I have counts data for 560 immune genes and I am trying to statistically analyse differences in these counts between Rh- and Rh+ individuals.
In my analysis sex and age are confounding factors. To correct for sex I split the group into males and females and looked at Rh+/- response in each separately through unpaired t tests in R. This gave me a p-value for each gene.
However, as age is also a confounding factor I need to create a non linear regression model to correct for age.
Can anyone advise me on how I go about doing this?
You first need to denote the variables you're working with. E.g., let diffCount - the difference in counts is a function of age and gender. Then build 2 regressions for each sex:
diffCountMale(age) = age*m_b0 + m_b1
diffCountFemale(age) = age*f_b0 + f_b1
The problem, however, is that the dependency may be non-linear. You can try applying transformations to Rh+ and Rg+ and age. I think for Rh+ and Rh- this will be sqrt(x), and for age it will be log. For a quick guide on data transformations, see https://xdplot.blogspot.com/p/data-transformations-guidelines.html
If you do not get a linear dependency, you may use the "loess" method (available in R). On one graph you then can show both diffCountMale and diffCountFemale functions. X = age, Y = diffCount. Then compare the curves
Hi,
this is absolutely not my field (so I may misunderstand the variables and context) but as far as I see, the most straightforward approach is to run a generalized additive model (GAM) with a nonlinear smooth for age. The GAM is a progression from the GLM regression, hence you can incorporate all sorts of error distributions. The model which would be done with R's mgcv package would look like this (I assume that counts is simply count variable and Rh is a binary variable denoting of two groups Rh- and Rh+):
counts ~ Rh + sex + s(age) + error
Here the s(.) operator estimates a nonlinear function for age from the data. A built in penalty avoids overfitting.
The code for this function in mgcv would look like this:
model
My suggestion is to start with some graphs.i don't think you know enough about the variables and graphs will help you. You may want to look at some possible interactions depending on your data. Best wishes , David Booth
BTW let's not forget that nonlinear models are about nonlinear functions of the variables. This regression so far is linear since the RHS is still a linear function. See your favorite linear statistical models text. From an old curmudgeon, David Booth
You should analyze the effects of age and sex and Rh status on the log counts in one model. Using log counts is important toachieve linearity and homogeneity of variance (you could alternatively use a negative binomial model with log-link, but it also works with the standard toolbox using log counts; the difference is that when using log counts you will get predictions of the mean logs instead of the log means, but this is anyway not your question; bith models give you the same estimates of the effects: log-ratios).
Since the relation between age and log counts is not of primary interest and presumanbly not linear, it's advisable to use some spline basis to model age, as Holger Steinmetz already proposed (Holger: this is also possible in a standard linear model using splines::ns()).
Additionally, as David Eugene Booth suggested, you might also consider interactions, so a full modelmight look like
log(counts) ~ Rh*Sex*ns(Age,df=3)
that might be reducable to
log(counts) ~ Rh + Sex*ns(Age,df=3)
that might give a simpler interprtation of the (sex- and age-adjusted) effect of Rh on the counts.
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