Background: Current studies of variable selection methods are based on small datasets for which the true underlying predictors and corresponding effect sizes may not be known precisely. We designed and implemented a large-scale simulation study to assess the ability of stepwise logistic regression variable selection and lasso regression methods to identify the correct underlying model. Methods: We simulated data based on a random multivariate distribution over an extensive range of covariate correlation structures, sample sizes, number of covariates, number of true predictors, and effect sizes. We considered correlation structures reflecting the scenarios of independence across all covariates; two low correlation blocks and a block of zero correlation; three blocks of high correlation, low correlation and zero correlation; and two blocks of high correlation with low cross block correlation and a block of zero correlation respectively. Results: Our results show that the performances of stepwise regression, lasso regression, and random forest algorithm (as measured by the AUC, detection of true predictors, selection of noise variables, and effect size estimation) are affected by the number of true predictor variables, the correlation between the variables in the dataset, and the sample size. The number of noise variables in the dataset, although significant in some cases, has only a marginal effect on a variety of model performance statistic. Our results show that stepwise regression procedures are more likely to capture a true predictor, more likely to correctly estimate the true effect sizes, and more likely to have lower false discovery rates. Moreover, stepwise model selection based on the BIC criteria obtained the highest average AUC (0.7515) closely followed by lasso regression, stepwise model selection based on the AIC criteria, ridge regression, and random forest algorithm. Conclusions: Stepwise procedures for variable selection are robust in the selection of the true underly predictor variables, estimation of corresponding effect sizes, and predictive model performance. Recommendations suggesting that stepwise procedures should be abandoned may be misguided.