I am synthesizing some data from a few observational studies for a meta analysis later, I calculated a weighted odds ratio using the M.H method, however I am not sure how to calculate the confidence intervals. I am not using any statistical software at the moment, just doing calculations and putting in the data into an excel file. Can I just calculate the standard error by adding all exposed and unexposed groups in the cases and controls, and then using the standard formula for standard error calculation and so on for C.I ? Or is there any specific method for calculating C.I of the M.H odds ratios.
A specific method for calculating confidence interval of Mantel-Haenszel Odds Ratio was first described in Clayton D. & Hills M. (1993) Statistical Methods in Epidemiology. Oxford University Press, Oxford. It is also reproduced in Page 183 of Essential Medical Statistics by Betty Kirkwood and Jonathan E. Sterne. The following steps should be followed to calculate the Mantel-Haenszel CI :
i) Here 95% CI ranges from OR/EF to OR*EF, where OR is Mantel-Haenszel Odds ratio and EF is the exposure factor;
ii) EF = exp (1.96* SE) , where exp is exponential and SE is the Standard error of the Mantel-Haenszel Odds Ratio;
iii) SE = Sqrt [V/(Q*R)];
iv) Now just think about a, b, c, d as the values the four cells of a 2 X 2 table of each stratum (Remember that using this approach we usually describe the simple Odds Ratio as (a*d)/ (b*c) ). Thus ai, bi, ci ,di represent the a, b, c, d values of the i-th stratum. Similarly ni is the sum of ai, bi, ci and di in the i-th stratum;
v) Using the above notational style,
Q = Sigma (i.e. summation of) [(ai*bi) / ni]
R = Sigma [(ci*di) / ni]
V = Sigma [(ai +bi)* (ci+di)*(ai+ci)*(bi+di)]/ [ni*ni*(ni-1)].
You can easily generate the 95% Ci in Excel itself provided you carefully translate the above to Excel formula. If you are still not sure, you can directly consult the books mentioned in the beginning.
Have a look at http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.228.3832
cheers
Vielen Dank Eik ! I did find a useful resource though , http://www.iarc.fr/en/publications/pdfs-online/epi/cancerepi/CancerEpi-14.pdf, now i am on my way to alot of work :)
I use review manager software from The Cochrane Collaboration (http://ims.cochrane.org/revman). If you prefer doing it your self, you can use the document for statistical algorithms used for the software (https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CC0QFjAA&url=http%3A%2F%2Fims.cochrane.org%2Frevman%2Fdocumentation%2FStatistical-methods-in-RevMan-5.pdf&ei=5TefUoHvO4S1rgHS04CYBQ&usg=AFQjCNEsR3Sci29bQ2qqQf585GbS763IrQ&sig2=dy4KypkO2lntewO-GkK5RA&bvm=bv.57155469,d.aWM) see page 4 and page 8
If you have the pooled estimate of MH relative risk (RRmh) and the MH chi-square (mhChi-sq) statistic, you can compute the 95% confidence interval. It is:
RRmh^(1 +/- 1.96xsqrt[mhChi-Sq])
reference: Hennekins & Buring, Epidemiology in Medicine, 1987, p. 309.
Mantel–Haenszel confidence intervals are appropriate when the odds are believed to be the same (homogeneous across strata). Under these assumptions, Mantel–Haenszel weights are designed to use the information efficiently. They are not intended to measure a composite odds ratio when the within-stratum odds ratios differ. In such conditions, we want a standardized ratio.
In the Figure above, Mantel–Haenszel odds ratio is 1.40. It measures the association between death and treatment while adjusting for age. A more general way to adjust for age is logistic regression; the outcome variable is case, and it is explained by age and exposed.
Logistic regression has advantages over the stratified-table approach. First, we obtained an estimate of the age effect: being 55 years or over significantly increases the odds of death. In addition to the point estimate, 4.22, we have a confidence interval for the effect: 2.17 to 8.20.
Hi
you can using STATA software and by metan command without calculation of standard error. a sample of this command is: "metan a b c d, or random"
if you have exposed and unexposed in cases and controls, this command calculates directly standard error and CI.
Best
I'm working with Rev Man, it is a good free programme to make the data analysis. I can recommend this programme.
A specific method for calculating confidence interval of Mantel-Haenszel Odds Ratio was first described in Clayton D. & Hills M. (1993) Statistical Methods in Epidemiology. Oxford University Press, Oxford. It is also reproduced in Page 183 of Essential Medical Statistics by Betty Kirkwood and Jonathan E. Sterne. The following steps should be followed to calculate the Mantel-Haenszel CI :
i) Here 95% CI ranges from OR/EF to OR*EF, where OR is Mantel-Haenszel Odds ratio and EF is the exposure factor;
ii) EF = exp (1.96* SE) , where exp is exponential and SE is the Standard error of the Mantel-Haenszel Odds Ratio;
iii) SE = Sqrt [V/(Q*R)];
iv) Now just think about a, b, c, d as the values the four cells of a 2 X 2 table of each stratum (Remember that using this approach we usually describe the simple Odds Ratio as (a*d)/ (b*c) ). Thus ai, bi, ci ,di represent the a, b, c, d values of the i-th stratum. Similarly ni is the sum of ai, bi, ci and di in the i-th stratum;
v) Using the above notational style,
Q = Sigma (i.e. summation of) [(ai*bi) / ni]
R = Sigma [(ci*di) / ni]
V = Sigma [(ai +bi)* (ci+di)*(ai+ci)*(bi+di)]/ [ni*ni*(ni-1)].
You can easily generate the 95% Ci in Excel itself provided you carefully translate the above to Excel formula. If you are still not sure, you can directly consult the books mentioned in the beginning.
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