[R] mgcv: beta coefficient and 95%CI

[clc]

In one of the papers...

We developed core models with a generalized additive Poisson regression
allowing for over-dispersion in the model (Wood, 2006). For each mortality
outcome, variations in seasonality, trends, mean temperature, and mean
humidity of current and previous days (lag 0–1) were fitted with penalized
cubic regression splines. Dummy variables were used to control the
variations for days of the week, holidays, and influenza epidemics. We added
a dummy variable for the 2003 severe acute respiratory syndrome (SARS)
epidemic. We chose 4 degrees of freedom (df) per year for smoothing function
of the trends and 3 df for temperature and humidity. The choice of df for
each smoothing function in the core models was made on the basis of observed
residual autocorrelations using partial autocorrelation function (PACF). For
the core models fitted to the mortality data, time variant confounding
factors were considered as adequately controlled if absolute values of PACF
coefficients were <0.1 for the first two lag days and there were no
systematic patterns in the PACF plots.

Following the construction of an adequate core model for each mortality
outcome, we entered visibility as a linear term into the regression model
and examined the effects of visibility on mortality for single day lags 0–5
days, lag 0–1, and distributed lag 0–4 days ([Schwartz, 2000] and [Zanobetti
et al., 2000]). The distributed lag effect take into account the possibility
that visibility can affect deaths occurring on the same day and on several
subsequent days. The net effect of visibility was the sum of the effect
estimates for all six days. We expressed the effect of visibility as the
percentage change in daily mortality with a decrease in the interquartile
range (IQR) of visibility as 100%×IQR×β, where β is the estimated Poisson
regression coefficient, and referred to as the excess risk (ER%).



in one of the figures, they reported "Estimated excess risks (ER%) for daily
mortality and associated 95% confidence intervals per interquartile range
decrease in visibility (6.5 km) at single lags 0–5, mean lag 0–1 (0–1) and
distributed lag (DL) for lag 0–4 days"


What do they mean??! Thanks a lot!
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