Background ― In medical research, longitudinal studies have important and functional roles. Generalized estimating equation (GEE) is used for the analysis of longitudinal and correlated data required to determine the correlation structure among responses. If this structure is set incorrectly, the parameter estimates will be consistent thus this method may not work. To improve the efficiency of parameter estimates, the quadratic inference function (QIF) method is therefore proposed. The objective of this study is to evaluate and compare the performance of these two methods. Methods ― This study was designed to compare the efficiency of parameter estimates using data from one blinded randomized clinical trial on the impact of probiotic drops on infantile colic. The effect of probiotic drops on crying time was modeled by GEE and QIF methods. Based on parameter estimates, the efficiency of the two methods was compared. Results ― The coefficient estimates of the two methods changed only slightly however, the relative efficiency of the parameter estimates from GEE and QIF was 1.23, when used on a mis-specified first-order autoregressive correlation structure. Therefore, for the specified correlation structure that is exchangeable, the relative efficiency was 1.001. The findings obtained from the QIF method showed that the mean baby crying had a significant difference on time between the two cases and control groups (P<0.001). Time (first, second and third weeks) was shown to be a major determinant of healing in infantile colic (P=0.001). Conclusion ― When selecting an incorrect correlation structure, the QIF method is more efficient than GEE. Thus, GEE can help researchers obtain more reliable results herein.