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Stratification and Interaction

Which Summary Measure to Use?
  • Weighted averages are usually best
  • Mantel-Haenszel is easy to compute and can handle zeros
  • MLE measures are difficult and typically require a computer

Weighted Average in MH Summaries

Consider the following table:


 Sample 1
 Sample 2
n
 30
 70
x_bar
 5
 8

Weighted average of population ->  ((30*5)+(70*8))/(30+70) = 7.1

The average mean is closer to the cohort with a larger sample size. We can calculate any weighted average with the general form:

image-1663597273168.png

Where theta_hat is an estimator, such as mean or OR.

The MH Odds Ratio and RR can be described as weighted averages:

image-1663597467897.png

Where the weights are (b*c)/n

image-1663597533686.png

Where (a/n_1) / (b/n_0) is the risk ratio in each stratum, (b*n_1 / n) is the weight

Assumptions of Mantel-Haenszel Summary Measures

  • Observations are independent from each other
  • All observations are identically distributed
  • The common effect assumption should hold:
    • Follow-up cohort study - The stratum-specific risk ratios are all equal across the strata
    • Case-control - The stratum specific odds ratios are all equal across the strata
  • MH measures are biased if the correctness of the common effect assumptions cannot be justified.
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