Microenvironment Exposure Weights Can Be Obtained from a Straightforward Statistical Model of Time-Location Data
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B. Rey deCastro1, Alison S. Geyh2, Andres Houseman3, Louise Ryan4, John D. Spengler5 1Westat, Rockville, MD. 2Department of Environmental Health Sciences, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD. 3Department of Work Environment, University of Massachusetts Lowell, Lowell, MA. 4CSIRO Mathematical and Information Sciences, New South Wales, Australia. 5Department of Environmental Health, Harvard School of Public Health, Boston, MA. Collection of time-location data is a common feature of personal exposure studies and is intended to provide a basis for time-weighted exposure averaging. Particular difficulties posed by the outcome -- multiple non-ordered microenvironments -- have precluded routine statistical analysis, but such multinomial outcomes may be modeled within a regression framework using the generalized logit model (or discrete choice model). Conveniently, this model predicts the proportion of subjects in each microenvironment at each time interval, which may be construed most usefully as exposure weights in a formulation of total exposure. This presentation demonstrates application of the generalized logit model to data from a study of schoolchildren (N = 95, 7-11 years old) in southern California who reported their time-location at 30-minute intervals in diaries for 4 days per month for 12 months (June 1995–May 1996; N = 171,000). A generalized logit model of the proportion of subjects in each of five microenvironment -- indoor-home, indoor-school, indoor-other, commuting, outdoors -- shows that while subjects spent substantial time indoor-home, there was substantial variation for other microenvironments at all temporal scales. Consistent with a daily academic schedule, indoor-school time predominates at the 30-minute timescale. Yet, at the day and month timescales most variation is in indoor-other. This suggests that important longer-term exposures may be missed because non-home and non-school indoor microenvironments are not often monitored. The model also found that autocorrelation of microenvironment location was most positively correlated with the previous 30-minute interval and tapered through the preceding 3 hours.
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Microenvironment Exposure Weights Can Be Obtained from a Straightforward Statistical Model of Time-Location Data
- 1. Introduction The Model Results Conclusions Microenvironment Exposure Weights Can Be Obtained from a Straightforward Model of Time-Location Data B. Rey de Castro, Sc.D. Westat Rockville, Maryland USA October 27, 2009 reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 2. Introduction The Model Results Conclusions Outline 1 Introduction Learning Objectives Motivation Time-Weighted Average Exposure Generalized Logit Model 2 The Model 3 Results 4 Conclusions reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 3. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Outline 1 Introduction Learning Objectives Motivation Time-Weighted Average Exposure Generalized Logit Model 2 The Model 3 Results 4 Conclusions reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 4. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Learning Objectives 1 Describe the benefits to total exposure assessment of generalized logit models for obtaining microenvironment exposure weights from time-location data 2 Introduce the generalized logit model within a context of a familiar linear regression framework 3 Demonstrate how the generalized logit model can yield exposure weights from time-location data reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 5. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Motivation Indirect exposure assessment reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 6. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Motivation Indirect exposure assessment Pollutant monitored in each microenvironment reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 7. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Motivation Indirect exposure assessment Pollutant monitored in each microenvironment Amount of time spent in each microenvironment reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 8. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Motivation Indirect exposure assessment Pollutant monitored in each microenvironment Amount of time spent in each microenvironment Structured diaries reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 9. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Time-Weighted Average Exposure t th time interval j th microenvironment T M Exposuretwa = exposure weighttj × concentrationtj t j time exposure weighttj = time tj total reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 10. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Time-Weighted Average Exposure When subjects each contribute the same amount of person-time at each observational interval, the proportion of time spent in a microenvironment is equal to proportion of subjects in a microenvironment timetj exposure weighttj = timetotal subjectstj = subjectstotal = ptj 0 ≤ ptj ≤ 1 reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 11. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Generalized Logit Model Outcome “Which microenvironment are you in and when?” Unordered categories Binary logistic regression Special case (2 categories) Also known as Discrete choice model Multinomial model reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 12. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Generalized Logit Model Regression framework Temporal predictors provide exposure weights Subject-specific predictors P Pr [Yt = j] log = β0j + βpj Xpt , j = 1, 2, 3, . . . , M Pr [Yt = 1] p=1 reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 13. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Generalized Logit Model Predicts probability of being in jth microenvironment at time t 1 Pr [Yt = 1] = P , (ref.j = 1) 1+ p=1 exp(β0j + β1j X1t + . . . + βpj Xpt ) exp(β0j + β1j X1t + . . . + βpj Xpt ) Pr [Yt = j] = P , (j > 1) 1+ p=1 exp(β0j + β1j X1t + . . . + βpj Xpt ) reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 14. Introduction Learning Objectives The Model Motivation Results Time-Weighted Average Exposure Conclusions Generalized Logit Model Time-Weighted Average Exposure Predicted probabilities are time-location exposure weights timetj exposure weighttj = timetotal subjectstj = subjectstotal = ptj exp(β0 j+β1j X1t +...+βpj Xpt ) = 1+ P , (j > 1) p=1 exp(β0j +β1j X1t +...