Studying the essence of syndromes (Zheng) in traditional Chinese medicine (TCM) is a fundamental challenge in basic theoretical research of TCM. The relationship between any given syndrome and biochemical indicators is one of the important aspects of the study. As the indexes selected in each study are specific to a particular Western medical disease diagnosis, and the disease factor is inevitably introduced into the study, the effect of disease factor on the index changes cannot be assessed effectively by traditional data processing methods. This is known as "the same syndrome with different reasons", which has resulted in confusion in TCM research. This study aimed at providing a mathematical tool to address this issue. Based on information theory and the residual-split method, the syndrome information, which was covered in the index variation, was quantitatively calculated in this paper as an independent part of the disease factor. A mathematical model capable of objectively assessing and statistically testing the effect of the syndrome factor on the index changes was established. Applying this model to literature data of studies on the relationship between cyclic nucleotides and yang-deficiency syndrome showed following results. First, the values of yang-deficiency syndrome information were negative for cyclic adenosine monophosphate (cAMP) while positive for cyclic guanosine monophosphate (cGMP) in all included literature. This indicated that the group of yang-deficiency syndrome was correlated with an obvious trend of reduced cAMP levels and increased cGMP levels. Second, the statistical test results of yang-deficiency syndrome information of the two indexes were different among the literature included. The quality of original data was considered as a possible reason. Third, the significant differences between the yang-deficiency group of a specific disease and the normal group may, in some cases, be caused by a disease factor rather than a syndrome factor. The mathematical model provided a reasonable mathematical tool for the analysis of disease factor and syndrome factor in clinical research of TCM, suggesting that the mathematical model may give rise to innovative ideas and methods in the study of syndromes.