Estimating the Fraction of Disease Caused by One Component of a Complex Mixture: Bounds for Lung Cancer

Lung cancer illustrates many of the challenges of modeling cause and effect in very complex systems having only poorly understood causal mechanisms. When not enough is known to develop useful marginal and conditional probability distributions for uncertain quantities, it may be practical instead to develop bounds on uncertain quantities and causal relations. This chapter illustrates bounding for lung cancer risks. Other areas of quantitative modeling and operations research, from robust optimization to constraint logic programming, apply a similar insight: It is often practical to use limited available data to develop bounds on the likely consequences of actions, even if the data are not adequate to estimate informative, well-calibrated, probabilities for consequences. This chapter and Chapter 9 discuss risk bounds for uncertain complex systems. To illustrate how to develop bounds from data, we quantify bounds on preventable disease risks for two very different illnesses – lung cancer and penicillin-resistant bacterial infections, respectively.