Are the Mortality Effects of PM 10 the Result of

Inadequate Modeling of Temperature and Seasonality?

Leah WeltyEBEG

February 2, 2004Joint work with Scott Zeger

Is temperature/seasonality to blame?

• Temperature and season are important predictors of mortality

• Temperature and season are associated with air pollution (PM10)

• Seasonal effects > Temperature effects > PM 10 effects

• Previous NMMAPS analyses criticized for potential confounding of air pollution with temperature and seasonal effects

“Beyond controlling for time, of particular interest is the question of how fully to control for the potential effects of weather. […] The current analyses continue to include terms for weather, and the sensitivity analyses have further attempted to make estimates in the absence of extreme weather days (e.g., temperatures above or below a certain point). Smaller estimates of effect result from the newly revised analyses, however, and the possibility of subtler effects of weather within the normal climatic ranges continues. Thus, further exploration of weather effects is merited (for example by considering correlated or cumulative effects of multi-day temperature or humidity).”

-HEI Special Report, May 2003

Further Investigation:

We consider two alternate schemes for modeling temperature and season on mortality

• Part I:

Allow temperature effects to vary by season

• Part II:

Allow for non-linear functions of temperature to affect mortality over longer time periods

Outline

• Intro Distributed Lag Models (DLMs)

• Part I: Seasonality of Temperature Effects– Exploratory Analysis– Potential Model– Results on association of PM 10 and mortality

• Part II: Longer and non-linear DLMs– Potential Models– Results on association of PM 10 and mortality

Distributed Lag Models (DLMs)• Allow response to depend on exposure over several days

• Constrained distributed lags; step function

Example distributed lag functions

‘Total’ Temperature Effect

A one degree increase in temperature over each of the past 14 days increases log expected mortality by

= area under the distributed lag function. And

is approx % increase in mortality for 10 degree increase in temperature over past 14 days.

Distributed Lag Function by Month (New York City)

“Temperature” effects estimated in 4 month periods, 1987 - 2001

Individual Distributed Lag Coefficients by Time (New York City)

DLMs with Time Varying Coefficients

DLMs with Time Varying Coefficients

(covariates: intercept, age category (factor), dow (factor), dom, age by time interaction)

Estimated distributed lag coefficients and time trend (df = 4/yr) (New York City)

Total temp effect & time trend by df in time trend (Chicago)

Combined Temperature and Time Trend Predictors (Chicago)

Model Comparison by df/year in Time Trend (Chicago)

Status Report

• Temperature alone (even with distributed lags with seasonally varying coefficients) cannot explain all of the seasonal variation in mortality

• Models should include a season effect

• Difficult to distinguish practically between temperature and seasonality effects once seasonality is included

Next Step: add PM 10

DLMs with Time Varying Coefficients and PM 10 as a Predictor

(covariates: intercept, age category (factor), dow (factor), dom, age by time interaction)

• Model formulation:

• Consider PM 10 effect for

Estimated PM 10 effects by PM 10 lag, df in smooth of time

(Los Angeles)

Estimated PM 10 effects by city, PM 10 lag, df in smooth of time

Part I: Conclusions

• The slightly bad news– Cannot fully separate temperature effects on

mortality from seasonal effects on mortality

• The good news– Total temperature effects may vary by the degrees

of freedom in the time trend, but pollution effect estimates do not change substantially

Under our step function DLM for temperature with time varying coefficients:

Next step: What if we use other (more flexible) DLMs?

Part II: Non-linear DLMs

PM 10 effect by df, lag of PM 10, and # dist lag vars in model

Part II: Conclusions

• The bad news– There really isn’t any.

• The good news– PM 10 effect estimates do not change substantially by

the number of lag variables in the model, the df for the smoothness of the lags, or by the lag of PM 10.

Continuing Work

• Pooled PM 10 effect estimates for proposed DLMs

• Higher order formulations of DLMs, in particular for modeling interactions in distributed lags for temperature and for pollution

1. Alternate parametric forms

2. Semi-parametric, penalized splines with tapering

3. Bayesian formulation on lags