1. Relative risk: lung cancer and smoking ! thanks in advance for your help

.........................Smokers...................Non- Smokers
Iron Exopsure.......+..........-...................+..........-

Lung cancer.........111.......28..................11........10
No Lung cancer......99.......222.............. 159........190

1)Risk of lung cancer related to iron exposure. Whats its best estimate?

I say relative risk. or is it the odds ratio?

2) Calculate this risk.
Do i consider the non-smoker table or do i set a new table with the disease and the exposure being iron exposure regardless of smoking?

3) Does the risk of lung cancer related to iron exposure differ in the presence of smoking? Explain why using numbers.

I would highly appreciate your help. thanks a lot.

2. Re: Relative risk: lung cancer and smoking ! thanks in advance for your help

OR and RR usually differ in their use based on the temporality of the study design (i.e., prospective [RR] and retrospective [OR]). Both provide similar effect measures when outcomes are rare.

You can leave the columns and rows the same, but would have to modify your calculations accordingly. I typically would just restruction this contingency table so rows are exposure and columns are outcomes. You seem to have a third variable, are you wishing to stratify on it (Cochrane Mantel Haenzel test), or is your table incorrect. With this discrepancy the count data is not all there to examine iron exposure??, or are they exposed to iron in the smoking process?

Number 3 is up to you to try and figure out. If you cannot figure it out, submit your work and we can help you. Though you seem to be missing information in your post.

3. Re: Relative risk: lung cancer and smoking ! thanks in advance for your help

My experience is that the term "relative risk" often refers to ratios but not specific ratios (ie. relative risk could mean odds ratios or risk ratios and relative risk pretty much is just a colloquial term. That's my experience anyways)

.........................Smokers...................Non- Smokers..| Total
Iron Exopsure.......+..........-...................+..........-.....|

Lung cancer.........111.......28..................11........10...|
No Lung cancer......99.......222.............. 159........190.|
------------------------------------------------------|
Total...................210......250...............170........200

%.......................52.9.......11.2............6.4........5......

Ignore making ratios for now. Look at the percents. For non smokers without iron exposure we have a reference of 5% risk of developing lung cancer. Non smoking WITH iron exposure is 6.4%. For smokers not exposed to iron you have 11% and smokers exposed to iron is 52.9%.

The percentages are the risks. Odds always overestimate risk unless the disease is rare and even then it still is overestimating the risk but the overestimation is negligible.

The point I'm trying to demonstrate is that for your issue (1) relative risk means nothing other than using a ratio. It does not elicit a particular ratio to use even though the word "risk" is in it. When you answer say EXPLICITLY "Prevalence Odds Ratio" or Prevalence Ratio (This is Risk Ratio but because we're not dealing with incidence as far as I can tell from the data; you didn't say explicitly whether it's cumulative incidence or not so I defaulted to prevalence). If this is data from a case control, Exposure Odds Ratio is almost always proper. If this is cross sectional either PR (prevalence ratio) or POR (prevalence odds ratio) can work. Since this isn't a rare disease PR may "look" better and can communicate pretty well.

Because of the odds of developing lung cancer given smoking AND iron exposure being large (111/99) = 112% compared to the odds of non smoker no iron exposure (10/190)=5% the POR= 112/5=22.4 while the PR is (111/210)/(10/200)=10.5 both valid, I

Now, between smokers look at the difference in the percentages (52% compared to 11%). Risk difference is 52%-11% = 41%

At non smokers:

6.4% - 5% = 1.4%

Large risk difference; heavy effect modification.

I'll leave it to you if you want to do simple chisq tests. There's a website called OpenEpi where you can make easy 2x2's and even stratified 2x2 's that gives you many tests

@hlsmith this is just a stratified contingency table of counts not incidence so all he needs to do is make the non smokers and exposed to iron the reference group and find ratios against them for the other three columns.

4. Re: Relative risk: lung cancer and smoking ! thanks in advance for your help

Yes I see now that the first table is for smokers and the second for non-smokers (wasn't following all of their dashes). As referenced you can use Breslow Day Test of Homogeneity.

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