Estimating a Distribution Function of the Tumor Size at Metastasis

Xu, Jian-Lun; Prorok, Philip C.

doi:10.2307/2533840

Cited by 14 publications

(24 citation statements)

References 6 publications

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“…In addition, we note differences between our work and that by Xu and Prorok [26,27]. Xu and Prorok [26,27] further developed [25] by proposing additional assumptions to make the model identifiable in the general case.…”

Section: Discussionmentioning

confidence: 71%

“…Xu and Prorok [26,27] further developed [25] by proposing additional assumptions to make the model identifiable in the general case. In [26], Xu and Prorok assume that the odds ratio for detecting a tumor at given size before and after stage transition is constant for all tumor sizes, and known.…”

Section: Discussionmentioning

confidence: 99%

“…In [26], Xu and Prorok assume that the odds ratio for detecting a tumor at given size before and after stage transition is constant for all tumor sizes, and known. In [27], they assume that the hazard for detecting a tumor after the metastatic spread is constant and known. In both papers, the authors compare their results with the ones presented in [25], and report similar behavior.…”

Section: Discussionmentioning

confidence: 99%

“…The work presented here is related to that presented by Kimmel and Flehinger [25], and special cases of their model were investigated by Xu and Prorok [26,27]. Kimmel et al inferred the primary tumor volume when the disease transits from early to advanced clinical stage and explored the dependence of lung cancer detection on the volume and disease stage.…”

Section: Introductionmentioning

confidence: 93%

“…The random variable for the primary tumor volume M = V(T M ) at which the patient transitions from early to advanced stage is characterized by the cumulative distribution function F M (m;h) and the probability density function f M (m; h), where T M is the random variable for the time of stage transition, and h is a parameter vector. Because the time of transition is not observed, its distribution is nonidentifiable without making additional assumptions, as previously noted [25][26][27]. Implicit in our assumption is that the disease stage transition to the advanced stage is irreversible.…”

Section: Model Formulationmentioning

confidence: 98%

See 4 more Smart Citations

Modeling the transition of lung cancer from early to advanced stage

Pashkevich

Sigal

Plevritis

2009

Cancer Causes Control

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We present a stochastic parametric model of the natural history of lung cancer that predicts the primary tumor volume at the moment the disease transits from early to advanced stage. Our model also produces estimates for the probability of symptomatic detection as a function of tumor volume and clinical stage. We estimate model parameters by likelihood maximization using data from the Mayo Lung Project (MLP), which was a clinical trial that evaluated screening for lung cancer in the 1970s. Mayo Lung Project cancer cases reported in Stage III or greater, according to the 1979 AJCC staging for lung cancer, were considered advanced stage. Our estimator distinguishes between the cases detected because of clinical symptoms and cases detected by screening. For nonsmall cell lung cancer cases detected in MLP, we estimate that the median primary tumor diameter at the onset of advanced stage disease was 4.1 cm. In addition, we estimate that the rate of patients symptomatically detected with their disease increases as their primary tumor increases in size, and for patients with a primary tumor of a given size, the rate of symptomatic detection is 12.8 times greater among patients with advanced stage disease compared to patients with early stage disease.

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Section: Discussionmentioning

confidence: 71%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

Section: Model Formulationmentioning

confidence: 98%

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Modeling the transition of lung cancer from early to advanced stage

Pashkevich

Sigal

Plevritis

2009

Cancer Causes Control

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Estimation of the tumor size at cure threshold among aggressive non-small cell lung cancers (NSCLCs): evidence from the surveillance, epidemiology, and end results (SEER) program and the national lung screening trial (NLST)

Goldwasser

2017

Int. J. Cancer

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The National Lung Screening Trial (NLST) demonstrated that non-small cell lung cancer (NSCLC) mortality can be reduced by a program of annual CT screening in high-risk individuals. However, CT screening regimens and adherence vary, potentially impacting the lung cancer mortality benefit. We defined the NSCLC cure threshold as the maximum tumor size at which a given NSCLC would be curable due to early detection. We obtained data from 518,234 NSCLCs documented in the U.S. SEER cancer registry between 1988 and 2012 and 1769 NSCLCs detected in the NLST. We demonstrated mathematically that the distribution function governing the cure threshold for the most aggressive NSCLCs, G(x|Φ = 1), was embedded in the probability function governing detection of SEER-documented NSCLCs. We determined the resulting probability functions governing detection over a range of G(x|Φ = 1) scenarios and compared them with their expected functional forms. We constructed a simulation framework to determine the cure threshold models most consistent with tumor sizes and outcomes documented in SEER and the NLST. Whereas the median tumor size for lethal NSCLCs documented in SEER is 43 mm (males) and 40 mm (females), a simulation model in which the median cure threshold for the most aggressive NSCLCs is 10 mm (males) and 15 mm (females) best fit the SEER and NLST data. The majority of NSCLCs in the NLST were treated at sizes greater than our median cure threshold estimates. New technology is needed to better distinguish and treat the most aggressive NSCLCs when they are small (i.e., 5-15 mm).

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Modelling tumour biology–progression relationships in screening trials

Ghosh¹

2006

Statist. Med.

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There has been some recent work in the statistical literature for modelling the relationship between tumour biology properties and tumour progression in screening trials. While non-parametric methods have been proposed for estimation of the tumour size distribution at which metastatic transition occurs, their asymptotic properties have not been studied. In addition, no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for. We develop a unified approach to non-parametric and semi-parametric analysis of modelling tumour size-metastasis data in this article. An association between the models considered by previous authors with survival data structures is discussed. Based on this relationship, we develop non-parametric testing procedures and semi-parametric regression methodology of modelling the effect of size of tumour on the probability at which metastatic transitions occur in two situations. Asymptotic properties of these estimators are provided. The proposed methodology is applied to data from a screening study in lung cancer.

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Estimating a Distribution Function of the Tumor Size at Metastasis

Cited by 14 publications

References 6 publications

Modeling the transition of lung cancer from early to advanced stage

Modeling the transition of lung cancer from early to advanced stage

Estimation of the tumor size at cure threshold among aggressive non-small cell lung cancers (NSCLCs): evidence from the surveillance, epidemiology, and end results (SEER) program and the national lung screening trial (NLST)

Modelling tumour biology–progression relationships in screening trials

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