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I saw this question on another Stack Exchange site, and wondered, how do they even know that one person in China died from "air pollution"?

How do these studies that lump millions of people into categories know how to classify the deaths? Do they categorically assume that everyone with asthma that died was killed by air pollution? If so, wouldn't all such statistics be overstated from the start?

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    Did you read the studies linked in those answers? Or did you not find that information there? – YviDe Dec 19 '15 at 7:22
  • I think the term is just misleading. Air pollution might very well reduce life qualities, but if you consider everybody who died from the reduction of life qualities to have "died prematurely", no matter how vague this estimation is (i.e. considering every other factor to be equal, do they die three months earlier? Then more likely they'll actually die 10 years "earlier" already from another disease, say cancer), then this is not very helpful. Also, then you might as well consider almost everything in life to be "causing premature deaths" as well. – xji Dec 24 '15 at 5:40
  • @XiangJi there are actually very complex statistical methods going on in studies like these, it's not as easy as you seem to think, noone is saying "oh, they died a few months earlier than expected, so their death is attributed to air pollution". I don't know enough about these methods yet to write up an answer that a layperson can understand, though. who.int/phe/health_topics/outdoorair/databases/… has a section on it – YviDe Jan 3 '16 at 17:33
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Your question can basically be extended to all studies related to statistics. In simple terms you are generally looking for a relationship (e.g. between an increased number of deaths and air pollution levels). Of course finding such a relationship ALONE doesn't tell you anything about cause and effect. Even if you are only looking at deaths from diseases known to be linked to air pollution, you have to come up with a way to show that these factors depend on each other - that they are correlated.

Usually, you look at some sort of control group that will have almost all the exact same characteristics as the test group, except obviously for the one you actually care about. The more similar the two groups are, the better of course - ideally if you could find two identical cities, with identical people - with the only difference being the air pollution, then you could show a cause and effect easily. Since this will be very difficult to achieve, you instead have to use some sophisticated statistical methods to study correlation of your variables. You can start reading about those methods here: https://en.m.wikipedia.org/wiki/Correlation_and_dependence

So, as long as those studies you refer to follow common statistical procedures, which I will assume they did, then yes, you could staticstically show a relationship and argue that X-many more people died from an increased in air pollution.

[EXTENSION]

One of the studies in the link you provided is referring to a Research Letter in Nature (one of the most highly regarded scientific journals out there): http://www.nature.com/nature/journal/v525/n7569/full/nature15371.html

[Lelieveld et.al] are using a:

global atmospheric chemistry model to investigate the link between premature mortality and seven emission source categories

They are using a

sensitivity study that accounts for differential toxicity

They are focusing on

mortality related to PM2.5 and O3

and

estimate of overall health impact depending on assumptions regarding particle toxicity

So, basically, they build a global model that will be able to correlate higher particle toxicity values with the number of deaths in different regions. They also talk about a sensitivity study, which will test if any change of specific variables may have extreme effects on their model.

Our calculations of air pollution related mortality are based on the method of the global burden of disease [...] applying improved exposure response functions that more realistically account for health effects at very high PM2.5

Of course it is just a model and not the reality, so the accuracy of their results will depend on the accuracy of this model, which is explained in more detail here: http://www.ncbi.nlm.nih.gov/pubmed/23245609

Overall, this actually isn't so much of a direct study with X number of participants. Nobody actually collected health information from participants, but they are using previously generated information (from the World Health Organisation) on toxicity response the effects of air pollution onto a global level. I assume the WHO has collected thousands of samples and analysed clinical trial that do what I mentioned earlier - they study the effect of a particular change in your environment onto your health. So, by now knowing that O3 is actually actually reducing your life expectancy by X percent, they can make the aforementioned conclusions.

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    I don't think saying "they use sophisticated statistical methods" answers the OP's question. – Carey Gregory Mar 10 '16 at 19:20
  • I agree with @CareyGregory . The OP references specific studies and asks how "these studies" do it, so a discussion as to how those studies do it would be much more helpful. – YviDe Mar 10 '16 at 19:27
  • Alright, so I extended the answer a little - I'm sure it's still not satisfying for you, but I find this exercise sort of pointless, since all this information is in the actual link the OP already provided... – Chris Mar 10 '16 at 23:20
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    In all fairness, the OP's question is basically a request for an explanation of the statistical methods employed to answer broad questions like this. Since a "good" answer to such a question would fill a chapter in a stats textbook and that's not feasible here, your edits are sufficient for me to reverse my downvote. My complaint with your first answer was it simply made no attempt to provide detail.\ – Carey Gregory Mar 11 '16 at 0:22

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