Author Michael Jerrett and nine co-investigators and four student or post-doctoral investigators prepared the report “Spatiotemporal Analysis of Air Pollution and Mortality in California Based on the American Cancer Society Cohort” prepared under Contract #06-332 of State of California Air Resources Board Research Division.
The purpose of Jerrett was to investigate the relationship between particulate air pollution, stated as PM2.5, and mortality in the State of California.
On p. 6 it is stated, “All-cause mortality is significantly associated with PM2.5 exposure, but the results are sensitive to statistical model specification and to the exposure model used to generate the estimates” They derive an estimate of 1.08 hazard ratio, with a classical confidence interval between 1.00 and 1.15. They also claim that the risk associated with death due to cardiovascular disease (CVD) and PM2.5 is significant. The risk of PM2.5 with other causes of death they claim are insignificant.
There are three main criticisms that cast grave doubt about the conclusions of Jerret. I find further that the summary in the abstract—and therefore the only part of the report liable to be read by most—to be the result of either poor work or deliberate bias toward a predefined conclusion.
- The authors prepared, intensely investigated, and justified the use of a series of complex statistical models. There were nine models in total, each having particular strengths and weaknesses. Each had several subjective “knobs” and dials to twist. Only one model of the nine (LUR IND+Met; Fig. 22, p. 105) showed a “statistically significant” relationship between mortality and PM2.5, and that only barely, and in that model, only one submodel showed “significance.” The other eight models showed no relationship. Some models even hinted that PM2.5 reduced the probability of early mortality. With such a large number of tests and “tweaks”, the authors were practically guaranteed to find at least one “significant” result, even in the absence of any effect. Nowhere did the authors control for the multiplicity of testing, even though such controls are routine in statistical analyses of these sort.
- The authors only chose to report, in the Abstract (p. 7), on the one model that was “significant”, ignoring all others. They also departed from the main text and inflated the size of the hazard estimate: on p. 85 the estimates in Table 31 are based on a change in the interquartile range of PM2.5, but in the summary this is inflated to present a larger effect, presumably for emphasis. This behavior makes no sense statistically and is either sloppy writing or the result of purposeful choosing a result because of personal bias.
- The models were a mixture of Bayesian and frequentist methods, but incomplete mixtures. Substantial uncertainties remain in the model constructions such that the results are too certain, i.e. the confidence and credible intervals are too narrow. It is likely that were these uncertainties properly handled, even the one model which did show “significance” would not retain that significance.
Even assuming the models are trouble free, and the model that indicated significance was the only model worth showing, we have to consider that the authors claimed to have shown a relationship between PM2.5 and inhalation. Yet the authors never, not even in one case, measured the PM2.5 inhalation of any person. How, then, could the authors claim that PM2.5 inhalation is associated with early mortality? They cannot. At best, they can claim residence is associated with early mortality.
Instead of PM2.5 inhalation, the authors instead measured (with unaccounted for error; see Section 2) the residence of a sample of Californians. Residence was taken as a perfect, error-free, and unique proxy of PM2.5 inhalation. This is absurd, even on the authors own reasoning. About this, more in Section 2.
At the least, these criticisms call for additional study before any decisions are made regarding PM2.5 inhalation and mortality.
#1: Urban versus rural populations
Wide variances of mortality occur between urban and rural areas in California. Further, habits of life differ widely between the two. The authors write on p. 41:
Specifically across the United States, in the 1980s there were on average 6.2 excess deaths per 100,000 in non-metropolitan areas compared to metropolitan areas, and this number increased to 71.7 excess deaths for the period 2000-2004 .
This enormous and growing difference has profound consequences for any wide-region model of all-cause death. The authors’ answer was to include a single indicator (which would change the intercept of the model only) for whether a person lived in the Los Angeles Metropolitan area (p. 41). Even given the discrepancies in raw mortality statistics, this indicator was not even significant (p. 85, Table 31).
On p. 70 some of their estimates “became insignificantly elevated or were of borderline significance when the Los Angeles indicator and interaction terms were included.” Table 27 later lists this as insignificant for many causes. This is odd and should be explained.
At the least, this indicator should have been included (at least for research) as a multiplier (or interaction) for the other variables in the models besides just PM2.5. This would have changed the size of the effect of these variables inside and outside of LA.
Another difficulty is the rapid change in the differences of urban-rural death rates through time. No attempt was made by the authors to incorporate this in the models. This lack of control could certainly be in favor of “significance” of PM2.5 and all-cause mortality in the land use model.
