Modeling the Cell Carcinogenesis in Lung Cancer: Taking the Interaction Between Genetic Factors and Smoking into Account

1. Modeling the Cell Carcinogenesis in Lung Cancer: Taking the Interaction Between Genetic Factors and Smoking into Account Li Deng and Marek Kimmel Department of Statistics Rice University Nov 13, 2003

2. All the models considered are general for all solid tumors. Here we are more interested in lung cancer. Why?All the models considered are general for all solid tumors. Here we are more interested in lung cancer. Why?

3. Some facts on Lung Cancer Lung cancer has the leading mortality rate among all cancers in U.S. Strong correlation between cigarette consumption and lung cancer incidence (see the next page) About 85% lung cancer patients are smokers (former or current) About 10~15% of smokers develop lung cancer in their life time Both for females and males. Although breast cancer and prostate cancer have top incidence rate, the survival probability from these two types of cancers are higher than lung caner. increase of lung cancer after the increase of tobaccoBoth for females and males. Although breast cancer and prostate cancer have top incidence rate, the survival probability from these two types of cancers are higher than lung caner. increase of lung cancer after the increase of tobacco

4. The association between lung cancer and cigarette smoking Eight control studies in 1950’s and some cohort studies later confirm the cigarette smoking as an important risk factor for lung cancer. Women picked up the habit many years later, so the lung cancer incidence for females did not read its peak by 1992. But the lag between tobacco consumption and lung cancer incidence is pretty clear.Eight control studies in 1950’s and some cohort studies later confirm the cigarette smoking as an important risk factor for lung cancer. Women picked up the habit many years later, so the lung cancer incidence for females did not read its peak by 1992. But the lag between tobacco consumption and lung cancer incidence is pretty clear.

5. Approaches to modeling lung cancer incidence Nording(1953) and Armitage(1954) Multistage Model Two stage clonal expansion model (1979) Pompei and Wilson’s Beta Model (2001)

6. Nording (1953) and Armitage (1954) Multistage Model Motivation of this model (multistage model) Simple mathematical arguments: each stage the change probability is constant over lifetime.Motivation of this model (multistage model) Simple mathematical arguments: each stage the change probability is constant over lifetime.

7. The fitted log incidence curves using N-A model (I) The slope is the estimation of the k-1, the number of stages(mutations) required for tumor evolution They threw out those data at high age (between 25-75) Data source (1950 & 1951 England and Wales male and female death rates from various cancers) The slope is the estimation of the k-1, the number of stages(mutations) required for tumor evolution They threw out those data at high age (between 25-75) Data source (1950 & 1951 England and Wales male and female death rates from various cancers)

8. The fitted log incidence curves using N-A model (II) The slope is the estimation of the k-1, the number of stages(mutations) required for tumor evolution They threw out those data at high age (between 25-75) Data source (1950 & 1951 England and Wales male and female death rates from various cancers) The slope is the estimation of the k-1, the number of stages(mutations) required for tumor evolution They threw out those data at high age (between 25-75) Data source (1950 & 1951 England and Wales male and female death rates from various cancers)

9. The fitted log incidence curves using N-A model (III) Poor fit for the four types of cancer Prostate, Ovary and Uteri cancer might be hormone driven cancer. The model can not catch it. But lung cancer might be twisted by increase of cigarette smoking from 1900-1950.Poor fit for the four types of cancer Prostate, Ovary and Uteri cancer might be hormone driven cancer. The model can not catch it. But lung cancer might be twisted by increase of cigarette smoking from 1900-1950.

10. The fitted log incidence curves using N-A model (IV) Poor fit for the four types of cancer Prostate, Ovary and Uteri cancer might be hormone driven cancer. The model can not catch it. But lung cancer might be twisted by increase of cigarette smoking from 1900-1950.Poor fit for the four types of cancer Prostate, Ovary and Uteri cancer might be hormone driven cancer. The model can not catch it. But lung cancer might be twisted by increase of cigarette smoking from 1900-1950.

