Estimation of progression of multi-state chronic disease using the Markov model and prevalence pool concept

A multistate survival model of the natural history of cancer using data from screened and unscreened population

One of the main aims of models using cancer screening data is to determine the time between the onset of preclinical screen-detectable cancer and the onset of the clinical state of the cancer. This time is called the sojourn time. One problem in using screening data is that an individual can be observed in preclinical phase or clinically diagnosed but not both. Multistate survival models provide a method of modeling the natural history of cancer. The natural history model allows for the calculation of the sojourn time. We developed a continuous-time Markov model and the corresponding likelihood function. The model allows for the use of interval-censored, left-truncated and right-censored data. The model uses data of clinically diagnosed cancers from both screened and nonscreened individuals. Parameters of age-varying hazards and age-varying misclassification are estimated simultaneously. The mean sojourn time is calculated from a micro-simulation using model parameters. The model is applied to data from a prostate screening trial. The simulation study showed that the model parameters could be estimated accurately.

A Bayesian model for estimating multi-state disease progression

A growing number of individuals who are considered at high risk of cancer are now routinely undergoing population screening. However, noted harms such as radiation exposure, overdiagnosis, and overtreatment underscore the need for better temporal models that predict who should be screened and at what frequency. The mean sojourn time (MST), an average duration period when a tumor can be detected by imaging but with no observable clinical symptoms, is a critical variable for formulating screening policy. Estimation of MST has been long studied using continuous Markov model (CMM) with Maximum likelihood estimation (MLE). However, a lot of traditional methods assume no observation error of the imaging data, which is unlikely and can bias the estimation of the MST. In addition, the MLE may not be stably estimated when data is sparse. Addressing these shortcomings, we present a probabilistic modeling approach for periodic cancer screening data. We first model the cancer state transition using a three state CMM model, while simultaneously considering observation error. We then jointly estimate the MST and observation error within a Bayesian framework. We also consider the inclusion of covariates to estimate individualized rates of disease progression. Our approach is demonstrated on participants who underwent chest x-ray screening in the National Lung Screening Trial (NLST) and validated using posterior predictive p-values and Pearson's chi-square test. Our model demonstrates more accurate and sensible estimates of MST in comparison to MLE.

Mathematical modeling and the epidemiological research process

The authors of this paper advocate for the expanded use of mathematical models in epidemiology and provide an overview of the principles of mathematical modeling. Mathematical models can be used throughout the epidemiological research process. Initially they may help to refine study questions by visually expressing complex systems, directing literature searches, and identifying sensitive variables. In the study design phase, models can be used to test sampling strategies, to estimate sample size and power, and to predict outcomes for studies impractical due to time or ethical considerations. Once data are collected, models can assist in the interpretation of results, the exploration of causal pathways, and the combined analysis of data from multiple sources. Finally, models are commonly used in the process of applying research findings to public health practice by estimating population risk, predicting the effects of interventions, and contributing to the evaluation of ongoing programs. Mathematical modeling has the potential to make significant contributions to the field of epidemiology by enhancing the research process, serving as a tool for communicating findings to policymakers, and fostering interdisciplinary collaboration.

Retraction: estimation of progression of multi-state chronic disease using the Markov model and prevalence pool concept

This article has been retracted because the Editors are unable to ensure the scientific veracity of the findings or the ethical conduct of the authors despite an extensive investigation.