Higher CVD deaths, incidentally, are found in rural populations (where ambulances and hospitals are more distant). Since it was CVD deaths that were found significant by the authors, and since CVD made up a large proportion of overall deaths, it is likelier still that misspecification of urbal versus rural populations contributed to the bare significance of one of the authors’ models.
In short, what we might be seeing in these models is nothing more than a location effect unrelated to PM2.5.
#2 Per-person PM2.5 exposure
It must be clearly understood that no person’s PM2.5 exposure was ever measured. The statements that PM2.5 was associated with all-cause death is therefore a misnomer.
Instead of actually measuring PM2.5, the authors created a guess of exposure based on where each person in the database (at one time) lived (see the next section). The assumption is that merely living in an area is an error-free proxy for actual PM2.5 exposure. This, of course, is false.
And because it is false, it is true that the results from each model are too certain. At the least, the confidence intervals limits are too narrow. Since this is so, and since only one model barely reached classical statistical significance, it is more than likely that actual PM2.5 exposure is not significantly related to all-cause death.
Now, in creating their guess, the authors could have, but did not, create a per-person estimate of PM2.5 exposure. They instead averaged exposure data across months or event years (“constructing 12-month moving averages from January 1988 to December 2000” p. 41). Why “moving averages”? Why not use just the numbers themselves as estimates of PM2.5 exposure? No convincing justification is given.
The authors could have, but did not, create simple plots of all-cause death by exposure level, just as a sanity check. It is strange that these are missing given the plethora of other graphics.
#3 Uncertainty of PM2.5 exposure
This is a key criticism. Given that they could not directly measure PM2.5, the authors had to make a guess. The guess was input as certain and true into the models. That it, the authors did not take into account the uncertainty of the exposure.
The authors used Bayesian exposure models, but only picked the means, medians, or modes of the posterior distribution of PM2.5—and we are never sure which of these point estimates was finally used; there is more than a hint of data snooping here.
What they should have done is to pick a level of exposure implied by the posterior of PM2.5 and then computed the rest of the model and set that result aside. They should have then picked another level implied by the posterior, repeated the model fit and saved, etc. Then they could have weighted all these results together (the weights determined by the posteriors) and this weight would be the final answer.
No matter what, this answer derived from this proper analysis will be less certain than what they have shown. It is therefore extremely unlikely that any of the models would have showed statistical significance.
Curiously, the authors point out that their kriging estimates of PM2.5 look smooth and conclude that actual values of PM2.5 are smooth. But kriging, by design, produces smooth estimates. Statements like these cause concern that the authors do not fully understand the tools they are using.
#4 Uncertainty of land use model
The exact same criticism can be made for the land use model. Only point estimates were used, and no account of the uncertainty of land use was made. Once again, and taking into account the previous over-certainties, it is even more likely that none of the models would have showed statistical significance.
#5 Uncertainty of where a person lived
They did not control adequately for where a person lived. This is crucial because it is solely from where a person lived that the authors guessed at PM2.5 exposure. It appears the authors used the last address only: on p. 41-42 they say, “We assumed that each subject resided at their home address in 1982 throughout the follow-up period to December 2000.”
This will be true for some, but surely not all, persons in the database. Therefore, there must be large errors in estimating where a person lived. And that means large errors in PM2.5 exposure estimates, and therefore even larger errors in actual PM2.5 exposures.
Of course, and once more, this translates into model statements that are too certain.
#6 Uncertainty in dietary and demographic variables
The authors used diet and “beer, wine, and alcohol” self-report variables in their models. They also used Census-derived variables such as percent white residents (in a geographic area). All these variables are notoriously poor. These variables also changed over the period in question, but these changes were not incorporated into the models.
Using these variables as certain in the model, as before, creates over-confidence.
#7 Uncertainty in model diagnostics
Fig. 5 (p. 45) is supposed to be a check on model goodness (for just one model). Why so few points in this plot? Surely the authors have many more observations of PM2.5 than are indicated.
Further, the model does more poorly the larger PM2.5 is. Figs. 14 (p. 56) and 15 (p. 58) are other model checks. These too indicate very poor performance at higher values of PM2.5.
Since it is the authors’ conclusion that increasing PM2.5 is associated with premature death, poorer model performance at increased levels of PM2.5 calls that conclusion seriously into question.
#8 Other pollutants
The NOx, PM10, etc. models are presented as additional evidence, but they are not. These pollutants are highly correlated to PM2.5, and each is estimated in the same way, so reporting on them in the fashion the authors chose is essentially repeating the same information twice in the guise of independence.