ht_mal_int: Integrating hazard for the onset of th 1st malignant cell
In MILC: MIcrosimulation Lung Cancer (MILC) model

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

Cumulative hazard for the onset of the first malignant cell between two time points (ages).

1	ht_mal_int(lower, upper, g, d, smoking)

`lower`	age (years), lower limit of the integral
`upper`	age (years), upper limit of the integral
`g`	gender ("male", or "female")
`d`	smoking intensity group based on the average number of cigarettes smoked per day
`smoking`	binary variable indicating whether the person was smoking between ages "lower" and "upper" ("Y"=yes, "N"=no)

Integration from age ‘lower’ to age ‘upper’ 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 (see function 'HT_mal' for more details).

The value of the calculated integral, equal to the probability of developing the first malignant cell between ages "lower" and "upper".

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, t_mal

# The following examples calculate the probability of a man, who on average smokes 
# 30 cigarettes per day, to develop the first malignant cell:
ht_mal_int(0, 50, "male", 30, "Y")	# before the age of 50
ht_mal_int(0, 75, "male", 30, "Y")	# before the age of 75
ht_mal_int(45, 75, "male", 30, "Y")	# between the ages of 45 and 75