mgcv: relative risk from GAM with distributed lag

Hello everyone (incl. Simon Wood?),

I'm not sure that my original question (see below, including
reproducible example) was as clear as it could have been. To clarify,
what I would to like to get is:

1) a perspective plot of temperature x lag x relative risk.  I know
how to use plot.gam and vis.gam but don't know how to get plots on the
relative risk scale as opposed to  "response" or "link".

2) a plot of relative risk (accumulated across all lags) vs
temperature, given a reference temperature. An example of such a plot
can be found in figure 2 (bottom) of this paper by Gasparrini et al:
https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.3940

I've seen Simon Wood's response to a related issue here:
https://stat.ethz.ch/pipermail/r-help/2012-May/314387.html
However, I'm not sure how to apply this to time series data with
distributed lag, to get the above mentioned figures.

Would be really grateful for suggestions!

Jade

On Tue, 19 Jul 2022 at 16:07, jade.shodan at googlemail.com
<jade.shodan at googlemail.com> wrote:

Dear list members,

Does anyone know how to obtain a relative risk/ risk ratio from a GAM
with a distributed lag model implemented in mgcv? I have a GAM
predicting daily deaths from time series data consisting of daily
temperature, humidity and rainfall. The GAM includes a distributed lag
model because deaths may occur over several days following a high heat
day.

What I'd like to do is compute (and plot) the relative risk
(accumulated across all lags) for a given temperature vs the
temperature at which the risk is lowest, with corresponding confidence
intervals. I am aware of the predict.gam function but am not sure if
and how it should be used in this case. (Additionally, I'd also like
to plot the relative risk for different lags separately).

I apologise if this seems trivial to some. (Actually, I hope it is,
because that might mean I get a solution!) I've been looking for
examples on how to do this, but found nothing so far. Suggestions
would be very much appreciated!

Below is a reproducible example with the GAM:

library(mgcv)
set.seed(3) # make reproducible example
simdat <- gamSim(1,400) # simulate data
g <- exp(simdat$f/5)
simdat$y <- rnbinom(g,size=3,mu=g)  # negative binomial response var
simdat$time <- 1:400  # create time series
names(simdat) <- c("deaths", "temp", "humidity", "rain", "x3", "f",
"f0", "f1", "f2", "f3", "time")

# lag function based on Simon Wood (book 2017, p.349 and gamair
package documentation p.54
# https://cran.rstudio.com/web/packages/gamair/gamair.pdf)
lagard <- function(x,n.lag=7) {
n <- length(x); X <- matrix(NA,n,n.lag)
for (i in 1:n.lag) X[i:n,i] <- x[i:n-i+1]
X
}

# set up lag, temp, rain and humidity as 7-column matrices
# to create lagged variables - based on Simon Wood's example
dat <- list(lag=matrix(0:6,nrow(simdat),7,byrow=TRUE),
deaths=simdat$deaths, time = simdat$time)
dat$temp <- lagard(simdat$temp)
dat$rain <- lagard(simdat$rain)
dat$humidity <- lagard(simdat$humidity)

mod <- gam(deaths~s(time, k=70) + te(temp, lag, k=c(12, 4)) +
te(humidity, lag, k=c(12, 4)) + te(rain, lag, k=c(12, 4)), data = dat,
family = nb, method = 'REML', select = TRUE)

summary(mod)
plot(mod, scheme = 1)
plot(mod, scheme = 2)

Thanks for any suggestions you may have,

Jade