Considering the potentially nonlinear and lagged associations
between ambient temperature and adverse cardiovascular outcomes,
we used a distributed lag nonlinear model (DLNM) to estimate
the effects of temperature on OHCD mortality. Specifically, to establish a “cross-basis” function of temperature
based on the DLNM, we used a natural cubic spline with 5 df
to account for the nonlinear effect of temperature, and also used a
natural cubic spline with 5 df to account for the lagged effects (lag
space) of temperature. Because it is not easy to
determine the maximum lag of the effects, we alternatively used
multiple lag intervals including days 0e3, 0e7, 0e14 and 0e21. We
then introduced the “cross-basis” matrix of temperature into the
GAM. We further controlled for time trends (7 df per year in natural
functions) and day of the week, as well as the same-day air
pollutant concentrations (PM2.5 and O3). We first flexibly plotted
the relative risks (RRs) of the temperature-mortality association
curves. Then, we calculated the RR comparing the 1st percentile of
temperature to the minimum-mortality temperature (MMT) and
the RR comparing the 99th percentile of temperature to the MMT.
Further, to quantify these effects per an absolute change (1 C) in
temperature, we calculated them as the log-RR divided by the
range from the MMT to the corresponding temperature percentiles. In brief, the cold effect was defined as the percent
increase in daily mortality per 1 C decrease below the MMT, and
the heat effect was defined as the percent increase in daily mortality
per 1 C increase above the MMT.