The effect of not taking the random mating assumption into account

[JustinWyllie]

Hi

 

I am trying to understand twin studies and really coming up against a brick-wall, probably because of my lack of maths knowledge.

 

In particular I am trying to understand how making the "random mating assumption" when it should not be made (i.e. for the trait being studied random mating does not hold) could effect a study.

 

For example in an imaginary study:

 

In the mz set lets say there is a concordance factor of 80%. In the dz set 40%. The random mating assumption has been made.

 

However; in fact for this trait the random mating assumption should not have been made, it turns out, and in fact the dz group shared 75% of their genes not 50%. (This is an artificial example probably exaggerated).

 

I *think* that that means the genetic effect in this case would have been exaggerated.

 

But I am struggling to understand this and to show it mathematically.

 

Am I right and can anyone explain it to me?

 

Many thanks

 

--Justin Wyllie

[dmaiski]

it would mean that the genetic effect would be underestimated

 

MZ twins in theory share 100% of their genes, this means if its 100% genetic when 1 twin gets the trait so dose the othere (100% concordance)

DZ twins in theory share 50% of their genes, this means if its 100% genetic should result in 50% concordance (assuming both parents werent carriers/disease positive yada yada yada)

so the maths for enviormental contribution is

1-((MZc-DZc)*(MZg/DZg))=enviormental contribution

XXc=concordence

XXg=genetic similarity

so in the study if MZg/DZg was assumed to be 1/.5=2 but was actualy 1/.75=1.33

the resultant enviormental value for assumed would be 20% when they were actually 53%

[JustinWyllie]

Hi dmaiski

 

Thanks. So can I just check?

 

In the first study (when we thought that the random assumption could be made) the maths looks like this:

 

Environmental contribution = 1 - ((.8-.4)*(1/.5)) = 0.2

 

Once we corrected for 75% shared genes in the dz set:

 

Environmental contribution = 1 - ((.8-.4)*(1/.75)) = 0.47

 

So the corrected figure is that in this study the environmental contribution is higher than when we mistakenly assumed 50% shared genes in the dz group?

 

And, sorry, but can you explain the 1 - in the equation? Is that just 'not the genetic contribution'?

 

Many thanks again

 

--JW

[dmaiski]

(MZc-DZc)*(DZg/MZg)=genetic component of the trait

1-genetic component=environmental component (its just subtracting the genetic from the whole, along the assumption that there are only the genetic and environmental factors)

but yea you got the right idea now

the 53% was just from me not paying attention to what i was doing and forgetting to 1-X the numbers

 

 

 

 

[JustinWyllie]

Ok. Thanks. It is much clearer now.

 

I think you mean (MZc-DZc)*(MZg/DZg)=genetic component of the trait ? I think you are just testing me?

[dmaiski]

yes im testing you. you passed, your prize is a brain disection... YOUR brain, muahahahahahaha!!!!

just got it backwards (hey it made sense in my head, then pen got to paper and gibberish came out)