Comment on Schwartz, J.; Dockery, D.W.; Neas, M.L. 1996. Is daily mortality associated specifically with fine particles?; J. Air Waste Manage. Assoc. 46: 927–939

Dear Editor,

While recently reviewing a manuscript, I was led back to read a 1996 JA&WMA paper entitled, “Is daily mortality associated specifically with fine particles?” (Schwartz et al., 1996). This 19-year-old paper is iconic in the sense it is one of the first papers to apply sophisticated statistical techniques, leading to additional research by the same authors’ team (and other groups) that influenced the current U.S. Environmental Protection Agency (EPA) National Ambient Air Quality Standards (NAAQS) and World Health Organization (WHO) Guidelines, for particulate matter (PM) with an aerodynamic diameter (AD) nominally less than 2.5 μm (PM_2.5) (Laden et al., 2000; Schwartz, 2000; Schwartz, 2003; Zanobetti and Schwartz, 2005; Franklin et al., 2007; Schwartz et al., 2008; Zanobetti et al., 2014). However, I found it had some problematic areas that propagated, but if they are resolved, could further strengthen the team’s conclusions and give stronger support to the upcoming review of the current EPA PM_2.5 NAAQS.

The first problem is that in an approximate 9-year study period, the authors only collected integrated 24-hour PM_2.5 samples daily for part of that period during a subset of intensive health studies, and at least every-other-day for the rest of the study period (Schwartz et al., 1996). In order to increase the PM_2.5 sample size for comparison to the complete daily non-trauma mortality counts for the six monitored metropolitan areas, the authors needed to estimate the missing daily PM_2.5 values. They took the approach (page 930, top of right column) that “mortality was assumed to be associated with the mean of the non-missing particle concentrations on the same and previous day.” They repeated in a following paper (Laden et al., 2000; p. 942, mid-column), “As in our earlier study (1), we assumed that mortality was associated with the 2-day mean of the non-missing particle concentrations on the same and on the previous day.” This calculation of a 2-day mean is correct for every day sampling, and they explained “this had the effect of increasing the number of days included from 8,432 days with PM_2.5 measurements to 12,055 days with PM_2.5 measurements” (Schwartz et al., 1996).

However, this procedure of computing a running 2-day mean appears to be incorrect for every other day sampling. This is because it is equivalent to assuming their missing PM value on a given day-of-death is identical to the non-missing value on the previous day, and on the very next day, assuming that same missing PM value is identical to the non-missing value on that following day-of-death! It is not clear why the authors chose here (and in their related paper, Laden et al., 2000) such an unstable model for imputation of a missing value of PM_2.5 when a simple average of the PM_2.5 the day before and the PM_2.5 the day after the missing day might suffice.

A superior technique for estimating such missing data is to use the maximum likelihood Expectation-Maximization (E-M) algorithm that generates a set of imputed results to fill in the missing data (Mage et al., 1999). This E-M procedure estimates a set of missing-replacement values so that the mean, variance, and correlation structure of the original measured data sequence is identical to the mean, variance, and correlation structure of the completed data sequence that includes replacements for the missing values. If the authors now use this E-M algorithm to re-impute the missing PM mass concentrations (PM_2.5 and PM₁₀), as well as the mass concentrations of each missing PM component (such as sulfate) for each of these six cities, their reanalysis might have stronger support for the team’s conclusions (Schwartz et al., 1996; Laden et al., 2000; Schwartz, 2003).

The second problem noted is on page 930 at the bottom of the left column: “Previous analyses have shown the strongest association of daily mortality with particle concentration on the same day and on the previous day” (Schwartz et al., 1996). Then an author of a following paper wrote: “I then compared the mean of the PM₁₀ concentration on the day of death and the day preceding death to use as my exposure index” (Schwartz, 2000; p. 564, at the top of the left column). Another paper (Franklin et al., 2007) considered using both 0 day lags and 1 day lags for different cities, but fortuitously chose to use only the 1 day lag for consistency. This 0 day lag or same day as death usage appears to possibly violate Sir Bradford Hill’s fourth requirement for establishing causality, that is, “Temporality: Which is the cart and which the horse?” (Hill, 1965).

