Missing values, especially in small datasets, can introduce biases into your model. There are several data imputation methods (MICE, Amelia II), which use EM algorithms to "fill in" the missing values. (Examples: http://onlinelibrary.wiley.com/doi/10.1111/j.1541-0420.2005.00317.x/abstract;jsessionid=E8761B782A07D5528348E853CA10FD71.f04t02, http://www.jstatsoft.org/v45/i03/paper). Most of these imputation methods use a form of linear regression to impute the data, then linear models are fitted to the newly imputed data.
However, isn't the logic for this method circular since you're imputing data using a linear model, then fitting the imputed data with another linear model? Wouldn't that inflate c-statistics for fitting methods that use similar techniques to the imputation method? If so, are there any other techniques for handling datasets with missing values?