It is well-known that a smooth variety satisfying strong approximation is simply connected. In particular, the strong approximation property is not birationally invariant. Inspired by simply connected property and the example of affine space, Colliot-Thélène and Wittenberg asked if strong approximation property is invariant among smooth varieties up to a closed sub-variety of codimension at least 2. In this talk, we will show that this is true for a semi-simple simply connected quasi-split linear algebraic group. We also explain that such phenomena for strong approximation with Brauer-Manin obstruction. This is a joint work with Yang Cao and Yongqi Liang.