The University of Michigan Lung Cancer Screening Model (UM-LCSc) was developed to analyze lung cancer incidence by histology and evaluate the impact of screening on lung cancer incidence and mortality. The model assumes that two mutation (rate-limiting) events are required for the initiation of premalignant lung tumors, and it explicitly models the dynamics of premalignant and malignant tumors. Malignant tumors evolve through a stage progression model and can be detected clinically or through screening. The model was first fitted to lung cancer incidence by histology in the Nurses’ Health Study (NHS) and the Health Professionals’ Follow-up Study (HPFS) using a likelihood-based approach, and then calibrated to lung cancer incidence in the National Lung Screening Trial (NLST) and the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial (PLCO) via microsimulations of the carcinogenesis process (1,2). The UM-LCSc was used to estimate the benefits and harms of lung cancer low-dose computed tomography (CT) screening in the US (1-4).
The UM-LCSc assumes that normal stem cells become pre-initiated according to a Poisson process. Pre-initiated cells become initiated according to another Poisson process. Initiated cells (pre-malignant stage) expand clonally (called “promotion”) via a linear birth and death process. This means that each time when an initiated cell divides, it can produce two initiated cells or die/differentiate. An initiated cell can also divide into one initiated and one malignant cell. Malignant (preclinical stage) cells grow according to a linear birth and death process. Each parameter rate in the model depends on the cigarettes-per-day dose, with the exception that the rates in the malignant compartment are assumed to be independent of smoking. (5-7)
Model parameters vary by gender and histology (adenocarcinoma, other non-small cell, small cell). Once a tumor becomes malignant (preclinical), it goes through a stage-wise progression via a Markov-state transition model. The malignant stages are based on the American Joint Committee on Cancer (AJCC) classification (IA1, IA2, IB, II, IIIA, IIIB, and IV). Transition rates per stage λs are proportional to the number of cells in the corresponding preclinical compartment. At each stage the cancer can be detected with rate δs (per cell/year).
For each individual, the carcinogenesis process is simulated forward using a tau-leaping approach, which is based on Gillespie algorithm, generating all trajectories of possible stochastic events during the process within an interval of length tau (8,9). In particular, at each time step, we generate the number of mutations, cell divisions, and cell deaths of all cell types and tumors. We also generate the events of transitions between preclinical stages, and the clinical detection of preclinical cancers.
The screen detection probability is proportional to the total number of premalignant and malignant cells in a tumor at the time of a screening test. The proportionality constants σs vary by screening modality and histology. Once a cancer is detected, clinically or through screening, the model generates a time to lung cancer death based on a lung cancer survival function with cure by stage, histology, gender, and age at detection. The survival models (logistic or lognormal) with cure parameters were estimated using the NCI Cansurv program (10) and the SEER 17 2004-2008 lung cancer survival data (11).
References
- McMahon PM, Meza R, Plevritis SK, et al. Comparing Benefits from Many Possible Computed Tomography Lung Cancer Screening Programs: Extrapolating from the National Lung Screening Trial Using Comparative Modeling. PLoS ONE. 2014;9(6):e99978.
- Meza R, ten Haaf K, Kong CY, et al. Comparative analysis of 5 lung cancer natural history and screening models that reproduce outcomes of the NLST and PLCO trials. Cancer. 2014;120(11):1713-1724.
- de Koning HJ, Meza R, Plevritis SK, et al. Benefits and harms of CT lung cancer screening programs for high risk populations AHRQ Publication No. 13-05196-EF-2. Rockville, MD: Agency for Healthcare Research and Quality; 2013.
- de Koning HJ, Meza R, Plevritis SK, et al. Benefits and harms of computed tomography lung cancer screening strategies: a comparative modeling study for the U.S. Preventive Services Task Force. Ann Intern Med. 2014;160(5):311-320.
- Hazelton WD, Clements MS, Moolgavkar SH. Multistage Carcinogenesis and Lung Cancer Mortality in Three Cohorts. Cancer Epidemiol Biomarkers Prev. May 1, 2005 2005;14(5):1171-1181.
- Meza R, Hazelton WD, Colditz GA, Moolgavkar SH. Analysis of lung cancer incidence in the Nurses' Health and the Health Professionals' Follow-Up Studies using a multistage carcinogenesis model. Cancer Causes Control. 2008;19(3):317-328.
- Hazelton WD, Jeon J, Meza R, Moolgavkar SH. The FHCRC lung cancer model. Risk Analysis. 2012;32(S1):s99-s116
- Gillespie DT, Petzold LR. Improved leap-size selection for accelerated stochastic simulation. J Chem Phys. 2003;119(16):8229-8234.
- Higham DJ. Modeling and simulating chemical reactions. SIAM Rev. 2008;50(2):347-368.
- Cansurv, Version 1.1. 2012; Statistical Methodology and Applications Branch, Data Modeling Branch, National Cancer Institute.
- Tammemagi CM, Pinsky PF, Caporaso NE, et al. Lung cancer risk prediction: Prostate, Lung, Colorectal And Ovarian Cancer Screening Trial models and validation. J Natl Cancer Inst. 2011;103(13):1053-1068.
