Exposure measurement error in time-series studies of air pollution: concepts and consequences

Misclassification of exposure is a well-recognized inherent limitation of epidemiologic studies of disease and the environment. For many agents of interest, exposures take place over time and in multiple locations; accurately estimating the relevant exposures for an individual participant in epidemiologic studies is often daunting, particularly within the limits set by feasibility, participant burden, and cost. Researchers have taken steps to deal with the consequences of measurement error by limiting the degree of error through a study's design, estimating the degree of error using a nested validation study, and by adjusting for measurement error in statistical analyses. In this paper, we address measurement error in observational studies of air pollution and health. Because measurement error may have substantial implications for interpreting epidemiologic studies on air pollution, particularly the time-series analyses, we developed a systematic conceptual formulation of the problem of measurement error in epidemiologic studies of air pollution and then considered the consequences within this formulation. When possible, we used available relevant data to make simple estimates of measurement error effects. This paper provides an overview of measurement errors in linear regression, distinguishing two extremes of a continuum-Berkson from classical type errors, and the univariate from the multivariate predictor case. We then propose one conceptual framework for the evaluation of measurement errors in the log-linear regression used for time-series studies of particulate air pollution and mortality and identify three main components of error. We present new simple analyses of data on exposures of particulate matter < 10 microm in aerodynamic diameter from the Particle Total Exposure Assessment Methodology Study. Finally, we summarize open questions regarding measurement error and suggest the kind of additional data necessary to address them.

Exposure measurement error in time-series studies of air pollution: concepts and consequences

Misclassification of exposure is a well-recognized inherent limitation of epidemiologic studies of disease and the environment. For many agents of interest, exposures take place over time and in multiple locations; accurately estimating the relevant exposures for an individual participant in epidemiologic studies is often daunting, particularly within the limits set by feasibility, participant burden, and cost. Researchers have taken steps to deal with the consequences of measurement error by limiting the degree of error through a study's design, estimating the degree of error using a nested validation study, and by adjusting for measurement error in statistical analyses. In this paper, we address measurement error in observational studies of air pollution and health. Because measurement error may have substantial implications for interpreting epidemiologic studies on air pollution, particularly the time-series analyses, we developed a systematic conceptual formulation of the problem of measurement error in epidemiologic studies of air pollution and then considered the consequences within this formulation. When possible, we used available relevant data to make simple estimates of measurement error effects. This paper provides an overview of measurement errors in linear regression, distinguishing two extremes of a continuum-Berkson from classical type errors, and the univariate from the multivariate predictor case. We then propose one conceptual framework for the evaluation of measurement errors in the log-linear regression used for time-series studies of particulate air pollution and mortality and identify three main components of error. We present new simple analyses of data on exposures of particulate matter < 10 microm in aerodynamic diameter from the Particle Total Exposure Assessment Methodology Study. Finally, we summarize open questions regarding measurement error and suggest the kind of additional data necessary to address them.

Harvesting-resistant estimates of air pollution effects on mortality

A number of studies have recently shown an association between particle concentrations in outdoor air and daily mortality counts in urban locations. In the public health interpretation of this evidence, a key issue is whether the increased mortality associated with higher pollution levels is restricted to very frail persons for whom life expectancy is short in the absence of pollution. This possibility has been termed the "harvesting hypothesis." We present an approach to estimating the association between pollution and mortality from times series data that is resistant to short-term harvesting. The method is based in the concept that harvesting alone creates associations only at shorter time scales. We use frequency domain log-linear regression to decompose the information about the pollution-mortality association into distinct time scales, and we then create harvesting-resistant estimates by excluding the short-term information that is affected by harvesting. We illustrate the methods with total suspended particles and mortality counts from Philadelphia for 1974-1988. The total suspended particles-mortality association in Philadelphia is inconsistent with the harvesting-only hypothesis, and the harvesting-resistant estimates of the total suspended particles relative risk are actually larger-not smaller-than the ordinary estimates.

Testing simultaneous hypotheses in pharmaceutical trials: a Bayesian approach

The purpose of this paper is to compare the Bayes factor and the likelihood ratio test in a pharmaceutical trial where the two treatments are a new drug and a control (a positive control or a placebo). The goal is to jointly answer the questions (1) is the new drug or the control toxic? (2) Is the new drug more effective and safer than the control? We consider a bivariate model where each treatment is characterized by a target effect (a continuous primary response y) and by a side effect (a continuous supplementary response xi). Using a Bayesian approach, we account for the uncertainty resulting from prediction of the side effect, by making use of the physician's prior inputs about the target-toxicity relationship and the maximum tolerated target effects that are considered to be safe. Finally, we consider an example about a sleeplessness drug, and we show that the Bayes factor provides a more flexible and informative tool than the likelihood ratio test in simultaneous testing. Advantages are greater when the number of experimental subjects is small.