[R] Statistical question about logistic regression simulation

[Denis Aydin]

Hi R help list

I'm simulating logistic regression data with a specified odds ratio 
(beta) and have a problem/unexpected behaviour that occurs.


The datasets includes a lognormal exposure and diseased and healthy 
subjects.

Here is my loop:

ors <- vector()

for(i in 1:200){

# First, I create a vector with a lognormally distributed exposure:

n <- 10000 # number of study subjects
mean <- 6
sd <- 1

expo <- rlnorm(n, mean, sd)

# Then I assign each study subject a probability of disease with a
# specified Odds ratio (or beta coefficient) according to a logistic
# model:

inter <- 0.01 # intercept
or <- log(1.5) # an odds ratio of 1.5 or a beta of ln(1.5)

p <- exp(inter + or * expo)/(1 + exp(inter + or * expo))

# Then I use the probability to decide who is having the disease and who 
# is not:

disease <- rbinom(length(p), 1, p) # 1 = disease, 0 = healthy

# Then I calculate the logistic regression and extract the odds ratio

model <- glm(disease ~ expo, family = binomial)

ors[i] <- exp(summary(model)$coef[2]) # exponentiated beta = OR

}


Now to my questions:

1. I was expecting the mean of the odds ratios over all simulations to 
be close to the specified one (1.5 in this case). This is not the case 
if the mean of the lognormal distribution is, say 6.
If I reduce the mean of the exposure distribution to say 3, the mean of 
the simulated ORs is very close to the specified one. So the simulation 
seems to be quite sensitive to the parameters of the exposure distribution.

2. Is it somehow possible to "stabilize" the simulation so that it is 
not that sensitive to the parameters of the lognormal exposure 
distribution? I can't make up the parameters of the exposure 
distribution, they are estimations from real data.

3. Are there general flaws or errors in my approach?


Thanks a lot for any help on this!

All the best,
Denis

-- 
Denis Aydin
Institute of Social and Preventive Medicine at Swiss Tropical Institute 
Basel
Associated Institute of the University of Basel
Steinengraben 49 – 4051 Basel – Switzerland
Phone: +41 (0)61 270 22 04
Fax:   +41 (0)61 270 22 25
denis.aydin at unibas.ch
www.ispm-unibasel.ch