Identifiability of the joint distribution of age and tumor size at detection in the presence of screening.

In recent years, a stochastic model of cancer development and detection allowing for arbitrary screening schedules has been developed and applied to analysis of screening trials and population-based cancer incidence and mortality data. The model is entirely mechanistic, builds on a minimal set of biologically plausible assumptions, and yields the joint distribution of tumor size and age of a patient at the time of diagnosis. Whether or not parameters of the model can be estimated from data generated by cohort studies depends on model identifiability. The present paper provides a proof of this important property of the model.

[1]  S D Walter,et al.  Estimation of the duration of a pre-clinical disease state using screening data. , 1983, American journal of epidemiology.

[2]  R. Brookmeyer,et al.  Two-stage models for the analysis of cancer screening data. , 1987, Biometrics.

[3]  W F Heidenreich,et al.  Some Properties of the Hazard Function of the Two‐Mutation Clonal Expansion Model , 1997, Risk analysis : an official publication of the Society for Risk Analysis.

[4]  A Yu Yakovlev,et al.  Stochastic Models of Tumor Latency and Their Biostatistical Applications , 1996 .

[5]  S H Moolgavkar,et al.  Two-event model for carcinogenesis: biological, mathematical, and statistical considerations. , 1990, Risk analysis : an official publication of the Society for Risk Analysis.

[6]  A. Yakovlev,et al.  The University of Rochester model of breast cancer detection and survival. , 2006, Journal of the National Cancer Institute. Monographs.

[7]  Giovanni Parmigiani,et al.  Timing medical examinations via intensity functions , 1997 .

[8]  Giovanni Parmigiani,et al.  On Optimal Screening Ages , 1993 .

[9]  Roland Holland,et al.  Age‐dependent growth rate of primary breast cancer , 1993, Cancer.

[10]  P. Pinsky.  Estimation and Prediction for Cancer Screening Models Using Deconvolution and Smoothing , 2001, Biometrics.

[11]  Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology , 2002 .

[12]  A D Tsodikov,et al.  A distribution of tumor size at detection: an application to breast cancer data. , 1997, Biometrics.

[13]  A D Tsodikov,et al.  Discrete strategies of cancer post-treatment surveillance. Estimation and optimization problems. , 1995, Biometrics.

[14]  T. Louis,et al.  Screening for the early detection of cancer- II. The impact of screening on the natural history of the disease , 1978 .

[15]  Philip C. Prorok,et al.  The theory of periodic screening II: doubly bounded recurrence times and mean lead time and detection probability estimation , 1976, Advances in Applied Probability.

[16]  A Stochastic Model of Carcinogenesis and Tumor Size at Detection , 1997, Advances in Applied Probability.

[17]  W. Heidenreich.  On the parameters of the clonal expansion model , 1996, Radiation and environmental biophysics.

[18]  L. Tabár,et al.  Estimation of mean sojourn time in breast cancer screening using a Markov chain model of both entry to and exit from the preclinical detectable phase. , 1995, Statistics in medicine.

[19]  Michael Shwartz,et al.  A Mathematical Model Used to Analyze Breast Cancer Screening Strategies , 1978, Oper. Res..

[20]  L. Hanin,et al.  A nonidentifiability aspect of the two-stage model of carcinogenesis. , 1996, Risk analysis : an official publication of the Society for Risk Analysis.

[21]  N. Day,et al.  Simplified models of screening for chronic disease: estimation procedures from mass screening programmes. , 1984, Biometrics.

[22]  Marvin Zelen,et al.  On the theory of screening for chronic diseases , 1969 .

[23]  P. Hu,et al.  Planning clinical trials to evaluate early detection programmes , 1997 .

[24]  Thomas A. Louis,et al.  Screening for the early detection of cancer— III. Estimation of disease natural history☆ , 1978 .

[25]  M. Zelen,et al.  Parametric estimation procedures for screening programmes: Stable and nonstable disease models for multimodality case finding , 1999 .

[26]  L Edler,et al.  Modeling cancer detection: tumor size as a source of information on unobservable stages of carcinogenesis. , 2001, Mathematical biosciences.

[27]  S H Moolgavkar,et al.  Mutation and cancer: a model for human carcinogenesis. , 1981, Journal of the National Cancer Institute.

[28]  L. Blumenson,et al.  A mathematical analysis of the growth and spread of breast cancer. , 1969, Biometrics.

[29]  T. Louis,et al.  Screening for the early detection of cancer— I. The temporal natural history of a progressive disease state , 1978 .

[30]  A Y Yakovlev,et al.  A distribution of tumor size at detection and its limiting form. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[31]  A. Yu. Yakovlev,et al.  Optimal schedules of cancer surveillance and tumor size at detection , 2001 .

[32]  D. Berry,et al.  Effect of screening and adjuvant therapy on mortality from breast cancer , 2005 .

[33]  L G Hanin,et al.  Multivariate distributions of clinical covariates at the time of cancer detection , 2004, Statistical methods in medical research.

[34]  Philip C. Prorok,et al.  The theory of periodic screening I: Lead time and proportion detected , 1976, Advances in Applied Probability.

[35]  D. Atkins,et al.  The Cost-Effectiveness of Screening Mammography beyond Age 65 Years , 2003, Annals of Internal Medicine.

[36]  S. Moolgavkar,et al.  Two-event models for carcinogenesis: incidence curves for childhood and adult tumors☆ , 1979 .

[37]  Marvin Zelen,et al.  Scheduling Periodic Examinations for the Early Detection of Disease: Applications to Breast Cancer , 1998 .

[38]  M Zelen,et al.  Screening sensitivity and sojourn time from breast cancer early detection clinical trials: mammograms and physical examinations. , 2001, Journal of clinical oncology : official journal of the American Society of Clinical Oncology.

[39]  L. Blumenson.  Detection of disease with periodic screening: transient analysis and application to mammography examination , 1977 .

[40]  Alexander V. Zorin,et al.  Estimating the Natural History of Breast Cancer from Bivariate Data on Age and Tumor Size at Diagnosis , 2006 .

[41]  M. Shwartz,et al.  An analysis of the benefits of serial screening for breast cancer based upon a mathematical model of the disease , 1978, Cancer.

[42]  A D Tsodikov,et al.  On the optimal policies of cancer screening. , 1991, Mathematical biosciences.

[43]  J. Habbema,et al.  A model‐based analysis of the hip project for breast cancer screening , 1990, International journal of cancer.

[44]  A. Yakovlev,et al.  Testing goodness of fit for stochastic models of carcinogenesis. , 2002, Mathematical biosciences.

[45]  Marvin Zelen,et al.  Optimal scheduling of examinations for the early detection of disease , 1993 .