[Proportion and rate: connotation and understanding route].

Proportion and rate have multiple and overlapping meanings, which blur their concepts. Based on the existence of the states and the occurrence of the events and their measuring process, we first put forward the concept of "cumulative number of states in point time". Considering the general meaning of "rate" in mathematics and the units of the elements in indexes, this paper puts forward the concept of "the change of cumulative number of states in point time", which is equal to the commonly acknowledged concept "number of incident event within observation period" or "absolute rate", and further constructs relative rate and proportion. Proportions can be classified into three types: time-point (or rate-type) constitutional proportion, time-period incidence proportion and their synthesis, time-period constitutional proportion. The essential difference between relative rate and time-period proportions is whether the observation period is regarded as a one-unit-length fixed period which would be further moved to the description of the indexes. Furthermore, the sources populations of relative rate and proportions are exclusively those at the beginning of the observation period. Thus, we established a unified identification route about ratios, proportions, and rates, the basic indicators of categorical data in populations. These are applicable to both fixed and dynamic populations. The paper aims to clarify the connotation of the indexes and the feasible understanding route and provide some reference for the population researchers.