11. Age distributions of some cancer incidences in U.S. From incidence data(not mortality data) there is a consistent phenomenon that there is an overturn at high age in the incidence curve across many cancers. Data source( Hong Kong, U.S. Netherlands, standing for different pools of genes, culture, environment etc.) From incidence data(not mortality data) there is a consistent phenomenon that there is an overturn at high age in the incidence curve across many cancers. Data source( Hong Kong, U.S. Netherlands, standing for different pools of genes, culture, environment etc.)

12. Pompei and Wilson’s Beta Model (2001) Suppose T is the time to the onset of the first primary tumor Then the age distribution of the certain cancer incidence follows: Where k-1 is the number of mutations, (1-bt) is the overturn factor After observing all the downtrend of the mortality rate, Pompei et al posposed a Beta fitting to catch the decrease at the tail. Basically the Pompei et al model is very similar to N-A model except it adds one component (1-b) in to allow the curve to decease at high age. Interpretation of their model( their defense): some biological results which supports their hypothesis. Downtrend at the tail might also due to competing risk. If possible, only exclusion of major competing risk would back up this hypothesis more. His data is 1989_1995 Netherlands 95+ 1988-1992 Hong Kong 85+ 1988-1993 California 100+ U.S. 1993-1997 85+ data reliability and the data is the actual incidence rate (without competing risk adjustment) After observing all the downtrend of the mortality rate, Pompei et al posposed a Beta fitting to catch the decrease at the tail. Basically the Pompei et al model is very similar to N-A model except it adds one component (1-b) in to allow the curve to decease at high age. Interpretation of their model( their defense): some biological results which supports their hypothesis. Downtrend at the tail might also due to competing risk. If possible, only exclusion of major competing risk would back up this hypothesis more. His data is 1989_1995 Netherlands 95+ 1988-1992 Hong Kong 85+ 1988-1993 California 100+ U.S. 1993-1997 85+ data reliability and the data is the actual incidence rate (without competing risk adjustment)

13. Two-stage Carcinogenesis (MVK) Model (1979) The rise of the first malignant cell is the end point of the event From one single MC to a well developed tumor to death might be model as fix length time or following some distribution such as Gamma. Assumptions of the whole process: inhomogeneous Poisson, birth and death process of IC.The rise of the first malignant cell is the end point of the event From one single MC to a well developed tumor to death might be model as fix length time or following some distribution such as Gamma. Assumptions of the whole process: inhomogeneous Poisson, birth and death process of IC.

14. Mathematical Formula (I) T is a random variable How to find the distribution of T: P.G.F. Approach first studied by Kendall then proposed all most independent by Moolgavkar and Venson in 1979. Ricatti equation. No close form solution for time dependent parameter case.T is a random variable How to find the distribution of T: P.G.F. Approach first studied by Kendall then proposed all most independent by Moolgavkar and Venson in 1979. Ricatti equation. No close form solution for time dependent parameter case.

15. Mathematical Formula (II) Repeat the meaning of each parameters. One parameter increase, the curve can stay the same if we compensate this by increase some other variables. This lead to the identifiable problem. Repeat the meaning of each parameters. One parameter increase, the curve can stay the same if we compensate this by increase some other variables. This lead to the identifiable problem.

16. Properties of parameters in MVK model Among the four parameters, there are only three identifiable using incidence data (Heidenreich 1996). The conventional three combinations of the four parameters: Most of the time, we use this type of three combination because the biological meaning of the new parameters. We can also fix one of the parameter to make the inverse to be one-to-one.Most of the time, we use this type of three combination because the biological meaning of the new parameters. We can also fix one of the parameter to make the inverse to be one-to-one.

