Optimal Timing for Cancer Screening and Adaptive Surveillance Using Mathematical Modeling.

Cancer screening and early detection efforts have been partially successful in reducing incidence and mortality, but many improvements are needed. Although current medical practice is informed by epidemiologic studies and experts, the decisions for guidelines are ultimately ad hoc. We propose here that quantitative optimization of protocols can potentially increase screening success and reduce overdiagnosis. Mathematical modeling of the stochastic process of cancer evolution can be used to derive and optimize the timing of clinical screens so that the probability is maximal that a patient is screened within a certain "window of opportunity" for intervention when early cancer development may be observable. Alternative to a strictly empirical approach or microsimulations of a multitude of possible scenarios, biologically based mechanistic modeling can be used for predicting when best to screen and begin adaptive surveillance. We introduce a methodology for optimizing screening, assessing potential risks, and quantifying associated costs to healthcare using multiscale models. As a case study in Barrett's esophagus, these methods were applied for a model of esophageal adenocarcinoma that was previously calibrated to U.S. cancer registry data. Optimal screening ages for patients with symptomatic gastroesophageal reflux disease were older (58 for men and 64 for women) than what is currently recommended (age > 50 years). These ages are in a cost-effective range to start screening and were independently validated by data used in current guidelines. Collectively, our framework captures critical aspects of cancer evolution within patients with Barrett's esophagus for a more personalized screening design. SIGNIFICANCE: This study demonstrates how mathematical modeling of cancer evolution can be used to optimize screening regimes, with the added potential to improve surveillance regimes. GRAPHICAL ABSTRACT: http://cancerres.aacrjournals.org/content/canres/81/4/1123/F1.large.jpg.

Number and size distribution of colorectal adenomas under the multistage clonal expansion model of cancer.

Colorectal cancer (CRC) is believed to arise from mutant stem cells in colonic crypts that undergo a well-characterized progression involving benign adenoma, the precursor to invasive carcinoma. Although a number of (epi)genetic events have been identified as drivers of this process, little is known about the dynamics involved in the stage-wise progression from the first appearance of an adenoma to its ultimate conversion to malignant cancer. By the time adenomas become endoscopically detectable (i.e., are in the range of 1-2 mm in diameter), adenomas are already comprised of hundreds of thousands of cells and may have been in existence for several years if not decades. Thus, a large fraction of adenomas may actually remain undetected during endoscopic screening and, at least in principle, could give rise to cancer before they are detected. It is therefore of importance to establish what fraction of adenomas is detectable, both as a function of when the colon is screened for neoplasia and as a function of the achievable detection limit. To this end, we have derived mathematical expressions for the detectable adenoma number and size distributions based on a recently developed stochastic model of CRC. Our results and illustrations using these expressions suggest (1) that screening efficacy is critically dependent on the detection threshold and implicit knowledge of the relevant stem cell fraction in adenomas, (2) that a large fraction of non-extinct adenomas remains likely undetected assuming plausible detection thresholds and cell division rates, and (3), under a realistic description of adenoma initiation, growth and progression to CRC, the empirical prevalence of adenomas is likely inflated with lesions that are not on the pathway to cancer.

On the relationship between time-series studies, dynamic population studies, and estimating loss of life due to short-term exposure to environmental risks.

There is a growing concern that short-term exposure to combustion-related air pollution is associated with increased risk of death. This finding is based largely on time-series studies that estimate associations between daily variations in ambient air pollution concentrations and in the number of nonaccidental deaths within a community. Because these results are not based on cohort or dynamic population designs, where individuals are followed in time, it has been suggested that estimates of effect from these time-series studies cannot be used to determine the amount of life lost because of short-term exposures. We show that results from time-series studies are equivalent to estimates obtained from a dynamic population when each individual's survival experience can be summarized as the daily number of deaths. This occurs when the following conditions are satisfied: a) the environmental covariates vary in time and not between individuals; b) on any given day, the probability of death is small; c) on any given day and after adjusting for known risk factors for mortality such age, sex, smoking habits, and environmental exposures, each subject of the at-risk population has the same probability of death; d) environmental covariates have a common effect on mortality of all members of at-risk population; and e) the averages of individual risk factors, such as smoking habits, over the at-risk population vary smoothly with time. Under these conditions, the association between temporal variation in the environmental covariates and the survival experience of members of the dynamic population can be estimated by regressing the daily number of deaths on the daily value of the environmental covariates, as is done in time-series mortality studies. Issues in extrapolating risk estimates based on time-series studies in one population to estimate the amount of life lost in another population are also discussed.

Exploring heterogeneity in tumour data using Markov chain Monte Carlo.

We describe a Bayesian approach to incorporate between-individual heterogeneity associated with parameters of complicated biological models. We emphasize the use of the Markov chain Monte Carlo (MCMC) method in this context and demonstrate the implementation and use of MCMC by analysis of simulated overdispersed Poisson counts and by analysis of an experimental data set on preneoplastic liver lesions (their number and sizes) in the presence of heterogeneity. These examples show that MCMC-based estimates, derived from the posterior distribution with uniform priors, may agree well with maximum likelihood estimates (if available). However, with heterogeneous parameters, maximum likelihood estimates can be difficult to obtain, involving many integrations. In this case, the MCMC method offers substantial computational advantages.

Estimation of competing risks with general missing pattern in failure types.

In competing risks data, missing failure types (causes) is a very common phenomenon. In this work, we consider a general missing pattern in which, if a failure type is not observed, one observes a set of possible types containing the true type, along with the failure time. We first consider maximum likelihood estimation with missing-at-random assumption via the expectation maximization (EM) algorithm. We then propose a Nelson-Aalen type estimator for situations when certain information on the conditional probability of the true type given a set of possible failure types is available from the experimentalists. This is based on a least-squares type method using the relationships between hazards for different types and hazards for different combinations of missing types. We conduct a simulation study to investigate the performance of this method, which indicates that bias may be small, even for high proportion of missing data, for sufficiently large number of observations. The estimates are somewhat sensitive to misspecification of the conditional probabilities of the true types when the missing proportion is high. We also consider an example from an animal experiment to illustrate our methodology.