of these issues.

Fighting Cancer with Mathematics and Viruses

After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex antitumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these research fields to increase the value of the preclinical development and the therapeutic efficacy of the resulting treatments.