Estimation of a treatment effect based on a modified covariates method with \(L_0\) norm

In randomized clinical trials, we assumed the situation that the new treatment is not adequate compared to the control treatment as a result. However, it is unknown if the new treatment is ineffective for all patients or if it is effective for only a subgroup of patients with specific characteristics. If such a subgroup exists and can be detected, the patients can receive effective therapy. To detect subgroups, we need to estimate treatment effects. To achieve this, various treatment effect estimation methods have been proposed based on the sparse regression method. However, these methods are affected by noise. Therefore, we propose new treatment effect estimation approaches based on the modified covariate method, one using lasso regression and the other ridge regression, using the \(L_0\) $L_0$ norm. The proposed approach was evaluated through numerical simulation and real data examples. As a result, the results of the proposed method were almost the same as those of existing methods in numerical simulations, but were effective in real data example.