Simulation studies comparing different genetic methodologies using Stata

In a recent, genetic case-control study of myocardial infarction (MI), cases' children were used as controls. That paper described one method to analyze such data. We describe two other methods for analyzing such data and compared the three methods by simulation using Stata. Each subject is classified according to three genotypes, MM, MN and NN, where M is the mutant allele and N is the normal allele. The probability that a subject has each genotype depends on the population allele frequency P, the relative risk of disease for the MN genotype compared with the NN genotype R1, and the relative risk for the MM genotype compared with the NN genotype R2. The first analytic method ignores the case/child pairings, the second method does not, and the third method considers P a nuisance parameter and eliminates it by conditioning. We randomly generated either 200 or 300 case/child pairs for various values of P, R1, and R2. We generated 1,000 data sets and applied each of the three methods. All analyses were based on likelihood procedures and were implemented using the maximum likelihood (ml) procedure. The standard errors of MLEs from each method were compared. We estimated power by comparing the likelihood of the full model to the likelihood with the constraints that R1 and R2 using Stata's lrtest and counting the number of the 1,000 simulations which lead to rejection of the null hypothesis. For the simulations done under the null hypothesis, we counted the number of times the null hypothesis was rejected and compared this number with an expectation of 50 using an exact binomial test. The simulations showed that all methods provide unbiased estimates in populations with a homogenous P and have an appropriate Type I error rate. The method based upon case/child pairs was generally more powerful than the other two methods. In populations with sub-populations with different Ps only the conditional approach is unbiased, although the simulations showed that method 2 was robust. This paper illustrates the utility of using Stata for simulation studies comparing different analytic approaches in case association studies of genetics. It also illustrates how useful simulation studies can be in estimating power. Stata is very well suited for simulation studies because of its speed, the ease of posting the simulation findings, and its maximum-likelihood procedure.