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有害物質의 毒性評價方法論에 관한 고찰 : LD50推定法을 중심으로
高應麟 漢陽大學校 環境科學硏究所 1980 環境科學論文集 Vol.1 No.-
有害物質의 毒性水準을 計量化하여 표시해주는 指標로서 흔히 이용되고 있는 ??(50%有效量) 또는 ??(50%致死量)의 推定方法論에는 15餘種이 제시되어 있다. 이와 같이 많은 方法論들은 각기 서로다른 假定과 이론적 배경에 입각하여 유도된 것이기 때문에 상호관련성을 파악하지 못하고 있는 실제 실험가들의 입장에서 취사선택하는데는 어려움이 있게 되고 또한 誤解와 誤用의 가능성도 많은 것이다. 본 논문에서는 이들 여러 방법론 중에서 주요한것 6가지를 선택하여 각 방법론의 이론적 배경을 요약하고 구체적인 산출과정을 예시해주므로서 방법간의 차이점의 이해와 올바른 응용에 도움을 주는데 목적을 두고 있다. 여기서 선택된 방법론은 parametric法에 속한것 3가지와 non-parametric法에 속한것 3가지 모두 6가지로서 다음과 같다. (1) Probit분석법 (2) Logit분석법 (3) Spearman-Karber법 (4) 이동평균법 (5) Reed-Muench법 (6) 증감분석법 종합적으로 이들 각 방법론들간의 (1)가정 (2)구간추정 (3)실험계획 (4)기타 등을 중심으로 차이점과 장단점을 정리해 본 결과는 다음과 같다. 1. 모든 방법론이 갖고 있는 共通點 (1) 어떤 용량에서 반응을 나타낸 동물은 그보다 높은 용량에 의해서도 반응을 나타낼 것이다 라는 가정 (2) 따라서 용량별 반응률의 분포는 누적분포의 형태를 따른다고 본다. (3) 그리고 이 누적분포는 동물의 생체저항력분포(밀도함수)(Tolerance density function)의 積分과 일치한다고 본다. (4) 이 생체저항력분포는 對數用量上에서 對稱的인 모양을 나타낸다고 본다. (5) 따라서 ??(즉, 중앙치)는 이와같은 생체저항력분포의 평균치로서 추정할 수 있다. 2. 방법론간의 차이점과 장단점 (1) Probit법 가)點推定理論 : ① Tolerance분포의 모양을 정규분포로 가정한다. ② 반응률을 전환시켜 희기직선 분석법을 적용한다. 나) 區間推定 : ① Fieller의 구간추정공식을 이용한다. 다) 實驗計劃 : ① 대수용량의 간격은 일정하지 않아도 된다. ② 용량당 동물수도 일정하지 않아도 된다. ③ 타당성검정(모델에 대한)이 가능하다. 라) 기타 : ① 계산과정이 가장 복잡하나 Computer의 이용이 가능하다면 가장 추천할만한 방법이다. (2) Logit법 가) 點推定理論 : ① Tolerance 분포의 누적곡선은 Logistic 곡선을 따른다고 가정한다. ② 반응률을 전환시켜 희기직선 분석법을 적용한다. 나) 區間推定 : ① Filler의 구간추정공식을 이용한다. 다) 實驗計劃 : ① Probit법 때와 같다. 라) 기타 : ① 이 방법도 계산과정이 복잡하므로 Computer의 이용이 추천된다. ② 반응률의 전환식으로서 ⓐ?? ⓑ?? ⓒ?? 등이 있음으로 전환표를 이용할 때는 어느 것인가를 확인해야 한 다. 본 논문에서 제시된 것은 ⓐ의 것이다. (3) Spearman-Karber법 가) 點推定理論 : ① Tolerance 분포의 형태에 관해서는 대칭적이라는 가정만 세우고 있다. ② 따라서 non-parametric법에 속한다. 나) 區間推定 : ① 용량별 반응률의 분산을 이용한다. 다) 實驗計劃 : ① 대수용량의 간격이 일정하다. ② 용량당 동물수도 일정한 것이 바람직하다. ③ 반응률이 0%와 100%인 용량이 끼어있어야 한다. ④ 용량간의 간격이 좁을수록 정밀성이 높다. 라) 기타 : ① 계산과정이 대단히 간단하다. ② 구간추정도 간단하다. ③ 손쉽게 이용할 수 있는 가장 실용적인 방법이므로 적극 권장할 수 있다. (4) 이동평균법 가) 點推定理論 : ① Spearman-Karber법 때와 같다. 나) 區間推定 : ① 용량별 반응률의 분산을 적용한다. 다) 實驗計劃 : ① 반응률이 0%와 100%인 용량이 끼어있지 않아도 좋다. ② 이동평균치계산시 관측치들의 묶음의 크기는 3정도이다. 라) 기타 : ① 계산과정이 비교적 간단하다. ② 용량의 종류가 많을 때 이용할만한 방법이다(6이상). (5) Reed-Muench법 가) 點推定理論 : ① Spearman-Karber법 때와 같다. 나) 區間推定 : ① 없다. 다) 實驗計劃 : ① 대수용량간격이 일정하고 용량별 동물수도 일정함이 바람직하다. 라) 기타 : ① 계산과정은 간단하나 구간추정을 할 수 없다. ② 따라서 추천할만한 방법이 못됨. (6) 증감법 가) 點推定理論 : ① Tolerance 분포를 정규분로로 가정한다. 나) 區間推定 : ① 평균치의 표준오차 계산의 개념을 적용한다. 다) 實驗計劃 : ① 한마리씩 독립적으로 실험해야 한다. ② 실험중단기준은 없다. ③ 대수용량의 적절한 간격설정이 쉽지않다. ④ 대수용량의 간격은 일정해야 한다. 라) 기타 : ① 실험동물수에 절약을 기대할 수 있다. (약 30%~40%정도의 절약이 가능하다. ② 값비싼 동물실험시에 유용하다. The measurement of the level of toxicity based on the quantal (all or nothing) experiments is a common practice in toxicological experimentation and quite a variety of methods are proposed for estimating the median effective (or lethal) dose from such experimental data. Since the theoretical model and the conditions to be met in data vary with the methods proposed, misunderstanding and misuse of the methods are quite commonly encountered. To provide a handy manual for experimenters or statistical analysists engaged in toxicological experiment, the author has selected six representative examples of methodology(three from non-parametrict method and the other three from parametric method) and presented brief outlines of theoretical background, advantages, disadvantages and stepwise calculation procedures for practical application. The six methods presented in this paper are as follows. 