HT_mal: Calculate cumulative hazard for the 1st malignant cell
In MILC: MIcrosimulation Lung Cancer (MILC) model

Description Usage Arguments Details Value Author(s) References See Also Examples

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

1	HT_mal(t, gender, d, smok_status)

`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")

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{ν μ X (e^{(γ+2B)t}-1)}{γ+B(e^{(γ+2B)t}+1)}

with γ = α - β -μ and B=\frac{1}{2}(-γ + √{γ^2 +4 α μ})

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.:

α = α_0 [1+α_1 \cdot d^{α_2}]

and

γ = γ_0 [1+α_1 \cdot d^{α_2}]

where

X:	total number of normal stem cells
ν:	normal cell initiation rate
α:	division rate of initiated cells
β:	apoptosis rate of initiated cells
μ:	malignant conversion rate of initiated cells
d:	average number of cigarettes smoked per day

Cumulative hazard for the onset of the first malignant cell.

Stavroula A. Chrysanthopoulou

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.

ht_mal_int, t_mal

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# 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")