Little Odd-ratio/ relative risk confusion

[BobbyBear]

Hi, just a small doubt I'm having:
I'm given a cross tabulation table, such as undernourished status versus gender of the child:

-----------------------------undernourished

-----------------------------yes--------no

--------------------boy------37-------- 86
---------gender
--------------------girl-------40--------74suppose we are told to compute the relative risk of being undernourished with the reference group being boys,

I think we should compute: (40/(40+74)) / (38/(37+86))

and not the other way around, right?

Likewise, the odds ratio of being undernourished with the reference group being boys would be: (40/74) / (38/86) and not the other way around, I suppose?

I just want to make sure what "with the reference group being boys" means... I'm assuming it means it means odds of undernourished girls to odds of undernourished boys, but I'm not 100% sure if it means this or if it might mean we are interested in boys so it should be odds of boys to odds of girls?

thanks!

 

[SW VandeCarr]

Hi, just a small doubt I'm having:
I'm given a cross tabulation table, such as undernourished status versus gender of the child:

Suppose we are told to compute the relative risk of being undernourished with the reference group being boys,

I think we should compute: (40/(40+74)) / (38/(37+86))

and not the other way around, right?

Likewise, the odds ratio of being undernourished with the reference group being boys would be: (40/74) / (38/86) and not the other way around, I suppose?

I just want to make sure what "with the reference group being boys" means... I'm assuming it means it means odds of undernourished girls to odds of undernourished boys, but I'm not 100% sure if it means this or if it might mean we are interested in boys so it should be odds of boys to odds of girls?

thanks!

You could use either one as a comparison group, but it's often preferred to have a hypothesis about which group would be at lower risk as the comparison group before the data is collected an analyzed. In this case the girl's rate is 0.35 while the boy's rate is 0.30 resulting in a rate ratio of 1.17.

To test if this represents a statistically significant difference you could do a test comparison of two rates based on the normal distribution (Z score) if the normal assumption holds. The odds ratio is preferred by some. The ln$(\psi)$ (log odds) can be used in logistic regression. It is considered an estimate of the rate ratio and in this case it's 1.26. The rate ratio is of course exact but has less desirable mathematical properties.

Some points. You used 38 instead of 37 in your calculations of the boys rate so your answers would be slightly different than mine. In your table you usually will put your comparison group in the lower row. Then you can use the cross product ad/bc to calculate the odds ratio.

I don't like the term "relative risk". It's not a very meaningful description. I prefer rate ratio or odds ratio. It's not clear just what one is referring to with the term 'relative risk' although it is often used.

 

[HallsofIvy]

"with the reference group being boys" means that you are looking only at the boys, not the girls. And that means that you are wrong. There are 37 undernourished boys out of a total of 37+ 86= 123 boys. The probability of a boy being undernourished is 37/123.

 

[BobbyBear]

thank you both for your comments!

"with the reference group being boys" means that you are looking only at the boys, not the girls. And that means that you are wrong. There are 37 undernourished boys out of a total of 37+ 86= 123 boys. The probability of a boy being undernourished is 37/123.

... but if I am asked for an odds ratio, then I am not being asked for a ratio between girl undernourishment odds and boy undernourishment odds? Looking at boys alone, I can only have the odds of undernourishment in boys, not a ratio of odds... I think "with the reference group being boys" is simply stating that boys is the "comparison group", as SW VandeCarr put it, which means it is sort of the benchmark for any other group.
Does that make sense?

 

[blue_raver22]

I can confirm that your understanding of computing relative risk and odds ratio is correct. When the reference group is specified as boys, it means that we are interested in comparing the risk or odds of being undernourished for girls to the risk or odds for boys. So, your calculation of (40/(40+74)) / (37/(37+86)) for relative risk and (40/74) / (37/86) for odds ratio is correct. It is important to specify the reference group in order to accurately interpret and compare the results.