17. Parameter Estimation Based on a Simulation Study (I)

18. So far the simulation and all the presentation is about constant parameter case. That is the cancer occurs spontaneously and the all the original parameters are the same in lifetime. The population is homogenous. What makes this model more attractive than the other two is that it can incorporate covariates into the model thus it is possible to study the effects of risk factors. Also this type of incorporation allows us to interpret the impact of those risk factors in more straightforward way. So far the simulation and all the presentation is about constant parameter case. That is the cancer occurs spontaneously and the all the original parameters are the same in lifetime. The population is homogenous. What makes this model more attractive than the other two is that it can incorporate covariates into the model thus it is possible to study the effects of risk factors. Also this type of incorporation allows us to interpret the impact of those risk factors in more straightforward way.

19. The Influence of Smoking and Genetic Susceptibility on Mutation Cancer causes: acquired and inherited Another reason using MVK model when people quick smoking the hazard drop back to normal after years it is consistent with what has been observed in many studies 3. This is the diagram integrate both environmental exposure and genetic component inCancer causes: acquired and inherited Another reason using MVK model when people quick smoking the hazard drop back to normal after years it is consistent with what has been observed in many studies 3. This is the diagram integrate both environmental exposure and genetic component in

20. 1. How to define never, former and current smoker?1. How to define never, former and current smoker?

21. The data comes from M.D. Anderson Cancer center Epidemiology department The data comes from M.D. Anderson Cancer center Epidemiology department

22. Simulation Scenario

23. Experiment Design of Simulation Data If the person smokes, he/she starts smoking from 20 and stops at 70 The levels of smoking intensity: 0, 10, 20/day The mutagen sensitivity is 1 The levels of DNA repair capacity are: 0, 1/3 and 2/3 Gender: Female (0) and Male (1) There are 18 groups Each group contains 250 samples NO censoring

24. Simulation Results: Estimation Based on a Six-Parameter Model 250X 18 groups of data 100 bootstrap 10 initial random runs to find the maximum Model: mu=mu0*(1 + 3*log(ds) + 1.5*mutagen*drc + 0.5*gender); the same for v Data updated on Nov 8, 2003250X 18 groups of data 100 bootstrap 10 initial random runs to find the maximum Model: mu=mu0*(1 + 3*log(ds) + 1.5*mutagen*drc + 0.5*gender); the same for v Data updated on Nov 8, 2003

25. Discussion and Further Work Estimate the impact of cigarette smoking, DRC, mutagen sensitivities and gender on lung tumor development Modeling the downtrend of incidence curve: Competing risk Increased apoptosis and decreased cell divisions at high age Assume the DRC and mutagen sensitivities distribution among population and improve the fitness of incidence curve Waiting for data

26. Acknowledgement Dr. Olga Y Gorlova in Epidemiology Department in M.D. Anderson Cancer Center William Hazelton and E. Georg Luebeck in Fred Hutchinson Research Center This work is partially supported by Keck Trainee Fellowship and NCI CISNET grant

27. References “The age distribution of cancer and a multi-stage theory of carcinogenesis”, British J. of Cancer 1954 by Armitage and Doll. “Stochastic Models of Carcinogenesis.” By Tan, W.Y. 1991 “On the parameters of the Clonal Expansion Model”, Radiat. Environ. Biophy. 1996 by Heidenreich “Some Properties of the Hazard Function of the Two-Mutation Clonal Expansion Model”, Risk Analysis (1997) by Heidenreich, W.F. et al “Age distribution of cancer in mice: the incidence turnover at old age”, Toxicology and Industrial Health 2001 by Pompei and Wilson. “Biologically Based Analysis of the Data for the Colorado Uranium Miners Cohort: Age, Dose and Dose-Rate Effects”, Radiation Research 1999 by Luebeck et al “Genetic Susceptibility to Lung Cancer: The Role of DNA Damage and Repair”, Cancer Epidemiology 2003 by Spitz, M.R. et al. Gorlova et al., 2003, Human Heredity