1. A clinical information processing apparatus comprising: a memory device which stores a clinical information database including: registration case information for calculating a likelihood ratio including a multiplicity of registration cases about a plurality of comparison target patients, and to each of the multiplicity of registration cases a plurality of clinical-information items each of which is classifiable into a plurality of groups being correlated; and registration case information for calculating a degree of similarity including a multiplicity of registration cases about a plurality of comparison target patients, and to each of the multiplicity of registration cases a plurality of clinical-information items each of which is classifiable into a plurality of groups being correlated; a processing apparatus comprising: a target case obtainment unit that obtains, as a target classification of a target clinical item, a classification of each of a plurality of clinical-information items about a target patient; and a display control unit; a registration case information obtainment unit that accesses the memory device and obtains from the clinical information database the registration case information for calculating a likelihood ratio and the registration case information for calculating a degree of similarity; a likelihood ratio information calculation unit that calculates, based on the registration case information for calculating a likelihood ratio, likelihood ratio information for each combination of each classification of a key item of the clinical-information items and each classification of at least one clinical-information item other than the key item and the likelihood ratio information being obtained by calculating a likelihood ratio between a likelihood of belonging to one classification of the key item and a likelihood of belonging to any classification of the key item other than the one classification of the key item when a case belongs to each classification of the at least one clinical-information item other than the key item; a weighting coefficient determination unit that calculates, for each of the combinations, values in such a manner that the weight of the value become greater as the likelihood ratio corresponding to the combination is greater, and that determines weighting coefficients by weighting the calculated value in such a manner that a weight of the value corresponding to the target classification is greater than or equal to the weight of the value corresponding to the classification other than the target classification for each of the clinical-information items; a degree-of-similarity calculation unit that specifies, based on the determined weighting coefficient information, the weighting coefficient corresponding to each classification of the key item and each classification of at least one clinical-information item other than the key item for each of the registration cases included in the registration case information for calculating a degree of similarity, and that calculates a degree of similarity by using the specified weighting coefficient; a similar case output unit that: extracts, from among the registration case information for calculating a degree of similarity, the registration case, the calculated degree of similarity of which is higher than a predetermined value, as a similar case, which is similar to the target case; retrieves similar case information related to the extracted similar case; and outputs the retrieved similar case information to the display control unit; and a display device which is controlled by the display control unit of the processing apparatus, and displays the similar case information.