AbstractIn causal studies, the near‐violation of the positivity may occur by chance, because of sample‐to‐sample fluctuation despite the theoretical veracity of the positivity assumption in the population. It may mostly happen when the exposure prevalence is low or when the sample size is small. We aimed to compare the robustness of g‐computation (GC), inverse probability weighting (IPW), truncated IPW, targeted maximum likelihood estimation (TMLE), and truncated TMLE in this situation, using simulations and one real application. We also tested different extrapolation situations for the sub‐group with a positivity violation. The results illustrated that the near‐violation of the positivity impacted all methods. We demonstrated the robustness of GC and TMLE‐based methods. Truncation helped in limiting the bias in near‐violation situations, but at the cost of bias in normal conditions. The application illustrated the variability of the results between the methods and the importance of choosing the most appropriate one. In conclusion, compared to propensity score‐based methods, methods based on outcome regression should be preferred when suspecting near‐violation of the positivity assumption.