EHS 655 Lecture 16 Exposure variability and modeling

EHS 655 Lecture 16: Exposure variability and modeling

What we’ll cover today o Probabilistic (e. g. , Monte Carlo) analysis n o Beyond this class, but we’ll discuss a bit Poisson regression (very briefly) n Beyond this class, but we’ll discuss a bit 2

Probabilistic analysis o More computationally challenging than deterministic models (e. g. , regression models we have explored) o Provides ability to consider n n Population distributions Sources and magnitude of uncertainty 3

Types of probabilistic analysis o One-dimensional n o Two-dimensional n o Variability among individual exposures or uncertainty around single exposure metric Estimate variability and uncertainty around population distribution Monte Carlo simulation approach often used n n n Draws randomly from defined distributions Repeat this over and over to create new distribution Need specialized software 4

Example probabilistic approach – component distributions What goes into dose estimate for ingested chemicals? Intake rate Concentration Body weight Exposure frequency Adgate, Ramachandran, 2007 5

How Monte Carlo analysis works 6

Monte Carlo analysis o Back to uncertainty and variability o Uncertainty n n Lack of knowledge about specific factors, parameters, models Includes parameter uncertainty (measurement errors, sampling errors, systematic errors) Includes model uncertainty (uncertainty due to necessary simplification of real-world, mis-specification of model structure, model misuse, inappropriate surrogate variables) Includes scenario uncertainty (descriptive errors, aggregation errors, errors in professional judgment, incomplete analysis) 7

Monte Carlo analysis o Variability n n n Observed differences attributable to true heterogeneity or diversity in population or exposure parameter. Result of natural random processes and environmental, lifestyle, and genetic differences among humans Usually not reducible by further measurement or study (but can be better characterized) 8

Monte Carlo analysis o Possible to do in Stata, but cumbersome n o http: //blog. stata. com/2015/10/06/monte-carlo-simulationsusing-stata/ Specialized software available, e. g. n n n Crystal Ball @RISK Risk Solver 9

Probabilistic analysis results Adgate, Ramachandran, 2007 10

Probabilistic analysis results Smith, 1994 11

Probabilistic models Finley BL, Paustenbach DJ. 1994

Poisson regression o Response variable is a count o Don’t have count data in our dataset, but if we did, could ask things like: n n n What is the expected number of peak exposures over 140 d. BA given their job title? What is the expected number of TWAs >85 person given their construction site type Etc 14

Poisson regression o Independent variable(s) can be continuous or categorical Stata: poisson depvar indepvar, cluster(idvar) irr to account for clustering by subject IRR = incident rate ratio, rate at which count events occur Stata: mepoisson depvar indepvar || idvar: , irr to run a full random effects model 15

Resources o Monte Carlo simulation software n n o EPA Guiding Principles for Monte Carlo Analysis n o http: //www. lumina. com/technology/monte-carlo-simulationsoftware/ http: //www. oracle. com/us/products/applications/crystalball /overview/index. html https: //www. epa. gov/sites/production/files/201411/documents/montecar. pdf Poisson regression n http: //stats. idre. ucla. edu/stata/output/poisson-regression/ 16