+βpj Xpt ) reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 15. Introduction The Model Results Conclusions Outline 1 Introduction Learning Objectives Motivation Time-Weighted Average Exposure Generalized Logit Model 2 The Model 3 Results 4 Conclusions reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 16. Introduction The Model Results Conclusions Outcome: Microenvironments Harvard Southern California Exposure Study Indoor-home Indoor-school Indoor-other Commuting Outdoors reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 17. Introduction The Model Results Conclusions Subjects 95 children 7- to 11-years-old Sex Age Male Female 7 years 8 9 8 8 12 9 6 9 10 11 13 11 8 11 reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 18. Introduction The Model Results Conclusions Time 12 months June 1995 - May 1996 5 days per month Thursday - Monday 30 thirty-minute intervals per day 600 to 2030 reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 19. Introduction The Model Results Conclusions Data N = 171,000 1,800 longitudinal observations per subject Missing observations Multiple imputation reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 20. Introduction The Model Results Conclusions Outline 1 Introduction Learning Objectives Motivation Time-Weighted Average Exposure Generalized Logit Model 2 The Model 3 Results 4 Conclusions reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 21. Introduction The Model Results Conclusions Generalized Logit Model indoor home indoor school time of day sex day of week age Pr indoor other = + month nonwhite commuting lags 1-6 televisions outdoor reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 22. Introduction The Model Results Conclusions Time-of-Day: Weekday (Thursday, October) 100% Outdoor 90% Commuting 80% Indoor Other Probability [%] 70% 60% Indoor School 50% 40% Indoor Home 30% 20% 00 00 00 10 0 11 0 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0 20 0 0 0 :0 :0 :0 :0 :0 :0 :0 :0 :0 :0 :0 6: 7: 8: 9: Time-of-Day reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 23. Introduction The Model Results Conclusions Time-of-Day: Weekend (Saturday, October) 100% Outdoor 90% Commuting Indoor Other 80% Probability [%] 70% Indoor School 60% 50% Indoor Home 40% 30% 20% 00 00 00 00 0 0 0 0 0 0 0 0 0 0 0 :0 :0 :0 :0 :0 :0 :0 :0 :0 :0 :0 6: 7: 8: 9: 10 11 12 13 14 15 16 17 18 19 20 Time-of-Day reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 24. Introduction The Model Results Conclusions Day-of-Week: Midday (1100, October) 100% Outdoor 90% Commuting 80% Indoor Other Probability [%] 70% 60% Indoor School 50% 40% Indoor Home 30% 20% Thursday Friday Saturday Sunday Monday Day reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 25. Introduction The Model Results Conclusions Month: Midday (1100, Thursday) 100% Outdoor 90% Commuting 80% Indoor Probability [%] 70% Other 60% Indoor School 50% 40% 30% Indoor Home 20% Jun- Jul- Aug- Sep- Oct- Nov- Dec- Jan- Feb- Mar- Apr- May- 95 95 95 95 95 95 95 96 96 96 96 96 Month reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 26. Introduction The Model Results Conclusions Parameters: Treemap Visualization reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 27. Introduction The Model Results Conclusions Autocorrelation Maximum at previous 30-minute interval Tapers through previous 3 hours reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 28. Introduction The Model Results Conclusions Subject-specific Predictors Homes ≥ 5 televisions 21 percent less time outdoors Nonwhites 21 percent less time indoor-school 18 percent less time commuting reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 29. Introduction The Model Results Conclusions Outline 1 Introduction Learning Objectives Motivation Time-Weighted Average Exposure Generalized Logit Model 2 The Model 3 Results 4 Conclusions reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 30. Introduction The Model Results Conclusions Conclusions 1 Most time spent indoor-home reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 31. Introduction The Model Results Conclusions Conclusions 1 Most time spent indoor-home 2 Yet, there was substantial variation in time-location that differentiated exposure reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 32. Introduction The Model Results Conclusions Conclusions 1 Most time spent indoor-home 2 Yet, there was substantial variation in time-location that differentiated exposure 3 Influence of school schedule was clearly evident reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 33. Introduction The Model Results Conclusions Conclusions 1 Most time spent indoor-home 2 Yet, there was substantial variation in time-location that differentiated exposure 3 Influence of school schedule was clearly evident 4 Most time exchanged between indoor-home, indoor-school, and outdoors reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 34. Introduction The Model Results Conclusions Conclusions 1 Most time spent indoor-home 2 Yet, there was substantial variation in time-location that differentiated exposure 3 Influence of school schedule was clearly evident 4 Most time exchanged between indoor-home, indoor-school, and outdoors 5 Temporal factors strongest predictor of time-location reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 35. Introduction The Model Results Conclusions Conclusions 1 Most time spent indoor-home 2 Yet, there was substantial variation in time-location that differentiated exposure 3 Influence of school schedule was clearly evident 4 Most time exchanged between indoor-home, indoor-school, and outdoors 5 Temporal factors strongest predictor of time-location 6 To a lesser degree, television viewing & race predicted time-location reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 36. Introduction The Model Results Conclusions Conclusions 1 Most time spent indoor-home 2 Yet, there was substantial variation in time-location that differentiated exposure 3 Influence of school schedule was clearly evident 4 Most time exchanged between indoor-home, indoor-school, and outdoors 5 Temporal factors strongest predictor of time-location 6 To a lesser degree, television viewing & race predicted time-location 7 Autocorrelation was statistically significant reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 37. Introduction The Model Results Conclusions Learning Questions 1 Why is the generalized logit model useful and how is it related to other regression models? 2 How do you estimate total time-weighted exposure from the generalized logit model’s predicted proportion of subjects in each microenvironment at each time interval? reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 38. Introduction The Model Results Conclusions Next Steps Microenvironment exposure weights Microenvironment pollutant concentrations Estimate total exposures Another manuscript Longitudinal effect of temperature & precipitation? reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009
- 39. Introduction The Model Results Conclusions Acknowledgements Alison S. Geyh Louise Ryan Andres Houseman John D. Spengler Battelle-EPA grant On SlideShare: http://cli.gs/LAO3diary reyDecastro@westat.com 240-453-2947 reyDecastro@westat.com Exposure Weights & Time-Location @ NEPHC 2009