[R] mgcv: relative risk from GAM with distributed lag

[Simon Wood]

On 21/07/2022 15:19, jade.shodan--- via R-help wrote:
> 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".

- You are on the log scale so I think that all you need to do is to use 
'predict.gam', with 'type = "terms"' to  get the predictions for the 
te(temp, lag) term over the required grid of lags and temperatures. 
Suppose the dataframe of prediction data is 'pd'. Now produce pd0, which 
is identical to pd, except that the temperatures are all set to the 
reference temperature. Use predict.gam to predict te(temp,lag) from pd0. 
Now the exponential of the difference between the first and second 
predictions is the required RR, which you can plot using 'persp', 
'contour', 'image' or whatever. If you need credible intervals see pages 
341-343 of my 'GAMs: An intro with R' book (2nd ed).

> 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 guess this only makes sense if you have the same temperature at all 
lags. So this time produce a data.frame with each desired temperature 
repeated for each lag: 'pd1'. Again use predict.gam(...,type="terms"). 
Then sum the predictions over lags for each temperature, subtract the 
minimum, and take the exponential. Same as above for CIs.

best,

Simon

> 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 using googlemail.com
> <jade.shodan using 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
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-- 
Simon Wood, School of Mathematics, University of Edinburgh,
https://www.maths.ed.ac.uk/~swood34/