Abstract: Causal effect analysis is an important and popular method in clinical statistics, which typically conducted based on the observational data. However, the analysis based on observed data may be affected by unobserved variables, which may produce bias, leading to estimate the causal effects inaccurately. Existing methods ignore the unobserved variables or are unable to find appropriate proxy variables to weaken this bias, which fail to provide reliable estimation of the causal effects. To address this problem, this paper proposes the instrumental variable method, a more accurate computational method than traditional approaches in the realm of clinical statistic for drug efficacy analysis. This method incorporates the effect of unobserved into the error term, to estimate the accurate causal effect. Under some mild assumptions, the variables in the observational data is considered as instrumental variables. Then, the proposed method calculates the effects of butylphthalide (i.e., a drug) on patients with acute ischemic stroke (AIS) in the presence of unobserved variables. The causal effect of monthly prognosis and the confidence interval of this causal estimator is estimated. The study results show that the butylphthalide has a significant positive effect on the prognostic recovery of patients with acute ischemic stroke.

Key words: unobserved variable, instrumental variable, butylphthalide, causal effect estimation