Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.

Quantification of the smoking-associated cancer risk with rate advancement periods: meta-analysis of individual participant data from cohorts of the CHANCES consortium

BACKGROUND: Smoking is the most important individual risk factor for many cancer sites but its association with breast and prostate cancer is not entirely clear. Rate advancement periods (RAPs) may enhance communication of smoking related risk to the general population. Thus, we estimated RAPs for the association of smoking exposure (smoking status, time since smoking cessation, smoking intensity, and duration) with total and site-specific (lung, breast, colorectal, prostate, gastric, head and neck, and pancreatic) cancer incidence and mortality.

METHODS: This is a meta-analysis of 19 population-based prospective cohort studies with individual participant data for 897,021 European and American adults. For each cohort we calculated hazard ratios (HRs) for the association of smoking exposure with cancer outcomes using Cox regression adjusted for a common set of the most important potential confounding variables. RAPs (in years) were calculated as the ratio of the logarithms of the HRs for a given smoking exposure variable and age. Meta-analyses were employed to summarize cohort-specific HRs and RAPs.

RESULTS: Overall, 140,205 subjects had a first incident cancer, and 53,164 died from cancer, during an average follow-up of 12 years. Current smoking advanced the overall risk of developing and dying from cancer by eight and ten years, respectively, compared with never smokers. The greatest advancements in cancer risk and mortality were seen for lung cancer and the least for breast cancer. Smoking cessation was statistically significantly associated with delays in the risk of cancer development and mortality compared with continued smoking.

CONCLUSIONS: This investigation shows that smoking, even among older adults, considerably advances, and cessation delays, the risk of developing and dying from cancer. These findings may be helpful in more effectively communicating the harmful effects of smoking and the beneficial effect of smoking cessation.