I was wondering if there is some kind of known relation between the chance of getting cancer and the frequency of smoking cigarettes. A quick Google search did not yield results. Would any of you perchance know of a relation?
There is an approximately linear relationship between the total number of cigarettes a person smokes in their lifetime and the risk of getting lung cancer.
That is, each cigarette someone smokes increases their chance of getting cancer by about the same amount, whether it's their first cigarette or they've been smoking for 40 years.
Pack-years are a way of quantifying someone's total cigarette exposure; it's calculated by the number of packs someone smokes per day times the number of years they've smoked for. So someone who has smoked half a pack per day for 20 years would have a pack-year history of 0.5 * 20 = 10 pack-years.
The following graphs show the linear relationship between the odds of getting lung cancer (relative to non-smokers) versus pack-years smoked.
Source: Lubin and Caporaso (2006), "Cigarette Smoking and Lung Cancer: Modeling Total Exposure and Intensity"