19. Causal Inference and Missing Data Problems

Well established physical theories are developed under rigorous mathematical reasoning and tightly controlled laboratory experiment tests. In randomized clinical trials for the comparison between treatment and control, patients are randomly assigned to one of the two groups. As a consequence, baseline profiles are balanced between the two arms, i.e., they have the same distribution. In observational medical studies or epidemiological researches, however, insights from biology and intuition may suggest possible treatment effects while the underlying experiments may not have a rigorous design, which lead to unbalanced baseline patient characteristics between groups. Similarly in evidence based economic studies, there is no control over intervention programs. As a result participation may not be completely at random. Some individuals may be more likely to participate than others. The fundamental problem of causal inference is that we can only observe one of the two potential outcomes for a particular subject. It is impossible to conduct a paired t-test for the assessment of treatment effects. On the other hand, the unpaired two sample t-test or Wilcoxon test may produce biased results for treatment effects since they fail to adjust for baseline covariates.