MILC (version 1.0)

HT_mal: Calculate cumulative hazard for the 1st malignant cell

Description

Cumulative hazard up to age t for the onset of first malignant cell, given gender, smoking status and smoking intensity.

Usage

HT_mal(t, gender, d, smok_status)

Arguments

t

age

gender

gender ("male", or "female")

d

smoking instensity (number of cigarettes)

smok_status

whether the individual is a smoker ("Y") or not ("N")

Value

• Cumulative hazard for the onset of the first malignant cell.

Details

Integration from age 0 to age t of the hazard rate h(t) for the onset of the first malignant cell, as described by the Two-Stage Clonal Expansion (TSCE) carcinogenesis model: $$h(t) = \frac{\nu \mu X (e^{(\gamma+2B)t}-1)}{\gamma+B(e^{(\gamma+2B)t}+1)}$$ with $\gamma = \alpha - \beta -\mu$ and B=$\frac{1}{2}(-\gamma + \sqrt{\gamma^2 +4 \alpha \mu})$ Power laws express the effect of smoking on the hazard for the onset of the first malignant cell, given smoking intensity d at age t, i.e.: rcl{ $\alpha = \alpha_0 [1+\alpha_1 \cdot d^{\alpha_2}]$ and $\gamma = \gamma_0 [1+\alpha_1 \cdot d^{\alpha_2}]$ } where rl{ X: total number of normal stem cells $\nu$: normal cell initiation rate $\alpha$: division rate of initiated cells $\beta$: apoptosis rate of initiated cells $\mu$: malignant conversion rate of initiated cells d: average number of cigarettes smoked per day }

References

Moolgavkar, S. H., and Luebeck, G. (1990) Two-event model for carcinogenesis: Biological, mathematical, and statistical considerations. Risk Analysis, 10(2):323-341. Heidenreich, W. F., Luebeck, E. G. and Moolgavkar, S. H. (1997) Some properties of the hazard function of the two-mutation clonal expansion model. Risk Analysis, 17(3):391-399. Hazelton, W. D., Clements, M. S. and Moolgavkar, S. H. (2005) Multistage carcinogenesis and lung cancer mortality in three cohorts. Cancer Epidemiology Biomarkers & Prevention, 14(5):1171-1181. Hazelton, W. D., Luebeck, E. G., Heidenreich, W. E. and Moolgavkar, S. H.(2001) Analysis of a historical cohort of chinese tin miners with arsenic, radon, cigarette smoke, and pipe smoke exposures using the biologically based two-stage clonal expansion model. Radiation Research, 156(1):78-94. Meza, R., Hazelton, W. D., Colditz, G. A. and Moolgavkar, S. H. (2008) Analysis of lung cancer incidence in the nurses' health and the health professionals' follow-up studies using a multistage carcinogenesis model. Cancer Causes & Control, 19(3):317-328.

See Also

ht_mal_int, t_mal

Examples

# Cumulative hazard of the onset of the first malingant cell for a man, 50 years old, 
# who smokes 15 cigarettes per day on average.
HT_mal(50, "male", 15, "Y")