An indicator quantitatively comparing two treatment effect sizes on responder and non-responder groups--exponential of estimated interaction parameter.

Sometimes a specific treatment is effective in one subgroup but not in another. An indicator allowing quantitative comparison of treatment effect in two subgroups would be useful in clinical medicine. We have developed such an indicator. It is obtained by calculations using Cox's proportional hazard or logistic model with therapy, subgroup, and confounding explanatory variables. The parameter of the interaction between therapy and subgroup can be estimated and tested statistically. The exponential value of the interaction parameter is what we tentatively call the "hazard ratio ratio", meaning the ratio between the treatment effects in two subgroups. The 95% confidence interval of the indicator can also be calculated. As a numerical example, the hazard ratio between the survival times of postoperative gastric cancer patients treated by adjuvant immunochemotherapy and patients without adjuvant immunochemotherapy in a subgroup with high serum glycosidically bound sialic acid (SA) level was lower than that in a low-SA subgroup using an estimate for hazard ratio ratio of less than 0.5 with statistical significance. We propose this indicator be used as a "responder/non-responder ratio" of therapy effect.