## 5.3 Mantel-Haenszel OR

We saw that socio-economic status may be confounding the relationship between creche attendance and lower respiratory tract infection. Thus we should examine the odds ratio for the effect of creche attendance on lower respiratory tract infection in each stratum of SES separately. We can then combine these estimates by taking a weighted average to come up with a summary value. We call this the effect of creche attendance controlled for socioeconomic status - in the case of odds ratios, we call this the Mantel-Haenszel odds ratio.

Intuitively, we have here tried to control for confounding by SES. When we look at the relationship between LRTI and creche attendance within a stratum of SES, since everyone has the same SES, any association between LRTI and creche attendance should not be due to SES.

In R, we use epiDisplay’s mhor command to conduct this test, providing the odds ratio, 95% confidence interval, and p-value for each stratum and overall. The test for homogeneity of ORs tests the hypothesis that the ORs in the strata are the same (i.e. it tests for effect modification)

```
#--- Get the Mantel-Haenszel OR
creche %$% mhor(lrti, creche, socio, graph = F)
```

```
##
## Stratified analysis by socio
## OR lower lim. upper lim. P value
## socio Average SES 3.45 1.25 8.71 0.008581
## socio Very low SES 3.42 1.06 13.15 0.028547
## M-H combined 3.46 1.72 6.96 0.000299
##
## M-H Chi2(1) = 13.1 , P value = 0
## Homogeneity test, chi-squared 1 d.f. = 0 , P value = 0.981
```

Exercise 13.4: Using the results above:

- what is the MH odds ratio controlling for SES and what does it mean?

- How does this differ from the OR for the effect of creche attendance on lower respiratory tract infection ignoring SES?

- Why has the OR decreased?

- Interpret the 95% CI for the MH OR.