Solved – Calculating a pooled odds ratio from an adjusted odds ratio

meta-analysisodds-ratiostata

I have individual adjusted odds ratios from different articles, and I want to combine them to calculate a pooled odds ratio, e.g., aOR 2.13(1.43-3.18) and aOR 1.47(0.54-3.98).

So, is there any formula or guidance on how to combine them? The adjusted odds ratios are from articles, and I don't have the entire data set related to these two articles.

Best Answer

Systematic Reviews in Health Care: Meta-analysis In Context is an excellent resource if you're looking to do a meta-analysis (in healthcare or otherwise - if you're not in health, ignore their overt fondness for clinical trials).

They also include extensive documentation for conducting a meta-analysis in Stata beyond just a pooled estimate of effect. That is where I would head to first.

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Confidence Interval – Calculating Odds Ratio and Confidence Interval in Meta-Analysis

I did the following in Stata, the first is fixed effect and the second is random effect. I got different answers than you did.

           Study     |     ES    [95% Conf. Interval]     % Weight
---------------------+---------------------------------------------------
1                    |  2.700       1.800     4.000         63.47
2                    |  1.300       0.500     3.400         36.53
---------------------+---------------------------------------------------
I-V pooled ES        |  2.189       1.312     3.065        100.00
---------------------+---------------------------------------------------
 Heterogeneity calculated by formula
  Q = SIGMA_i{ (1/variance_i)*(effect_i - effect_pooled)^2 } 
where variance_i = ((upper limit - lower limit)/(2*z))^2 



 Heterogeneity chi-squared =   2.27 (d.f. = 1) p = 0.132
  I-squared (variation in ES attributable to heterogeneity) =  56.0%

  Test of ES=0 : z=   4.89 p = 0.000

. metan or ll ul, effect(Odds Ratio) null(1) lcols(trialname) texts(200) random

           Study     |     ES    [95% Conf. Interval]     % Weight
---------------------+---------------------------------------------------
1                    |  2.700       1.800     4.000         55.93
2                    |  1.300       0.500     3.400         44.07
---------------------+---------------------------------------------------
D+L pooled ES        |  2.083       0.721     3.445        100.00
---------------------+---------------------------------------------------
 Heterogeneity calculated by formula
  Q = SIGMA_i{ (1/variance_i)*(effect_i - effect_pooled)^2 } 
where variance_i = ((upper limit - lower limit)/(2*z))^2 

  Heterogeneity chi-squared =   2.27 (d.f. = 1) p = 0.132
  I-squared (variation in ES attributable to heterogeneity) =  56.0%
  Estimate of between-study variance Tau-squared =  0.5488

  Test of ES=0 : z=   3.00 p = 0.003

Solved – Calculate combined odds ratio between two factors

Typically you combine by taking the weighted average of the log of the odds ratio and then exponentiating. If the sizes of the data sets are roughly equal for your odds ratios then it's the average of the log odds. Some people weight just by N but I think it's recommended to use 1/SE.

EDIT I didn't check your paper for what they meant by combined OR. They mean a group of subjects that have two risk factors as opposed to either one separately. You can't get it from the individual risk factors or an interaction in a model of the risk factors. It's a part of the research design. Unless your var1:var2 is that group of subjects containing both risk factors it's not what you need. Read the methods in the paper carefully. The Alzheimer's example makes it clear.

Best Answer

Related Solutions

Confidence Interval – Calculating Odds Ratio and Confidence Interval in Meta-Analysis

Solved – Calculate combined odds ratio between two factors

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