1) Probit analysis 3)Spearman-Karber method 4) Moving average method 5) Reed-Muench method and 6) Up and down method. In addition to the brief description of model and the demonstration of detailed scheme of computation based on some artificial experimental data, the following points were stressed. 1. The common assumptions to all methods It is assumed in any method of estimating the median effective dose that (a) at a given dose level those animals will respond whose tolerance doses are at or below that level. (b) the expected response rate at successive dose levels will therefore describe the probability integral of the tolerance density function. (c) the tolerance density function is symmetrical of the doses expressed in their logarithm. 2. Comparison of methods (1) Probit analysis a) Model : The normal density function is assumed for tolerance function. The estimation of median effective dose is based on the iterative linear regression analysis between transformed variables (probits) and log doses. b) Interval estimation : Fieller's theorem is applied. c) Experimental design : The constant number of subjects per dose and the constant log dose interval are preferred but not strictly required. It provides validity test which many other methods lack. d) Others : The computation is rather laborious. This method is highly recommendable when computer program is available. (2) Logit analysis a) Model : The cumulative tolerance distribution assumed to follow logistic function. The estimation of median effective dose is based on the iterative linear regression analysis between transformed variables (logit) and log doses. b) Interval estimation : Fieller's theorem is applied. c) Experimental design : The same as in Probit analysis. d) Others : Three commonly used transformation formulas are available. In applying the logit tranformation tables, care should be taken to confirm which formula was used. (3) Spearman-?? method a) Model : No assumption except "symmetric" is made to the tolerance density function. b) Interval estimation : The variances of response rates are utilized in estimating the confidence interval. c) Experimental design : The log dose interval and the number of subjects at each dose are recommended to be held constant. Expreme doses (i.e., doses which yield 0% and 100% responses) are to be included in the data. To improve the precision, it is recommended to narrow the dose intervals, that is, to use a few subjects at each of many doses rather than to use many subjects at each of a few doses. d) Others : The calculation is very simple and still the interval estimation is available. It is a highly recommendable method for practical use. (4) Moving average method a) Model : Symmetry is assumed for tolerance density function. b) Interval estimation : The variances of response rates are utilized. c) Experimental design : The number of dose level should exceed the span of moving average. The allocation of the extreme dose levels as in Spearman-?? method is not required. d) Others : If enough doses are used, this method of estimation with a span of 3 or greater may be preferable to the Spearman-Karber method. (5) Reed-Muench method a) Model : Only the symmetry is assumed in tolerance density function. b) Interval estimation : Not