Nonparametric Estimation of Solid Cancer Size at Metastasis and Probability of Presenting with Metastasis at Detection

Xu, Jian-Lun; Prorok, Philip C.

doi:10.2307/2533959

Cited by 8 publications

(23 citation statements)

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“…and it is probable that the disease w-ould be better controlled if smaller tumours could be detected (Tabar et al 1992: see also Flehinger. 1991 andXu andProrok. 1997 for theoretical discussions).…”

mentioning

confidence: 99%

The growth law of primary breast cancer as inferred from mammography screening trials data

Hart

Shochat²,

Agur³

1998

Br J Cancer

154

111

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Summary Despite considerable progress in understanding tumour development. the law of growth for human tumours is still a matter of some dispute. In this study, we used large-scale mammography screening trial data to deduce the growth law of primary breast cancer. We compared the empirical tumour population size distributions of primary breast cancer inferred from these data to the distributions that correspond to various possible theoretical growth functions. From this. we showed that the data are inconsistent with the exponential, logistic and Gompertz laws, but support power law growth (exponent = 0.5). This law indicates unbounded growth but with slowing mass-specific growth rate and doubling time. In the clinical size ranges, it implies a greater decline in the mass-specific growth rate than would be predicted by the Gompertz law using the accepted parameters. This suggests that large tumours would be less sensitive to cycle-specific therapies. and be better treated first by non-cell cycle-specific agents. We discussed the use of our study to estimate the sensitivity of mammography for the detection of small tumours. For example, we estimated that mammography is about 30% less sensitive in the detection of tumours in the 1 to Flehinger. 1991 and Xu and Prorok. 1997 for theoretical discussions). Nex ertheless. the benefit of screening. especiall in youncer women (< 50 Xyears). still remains somew-hat controv-ersial (Fletcher et al. 1993: Tabar et al. 1995 In the present w-ork. we employed extensive clinical data from large mammogaraphv screening trials that should be representatiVe of the general population. Usinc mathematical tools. we extracted from these data useful information about breast cancer growth.

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confidence: 99%

The growth law of primary breast cancer as inferred from mammography screening trials data

Hart

Shochat²,

Agur³

1998

Br J Cancer

154

111

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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: 73%

“…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%

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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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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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“…There has been a rich literature existing on statistical models for tumor progression in which the property considered was size of the tumor (Kimmel and Flehinger, 1991;Xu and Prorok, 1997). However, no such development has occurred for gene expression profile and its effects on tumor progression.…”

Section: Introductionmentioning

confidence: 99%

Empirical Bayes Identication of Tumor Progression Genes from Microarray Data

Ghosh

Chinnaiyan

2007

Biometrical J

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The use of microarray data has become quite commonplace in medical and scientific experiments. We focus here on microarray data generated from cancer studies. It is potentially important for the discovery of biomarkers to identify genes whose expression levels correlate with tumor progression. In this article, we propose a simple procedure for the identification of such genes, which we term tumor progression genes. The first stage involves estimation based on the proportional odds model. At the second stage, we calculate two quantities: a q-value, and a shrinkage estimator of the test statistic is constructed to adjust for the multiple testing problem. The relationship between the proposed method with the false discovery rate is studied. The proposed methods are applied to data from a prostate cancer microarray study.

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Nonparametric Estimation of Solid Cancer Size at Metastasis and Probability of Presenting with Metastasis at Detection

Cited by 8 publications

References 0 publications

The growth law of primary breast cancer as inferred from mammography screening trials data

The growth law of primary breast cancer as inferred from mammography screening trials data

Modeling the transition of lung cancer from early to advanced stage

Empirical Bayes Identication of Tumor Progression Genes from Microarray Data

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