Comparing odds ratio (OR) from fitting independence, marginal and conditional models in analyzing the individual matched case-control studies with simulation data

One of the popular studies in medical sciences for finding risk factors and the reason of the disease, are case-control studies that the important index we can calculate is odds ratio. but some confounders which effect on response variable challenge the OR’s validity and present OR more or less than the real value. One way of omitting the effect of confounder is designing matched studies. Logistic regression is one of the general method for modeling this studies. This article compares 3 logistic regression model: independence, marginal and conditional.

This study has been conducted on correlated simulated data. Thus the data is simulated from bivariate normal distribution with the correlation coefficients (0,0.2,0.4,0.6,0.8). Then with changing cut-off points at(0.05,0.25), (0.25,0.1), (0.25,0.15), (0.25,0.25) for their c.d.f, we convert continues distribution to categorical binary distribution which data are related together. Then 3 logistic regression model in independence, marginal and conditional version fit to data and calculate OR. With 10000 times iteration, we compare 2.5 and 97.5 percentiles values and the median OR percentile value at the above cut-off points for all there models.

When the correlation is zero, all three models have the same quantity for OR and also changing in point have the same coefficient. But with the increasing correlation between the observations, OR between marginal model and independence model is not different. But its value will vary with the conditional model. For example, the cut-off point (0.25,0.1) and when the correlation is 0.6, median of OR that obtained in marginal model and independence model is 2.8, but in conditional model this quantity is 5 and it is twice of fitted value.

When the correlation between observation is high, using of conditional model is more correctly method and with increasing this correlation, our error rate by using independence or marginal model rises. But when correlation between observations is negligible, using of the three models give similar estimates.