How do they determine secondhand smoke related illnesses?

They didn’t, it is just assumed and cannot be proven.

So it’s mostly just propaganda meant to scare people?

There is a correlation, it’s just hard to prove. There are so many causes for cancer it’s hard to pin it down to one factor.

“The dangers of secondhand smoke, an unexplainable phenominon”

Probably when people have these diseases and they’re questioned in the hospital, they ask “do you live with a smoker?” When the person answers yes, it’s probably reported to federal health authorities.

Does this help at all??
http://www.cancer.org/cancer/cancercauses/tobaccocancer/secondhand-smoke

The idea that a particular case can’t be absolutely proven to be caused by second hand smoke is a disengenous argument.

That was the main strategy of tobacco “scientists” employed by cigarette companies who fought very hard to give cancer and respiratory disease to millions of smokers.

It’s as if someone comes in after a tsunami that kills thousands, and picks one body up on the beach and says, “This man may have died of a heart attack BEFORE the water hit! You can’t prove it didn’t happen! This talk of dangerous tsunamis is just propaganda meant to scare people!”

I agree with @jca that they are likely backing into the question.

“You have a disease.”
“Do any of these apply?”

What’s not taken into account is the time frame of the “Were you a secondhand smoker?” question, the Babyboomers reaching maturity, and the technology of diagnosing cancer.

Cripes, I should have given this argument up 15 years ago when I quit smoking, but I still think it’s a real, vital issue.

Through Epidemiological studies.

In retrospective studies, people were asked if they were exposed to secondhand smoke. In prospective studies, people were followed over time to determine whether/how much exposure occurred during the study.

In retrospective case-control studies, outcomes (such as cardiovascular disease) are determined, then exposures (such as secondhand smoke) are asked about retrospectively. Participants in the study are then categorized in a 2×2 table (for the most simplistic explanation):
...................................outcome (-)............outcome (+)
exposure (-)................. group 1….............. group 2
exposure (+)................ group 3….............. group 4
Ratios are calculated to determine study odds of outcome given exposure.

In cohort studies (could be either retrospective or prospective), the study occurs in the other direction. Participants are first grouped based on exposure, and then it is determined whether they developed the outcome. Similar calculations are made and risk/odds are determined.

Any good study would also consider many different aspects of both exposure and outcome… such as the duration of exposure, types of smoke, some proxy for a cumulative “amount” of exposure, the various environments of exposure (only at home? also at work?), diagnostic guidelines, how to count loss to death or loss to follow-up, as well as demographic features such as age, race, sex, etc.

These would be based on clinical trials… and not just a question that may have been asked by a doctor and recorded in your medical record.