Methods and Description

Note: This page is a work in progress!

Overview

This package contains functions that streamline an analytical pipepline for estimating relative risks and attributable numbers.

Although situated in the contenxt of climate change and city-level health impacts, there are not any physical limitations on applying this code to other signals and responses.

This package is drawn heavily from the work of Dr. Antonio Gasparrini.

Chad Milando, PhD (cmilando[at]bu.edu); Alexis Arlak (aarlak[at]bu.edu); Gregory Wellenius, ScD (wellenius[at]bu.edu). The Center for Climate and Health, Boston University School of Public Health.

Exposures

We applied a distributed lag non-linear modeling (DLNM) framework to capture both the non-linear and lagged effects of temperature exposure. Gasparrini 2011 describes these methods, and the R package dlnm.

This approach represents exposure as a crossbasis matrix with separate components for exposure magnitude and lag. The interpretation of the crossbasis matrix is that it allows the model to account for nonlinear associations in exposure and in time. For example, temperatures of 100 °F do not have double the impact of temperatures of 50 °F, and exposures 2 days prior impact populations differently than those 1 day prior or 3 days prior.

Turning a single exposure time-series into a crossbasis matrix is done via the crossbasis() function as part of dlnm and users must specify several function arguments:

• maxlag, the maximum lag
• arvagr, the nature of the non-linear relationship with exposure magnitude
• arglag, the nature of the non-linear relationship with exposure timing

More details on how to specify maxlag, arglag, and argvar can be found in the dlnm documentation.

For cityClimateHealth we chose some default values for these arguments, specifically for the case study of looking at warm-season temperature and mortality/morbidity:

• maxlag = 5
• argvar: natural spline with knots at the 50th and 90th percentiles of the exposure distribution.
• arglag: a natural spline with two evenly spaced log-knots between 0 and a maximum lag of 8 days.

If other exposures / timings are desired, the user will need to adjust these arguments accordingly.

Outcome

Any time-series of outcomes will work.

Timing

You can use a variety of timings: * daily * weekly * monthly

Model types

We can perform exposure-outcome analyses several ways:

• space-time stratified case-crossover – time is controlled by assigning a strata variable and comparing counts (or rates) of outcomes within strata. a common strata choice is [spatial unit]:[year]:[month]:[day of week]. The following model types can be used in this study design:

  • Conditional logistic
  • Poisson
  • Conditional Poisson

  Gasparrini and Armstrong provide analysis that show that these provide the same results, although Conditional Poisson is more computationally efficient because the strata terms are conditioned out and not modeled.

• time-series – time is controlled by a natural spline with a specific number of knots for year, day of year, season, and decade. additional control is added by a categorical variable for day of week. The common choices for splines knots in this case are: XYZ, see ref

Conditional logistic

See Darren’s paper. we are working to implement this code.

Code examples includee: *

Conditional Poisson

We used a time-stratified case-crossover study design, specifically a single-stage conditional quasi-Poisson model with strata defined by ZIP Code Tabulation Area (ZCTA), year, month, and day of week.

The conditional Poisson approach enables efficient estimation of model coefficients without requiring estimation of strata-specific intercepts.

At the strata level, the model takes the form: log(yₛ,ᵢ) = αₛ + βwₛ,ᵢ + holiday. Here, the daily count of emergency department visits (yₛ,ᵢ) depends on a strata-specific intercept (αₛ), which is calculated in post-processing due to the conditional Poisson formulation, crossbasis weights (wₛ,ᵢ), and an indicator for federal holidays.

Strata with no outcomes are excluded

There are minimums that each strata must include: * x

Code examples includee: *

Time-series

we are working to implement this code.

Code examples includee: *

Model structures

1-stage

A single-stage model pools statistical coefficients across all strata, while the quasi-Poisson formulation adjusts variance to account for over-dispersion in the observed outcome.

Code examples includee: *

2-stage

[…]

Code examples includee: *

Spatial Bayesian methods

[…]

Attributable numbers

After fitting the model, we calculated the number of emergency department visits attributable to high ambient summertime temperatures for each year. This requires defining a reference temperature, which serves as the baseline for comparison. We selected 75°F as the reference, corresponding to the average summertime daily maximum temperature.

The attributable number represents the additional health impacts occurring when temperatures exceed this baseline. In practical terms, it reflects the potentially avoidable emergency department visits that could be prevented if risks on very hot days were reduced to those observed on an average summer day.

For example, using 75°F as the reference, if a day reaches 100°F and is associated with 1,000 additional emergency department visits, this means that compared to a 75°F day, there were 1,000 excess visits at 100°F. Changing the reference temperature (for example, to 80°F or 70°F) would change the estimated attributable number accordingly.

Code examples includee: *