Multi-site Time Series Analysis

Transcription

1 Multi-site Tie Series Analysis Exposure Lag SAMSI Spatial Epideiology Fall 2009 Howard Chang 1

2 Distributed Lag Model Toxicological evidence suggests the effects of exposure ay be seen over several subsequent days. Selecting a single best fitting lag can result in inconsistencies across studies. Differences in lag structure can also be observed across cities. Not every one in the population is affected by the pollution siilarly and interpretation of the exposure-response curve is difficult. Daily pollution level are often highly correlated. An alternative approach is to us a ulti-day oving average (2 or 3 days). However, any pollutants are not easured daily. 2

3 Distributed Lag (DL) Model Key Idea The rate of an adverse outcoe can be viewed as an accuulation over the previous L days: logµ t = lognt + α+ β0xt + β1xt βlxt L+ confounders We can define an overall (cuulative) effect as β = β + β Other interpretation: (1) arginal effect of a unit increase in a weighted average pollution variable. (2) percentage increase in ortality associated with a one unit increase in air pollution on each of the previous days. The above refers to the unconstrained DL odel. Unbiased but, due to collinearity, this overall effect ay be poorly estiated. β L 3

4 4 Structured DL Model Assue the shape of the lag structure is a polynoial (Schwartz 2000). For exaple, a polynoial with degree K, coefficient at lag has the for: Too uch constraint can introduce bias. A single-day exposure odel is a very restrictive DL odel. = = K k k k 0 η β = = = = = = = K k t L k k L t K k k k t L x x x η η β

5 Structured DL Model Exaple PM 10 and daily ortality across 10 European cities Distributed lag fitted over 40 days Lag 1 Unconst. DL DL (K=4) Zanobetti, A., Schwartz, J., Saoli, E., Gryparis, A., Touloui, G., Peacock, J., Anderson, R. H., LeTertre, A., Bobros, J., Celko, M., Goren, A., Forsberg, B., Michelozzi, P., Rabczenko, D., Hoyos, S. P., Wichann, H. E., and Katsouyanni K. (2003). The teporal pattern of respiratory and heart disease ortality in response to air pollution. Environental Health Perspectives 111,

6 Structured DL Model Exaple Mortality due to cardiovascular diseases Zanobetti, A., Schwartz, J., Saoli, E., Gryparis, A., Touloui, G., Peacock, J., Anderson, R. H., LeTertre, A., Bobros, J., Celko, M., Goren, A., Forsberg, B., Michelozzi, P., Rabczenko, D., Hoyos, S. P., Wichann, H. E., and Katsouyanni K. (2003). The teporal pattern of respiratory and heart disease ortality in response to air pollution. Environental Health Perspectives 111,

7 Structured DL Model Exaple Mortality due to respiratory diseases Zanobetti, A., Schwartz, J., Saoli, E., Gryparis, A., Touloui, G., Peacock, J., Anderson, R. H., LeTertre, A., Bobros, J., Celko, M., Goren, A., Forsberg, B., Michelozzi, P., Rabczenko, D., Hoyos, S. P., Wichann, H. E., and Katsouyanni K. (2003). The teporal pattern of respiratory and heart disease ortality in response to air pollution. Environental Health Perspectives 111,

8 Structured DL Model Exaple Biological evidence supports that the effects of PM on cardiovascular syste are ore acute. For respiratory responses (such as pneuonia and chronic disorder), the progression ight be slower. Single day analysis is likely to under-estiate the overall effect of air pollution. Many studies observed siilar tapering behavior of the lag function. Zanobetti, A., Schwartz, J., Saoli, E., Gryparis, A., Touloui, G., Peacock, J., Anderson, R. H., LeTertre, A., Bobros, J., Celko, M., Goren, A., Forsberg, B., Michelozzi, P., Rabczenko, D., Hoyos, S. P., Wichann, H. E., and Katsouyanni K. (2003). The teporal pattern of respiratory and heart disease ortality in response to air pollution. Environental Health Perspectives 111,

9 Mortality Displaceent How uch (days ~ years) of life is lost due to air pollution? Bell, M., Saet, J., and Doinici, F. (2004b), \Tie-Series Studies of Particulate Matter, Annual Review of Public Health, 25,

10 Mortality Displaceent Hypothesis Harvesting Are the people who died attributable to air pollution would have died in a few days anyway? In this case, the public health ipact is less considerable. If the pool of at-risk (frail) population is being harvested by short ter exposure, we would expect: (1) Positive association at short tie scale (2) Negative (protective) association at longer tie scale until the frail population replenishes. 10

11 Mortality Displaceent Zanobetti and others (2002) Conducted a ulti-city analysis fro the APHEA-2 project to assess ortality displaceent using distributed lag odel. Polynoial DL odel was fitted at each city. The city-specific vector of coefficients were assued Norally distributed and pooled via axiu likelihood ethod. Copared to using an average exposure of current and previous day, cuulative risks due to PM 10 alost doubled across cities. Zanobetti A, Schwartz J, Saoli E, Gryparis A, Touloui G, et al The teporal pattern of ortality responses to air pollution: a ulticity assessent of ortality displaceent. Epideiology 13:

12 Mortality Displaceent Mortality and PM 10 across 10 European cities Zanobetti A, Schwartz J, Saoli E, Gryparis A, Touloui G, et al The teporal pattern of ortality responses to air pollution: a ulticity assessent of ortality displaceent. Epideiology 13:

13 Bayesian Multi-site DL Model Goal Constrain the DL coefficients and cobine inforation across counties. Priors: Constraint across lags through correlations National average lag function Peng RD, Doinici F, Welty LJ (2009). "A Bayesian hierarchical distributed lag odel for estiating the tie course of hospitalization risk associated with particulate atter air pollution," Journal of the Royal Statistical Society, Series C, 58 (1),

14 Bayesian Multi-site DL Model Saller heterogeneity at longer lags across sites: High correlation between neighboring large lags: Siilar correlation structure for the national average: Effects at larger lags are closer to zero Peng RD, Doinici F, Welty LJ (2009). "A Bayesian hierarchical distributed lag odel for estiating the tie course of hospitalization risk associated with particulate atter air pollution," Journal of the Royal Statistical Society, Series C, 58 (1),

15 Bayesian Multi-site DL Model National average lag function up to 14 days across 94 counties Peng RD, Doinici F, Welty LJ (2009). "A Bayesian hierarchical distributed lag odel for estiating the tie course of hospitalization risk associated with particulate atter air pollution," Journal of the Royal Statistical Society, Series C, 58 (1),

16 Bayesian Multi-site DL Model Posterior distributions of paraeters that control the soothness of the national average estiates Peng RD, Doinici F, Welty LJ (2009). "A Bayesian hierarchical distributed lag odel for estiating the tie course of hospitalization risk associated with particulate atter air pollution," Journal of the Royal Statistical Society, Series C, 58 (1),

17 Bayesian Multi-site DL Model County-specific estiates for ischeic heart disease Peng RD, Doinici F, Welty LJ (2009). "A Bayesian hierarchical distributed lag odel for estiating the tie course of hospitalization risk associated with particulate atter air pollution," Journal of the Royal Statistical Society, Series C, 58 (1),

18 Bayesian Multi-site DL Model Regional differences: North versus South Peng RD, Doinici F, Welty LJ (2009). "A Bayesian hierarchical distributed lag odel for estiating the tie course of hospitalization risk associated with particulate atter air pollution," Journal of the Royal Statistical Society, Series C, 58 (1),