Hi there,
I'm running a time-series estimating the effect of air pollution on mortality and I had a question. In my model below, I'm using a spline term for the exposure (2-day moving avg PM2.5 exposure), and while the output is excellent, I'm not sure how to get the relative risk for increases of specific exposure increments (e.g. 10 units). Is this something I need to do using just a linear term for the exposure in the below model and run the spline term just to understand the dose-response? Any help is appreciated.
MODEL:
mod1<-gam(deaths ~ s(time,bs = "cr",fx=TRUE,k=39)+s(PM2days, bs="cr", fx=FALSE) + s(temp5days,bs = "cr",fx=FALSE)+as.factor(dow)+
s(rh,bs = "cr",fx=FALSE), family=quasipoisson, method="REML", data=data, na.action=na.omit)
summary(mod1)
mod1 <- getViz(mod1)
print(plot(mod1, allTerms = TRUE), pages = 2)
--
Output:
Family: quasipoisson
Link function: log
Formula:
deaths ~ s(time, bs = "cr", fx = TRUE, k = 39) + s(PM2days,
bs = "cr", fx = FALSE) + s(temp5days, bs = "cr",
fx = FALSE) + as.factor(dow) + s(rh, bs = "cr", fx = FALSE)
Parametric coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.8951311 0.0057329 1028.303 <2e-16 ***
as.factor(dow)Monday 0.0116073 0.0080437 1.443 0.149
as.factor(dow)Saturday -0.0019533 0.0080751 -0.242 0.809
as.factor(dow)Sunday -0.0119049 0.0080681 -1.476 0.140
as.factor(dow)Thursday 0.0003424 0.0080594 0.042 0.966
as.factor(dow)Tuesday 0.0124738 0.0080536 1.549 0.122
as.factor(dow)Wednesday -0.0123867 0.0080803 -1.533 0.125
Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1
Approximate significance of smooth terms:
edf Ref.df F p-value
s(time) 38.000 38.000 87.649 <2e-16 ***
s(PM2days) 3.533 4.195 2.881 0.0227 *
s(temp5days) 7.392 8.270 19.941 <2e-16 ***
s(rh) 4.723 5.743 40.525 <2e-16 ***
Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1
R-sq.(adj) = 0.691 Deviance explained = 69.6%
-REML = 2974.3 Scale est. = 3.9946 n = 2359
DATA:
A tibble: 6 x 26
Groups: Death_date [6]
Death_date deaths PM2.5 temp rh dow month monthfac year season PM2.5_lag1 PM2.5_lag2 PM2.5_lag3 PM2.5_lag4 PM2.5_lag5 temp_lag1
1 2010-06-01 122 84.9 41.5 15.6 Tues~ 6 Jun 2010 Summer NA NA NA NA NA NA
2 2010-06-02 100 108. 36.7 26.4 Wedn~ 6 Jun 2010 Summer 84.9 NA NA NA NA 41.5
3 2010-06-03 100 166. 34.0 38.2 Thur~ 6 Jun 2010 Summer 108. 84.9 NA NA NA 36.7
4 2010-06-04 93 79.1 33.3 42.6 Frid~ 6 Jun 2010 Summer 166. 108. 84.9 NA NA 34.0
5 2010-06-05 140 137. 33.4 39.8 Satu~ 6 Jun 2010 Summer 79.1 166. 108. 84.9 NA 33.3
6 2010-06-06 158 98.2 31.4 53.1 Sund~ 6 Jun 2010 Summer 137. 79.1 166. 108. 84.9 33.4