OBJECTIVES:  In observational studies, subjects are assigned to treatment groups without the benefits of randomization, resulting in potential bias in the estimation of the treatment effect. We assess the performance of 5 different statistical methods used for bias correction and causal inference under different conditions -- multivariate regression (MR), propensity score matching (PSM), propensity score stratification (PSST), doubly robust estimation (DR) and inverse probability treatment weighting (IPTW). METHODS: We simulated the outcomes of two hypothetical treatments having three continuous covariates that are correlated with the treatments and with each other.  We varied the sample size, noise levels, and tested the methods under conditions of model misspecification.  To evaluate performance of the methods, we used two measures: correct identification of a statistically significant treatment effect (p < 0.05) and the root-mean-squared error for the treatment effect. RESULTS:  For the correct-specified models, IPTW performed well relative to other methods, particularly at small sample sizes.  At low noise levels and large samples sizes, all methods reliably identified a treatment effect. PSM lagged in performance for small sample sizes, and DR showed relatively weak performance under most conditions, especially under model misspecification and high noise levels.  For misspecified models, the relative order of performance was similar to that of the correct-specified models. The results at high noise level were poor even for large sample sizes. CONCLUSIONS: MR is an unintentionally popular choice for its ease of use and the belief that covariates may adjust well for treatment effects. Our results indicate that if covariates are correlated with each other or with the treatments, one should take great care in using MR unless the sample size is large. For small sample sizes, IPTW is often the best choice even for misspecified models. PSM is a reasonable choice under low noise levels and substantial sample sizes.