For example, if EPA’s 12:01 a.m.-to-midnight PM sampling scheme were employed, all persons dying that same day before midnight would have some PM mass collected by the monitor after they died. If 8:01 a.m.-to-8:00 a.m. PM sampling were employed, as for Steubenville, Ohio (Schwartz and Dockery, 1992), all persons dying before 8:00 a.m. in that same period would also have some PM mass collected by the monitor after they died. An anomaly could occur where the authors wrote: “We defined the hazard period—when a person is at risk for the triggering of an acute MI [Myocardial Infarction]—as the day of the patient’s hospitalization…suggesting that airborne particles are acting as a trigger of an MI” (Zanobetti and Schwartz, 2005). All the patients admitted for MI on that day would be associated with some PM that was collected by the monitor after that trigger was pulled and someone called 911. This event could even have been before 12:01 a.m. of the next day when they were admitted, resulting in a completely anomalous day for PM attribution (Mage, 2013). Resolving such temporality problems may also strengthen their conclusions.

A third problem is that the team seems cavalier in their usage (without definition; Mage et al., 1999; Mage, 1985; Mage, 2001) of the terms of PM exposure and PM dosage. On page 930, left column of the 1996 paper, one finds: “For the smooth functions of temperature and dew-point temperature, we chose to use 50% of the data, because we expected the dose-response relation between those variables and mortality to be much smoother.” How does one define a dose of dew-point temperature? In their 2008 paper, “The effect of dose and timing of dose on the association between airborne particles and survival,” they evaluated an ambient concentration-response relationship. But on page 64, the very same paragraph mentions all three: “Concentration-response modeling,” “the piecewise constant model of the exposure,” and “a step function dose-response curve” (Schwartz et al., 2008). They even made dose response their second key word in the abstract. In the abstract of a 2014 paper, they still called an ambient PM_2.5 concentration an ambient PM_2.5 exposure six times (Zanobetti et al., 2014). Correcting such misnomers could make their work more understandable to the informed reader.

A fourth problem arises as the authors assume, with some validity, that a time-averaged ambient PM concentration may be a reasonable (but not exact) proxy for all nearby subject’s time-averaged exposures to ambient PM (Schwartz, 2003; Mage, 2001; Wilson and Suh, 1997). There is an excellent analysis by some of the team authors and others, on PM measurement error and Berkson error (“in which one assumes that the average value of the true exposure (x) to ambient PM within each stratum of measured ambient PM concentration z equals z”) (Zeger et al., 2000). The authors considered how a subject’s health effect from ambient PM is correlated with their time-weighted exposure (X) to ambient PM over period T as X = T ⁻¹∫ x dt. However, the subjects’ health effect is dependent on inhalation rate (v m³/min) - deposition fraction (y) - time-weighted exposure (X) to ambient PM over period T as X = (―VY T)⁻¹∫ (x v y) dt. This is because two subjects with such identical exposure (x) to ambient PM will have different ambient-PM-deposited mg doses because of their quite different inhalation rates and modes (oral, nasal, oronasal—a function of their different ages, genders, and physical activities), and different deposition fractions (a function of their different pulmonary morphologies) (Mage, 1985). The authors could caveat their conclusions accordingly.

In summary, the pulmonary toxicity of an inhaled molecule depends upon its molecular structure, not its molecular weight (Mage, 1983; Mage, 2002). The chemical composition of the dose of airborne particles deposited in the lungs determines the potency of those particles. The same mass deposition of particles does not imply the same health effect because of these composition differences” (Mage, 1983; Mage, 2002). I would suggest that the authors might consider reanalyzing their incomplete daily data sets by imputing the intermediate missing values of mass and composition by using the E-M algorithm. Then, perhaps the team might also consider redefining the independent variable of a daily or two-day average ambient PM concentration as the mean of the ambient PM concentrations on the one or two days immediately preceding the day of MI admission or death, to satisfy the temporality requirement (Hill, 1965).

Sincerely,

David T. Mage, Ph.D.

World Health Organization (WHO; retired);

U.S. Environmental Protection Agency (EPA; retired)

Acknowledgment

I have discussed this letter with some of my friends and former EPA colleagues. I value their comments now as always, and any opinions expressed or errors in fact within this letter are entirely my own.