Rosenbaum’s sensitivity analysis framework has several limitations: 1. It is mostly applicable to matched observational studies; 2. It only tests the sharp null hypothesis; 3. It assumes treatment effect homogeneity to obtain a confidence interval of the causal effect. Seeking to overcome these limitations, we propose a new approach to sensitivity analysis based on the inverse probability weighting estimator. The key ideas are to use numerical optimization to estimate the causal effect bound and to use the percentile bootstrap to quantify the sampling uncertainty.