Entering edit mode

Hi all, I have recently started a project on modelling a polygenic risk score model to evaluate its utilitiy in predicting a certain disease. After doing some reading, I have come across various models for unweighted and weighted Genetic Risk Score models.

I am wondering about the use of odds ratio (OR) versus the Beta-coefficient of each SNP variant in a risk score model. For instance, here they used the Beta-coefficient in their model, while here they used the odds ratio. Is there any difference in using the odds ratio versus the Beta-coefficient in a risk score model? Also, I noticed that some papers use log(OR) rather than ln(OR), is there a major difference between both?

Thanks!

Entering edit mode

Hey dude / dudette,

The odds ratio (OR) is the exponent of the beta coefficient. The beta coefficient itself is the unit increase in the exposure. A practical example will explain it better:

```
modeling <- data.frame(
condition=factor(c(rep("A",100), rep("B",100)), levels=c("A", "B")),
gene1=c(runif(100), runif(100)))
head(modeling)
condition gene1
1 A 0.3607443
2 A 0.3268301
3 A 0.4237005
4 A 0.7621534
5 A 0.1456797
6 A 0.3201094
```

Note that we have set `A`

as the reference level.

```
model <- glm(condition ~ gene1, data=modeling, family=binomial(link='logit'))
summary(model)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.03767 0.30014 -0.126 0.900
gene1 0.07294 0.51258 0.142 0.887
```

Here, the beta coefficient for *gene1* in relation to condition B versus A is 0.07294. So, *gene1* increases in expression in condition B (if it decreased, the beta coefficient would be negative). This is not a statistically significant finding, though, with *p*=0.887.

We can also test the *gene1* via the Wald test on the beta coefficient:

```
require(aod)
wald.test(b=coef(model), Sigma=vcov(model), Terms=2)
Wald test:
----------
Chi-squared test:
X2 = 0.02, df = 1, P(> X2) = 0.89
```

```
exp(cbind(OR=coef(model), confint(model, level = 0.95)))
OR 2.5 % 97.5 %
(Intercept) 0.9630288 0.5333548 1.737047
gene1 1.0756700 0.3930383 2.949061
```

So, odds ratio is just 1.1, which, as you can tell, is not huge and only reflects a slight increase.

The log OR is just the natural logarithm of the OR. With regard to why we may even want to use log OR over OR, well, there are probably many reasons. One is that we can calculate the Z score from the log OR:

```
OR <- 1.0756700
lowerCI <- 0.3930383
upperCI <- 2.949061
logOR <- log(OR)
logORlowerCI <- log(lowerCI)
logORSE <- (logOR - logORlowerCI) / 1.96
```

Then calculate Z:

```
logOR / logORSE
[1] 0.1420052
```

Kevin