I've been asked to provide advice to a researcher and this has me puzzled.
The researcher has an estimated standardised mortality rate (SMR) for the whole population of interest. He wants to compare the SMR of a treatment group which is a subset of the whole population used for the estimated population SMR. He is keen for a p-value at the end.
How would you analyse the difference in SMR? My first instinct is Chi Goodness of Fit, but can you use that if you only have rates not raw numbers for the estimated SMR? Or is it more appropriate to calculate a 95% confidence interval of the treatment group SMR, which would demonstrate statistical difference, but not the p-value that the researcher is after. Or would a survival analysis like a cox regression be more appropriate?
Any advice would be much appreciated.
I'm sorry but there are no tests for comparing a subset of a population with the population. Since everyone is a member of the same population, u couldn't conclude that there is a difference unless you have 2 populations to compare. You could ask if there is a difference between the treatment group and the rest of the population in which case the treatment group would not belong to the population but to a second population. Can you get some kind of standard error? If not, I would try a two sample Kolmogorov-Smirnoff test because that has better theoretical properties than Chi-square. A reference to get you started is Randles and Wolfe, Intro to the Theory of Nonparametric Statistics, Wiley P. 382. Another possibility might be Hollander and Wolfe, Nonparametric Statistical Methods, Wiley, pp 219 ff. The way I would handle this would be to compare the original two data samples(not with one being pooled with the other) and try to conclude if you were dealing with 2 different populations. I would ignore the SMR for the time being because of what I said in the beginning because one data set is a subset of the other as I understand it so the two SMRs would not be for different possible groups... Best wishes.
I'm sorry but there are no tests for comparing a subset of a population with the population. Since everyone is a member of the same population, u couldn't conclude that there is a difference unless you have 2 populations to compare. You could ask if there is a difference between the treatment group and the rest of the population in which case the treatment group would not belong to the population but to a second population. Can you get some kind of standard error? If not, I would try a two sample Kolmogorov-Smirnoff test because that has better theoretical properties than Chi-square. A reference to get you started is Randles and Wolfe, Intro to the Theory of Nonparametric Statistics, Wiley P. 382. Another possibility might be Hollander and Wolfe, Nonparametric Statistical Methods, Wiley, pp 219 ff. The way I would handle this would be to compare the original two data samples(not with one being pooled with the other) and try to conclude if you were dealing with 2 different populations. I would ignore the SMR for the time being because of what I said in the beginning because one data set is a subset of the other as I understand it so the two SMRs would not be for different possible groups... Best wishes.
I agree with Dr Booth and would go for CIs for SMR, or comparative mortality figures (better). More on this subject:
http://jpubhealth.oxfordjournals.org/content/23/1/40.full.pdf
Thank you. I couldn;t understand why the focus on SMR. Personally I think the researcher needs to go back to his research question and confirm what it is he is trying to find out.
I will investigate the two sample Kolmogorov-Smirnoff test and thank you Dr Martins for the very useful reference.
It's nice to know I wasn;t missing something really obvious!
The whole problem of the validity of comparing SMRs for subcohorts is dealt with thoroughly in Breslow and Day vol 2 IARC 1987, p91-103 .
formally stratum specific death rates for each exposure class must be proportional to the external standard rates.
you would not compare the exposure class SMR to the total SMR but to the unexposed group SMR.
Interesting discussion indeed. David Schmidt, I also don't see much need to focus on the SMR in this case. As David Booth has put it, you have a problem dealing with SMRs from a population and its subset. Many would standardise in any case if they want to compare across DIFFERENT populations. Best wishes from Ghana.
It is unclear why the researcher is interested in comparing SMR of the whole population with SMR of subset of the whole population. As mentioned in most of the earlier postings, you have a problem dealing with SMRs from a population and its subset. Of course there is a way, proposed by Breslow and Day, to compare Two different groups SMR as also mentioned by James.
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