In clinical chemical inspection, we measure human body fluids such as various sera. It is important to manage the accuracy of measurement because measurement values contain measurement errors. The Japan Medical Association and the Japanese Association of Medical Technologists conducted a survey for all institutions to improve the quality of accuracy management. In the survey, the same samples of sera were distributed to the participating institutions, and the resulting measurement values were studied in order to gauge measurement ability. The survey is conducted once a year, and about 2300 institutions take part in it.
　The samples distributed as part of the survey are artificially synthesized 'controlled sera'. The properties of a controlled serum must be similar to those of the natural serum sampled from humans because, of course, we measure a natural serum in clinical chemical inspection. But it is difficult to investigate all of the various physical and chemical properties of a controlled serum.
　 In this paper, we propose a method to statistically analyze the similarity between a controlled serum and its natural counterpart by comparing measurement values of both at each institution. The method considered with the functional relation because measurement values contain errors.
　The proposed method makes it possible to identify controlled sera whose properties differ from their natural counterparts, by analyzing measurement values of the regular measure.

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　This paper gives a collapsibility condition for a partial regression coeffcient in a linear regression model. It is shown that the collapsibility condition is useful as a covariate selection criterion when the regression model is used to estimate a causal effect of a treatment variable in observational study. Consider a full model y=Xβ_x・wu+Wβ_w・xu+Uβ_u・xw+ε and a reduced model y=Xβ_x・w+Wβ_w・x+ε*. We will say that U is collapsible with respect to X - Y relationship whenever β_x・wu=β_x・w for the same sample.As a result of this paper, the collapsibility condition is given by X'U-X'W(W'W)^-1W'U=0 or β_u・xw=0. The algorithm for selecting a sufficient set of covariates satisfying the above collapsibility condition using the theory of undirected graphical model is also investigated.

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