available. c) Others : No assessment of precision is available. This method is not to be recommended. (6) Up and down method a) Model : The underline tolerance density function is assumed to be a normal curve. b) Interval estimation : It makes use of "standard error of the mean" concept in estimating the confidence interval. c) Experimental design : It requires each specimen be tested separately. There is no stopping rule as in general sequential analysis. The choice of log dose interval could be a difficult problem encountered in actual design. d) Others : This method requires fewer test animals, the savings may be of the order of 30~40%.
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한국인의 B형 간염 감염에 관한 실태조사와 통계적 분석 연구
고응린 한양대학교 의과대학 1986 한양의대 학술지 Vol.6 No.1
It has been widely accepted that Hepatitis B infection has emerged as a major public health problem throughout the world particulary in the areas where the prevalence of the disease is remarkably high. Quantitative assessment of disease occurrence, therefore, is of primary importance not only in designing the measures to meet the situation but also in evaluating the progress of such programs. Since 1965 when Australia antigen was discovered, much has been studied on all aspects of Hepatitis B ranging from the development of more appropriate laboratory techniques for the detection of serological markers to the clinico-epidemiological pattern analysis and explorationg of vaccine against the disease. With all such development, the assessment of the magnitude of disease occurrence in the country has not been at a satisfactory level even in the estimation of the positive rate of a marker such as HBsAg among the general population. Because of relatively easier access to the blood specimens and laboratory facilities, the studies and HBs marker's prevalence in the past were mostly confined to blood donors, hospital patients and special professional group all of which are far from being representative of the general population. Standardized HBs marker's positive rate among the general population To establish a standard value of HBs marker's positive rate among the Korean population, this study was designed to collect the data of serological findings of a total of healthy 6,296 visitors to the Red Cross Hospital in Seoul from October 1983 to October 1984. Also planned was to bring together a collection of recent studies for the synthesis of data pertinent to elucidation of HBsAg and anti-HBs positive rates of the Koreans. The synthesized data were limited to those of serological findings of healthy group tested by RIA and/or RPHA method. The substantial irregularities of age specific rates between the consecutive age groups were smoothed out by the method of moving average and the rates were applied to the population structure of Korea (1980 census data) to calculate the age standardized rate for each sex and sex-age standardized rate for an overall rate. The salient findings were (1) Age-standardized HBsAg positive rate for the male population was estimated by 8.6% and for the females by 7.3% (Table 7). (2) Sex-age-standardized HBsAg positive rate for whole population of Korea was estimated by 8.0% (Table 7). (3) Age-standardized anti-HBs positive rate for the male population was estimated to be 15.8% and for the females to be 21.7% (Table 8). (4) Sex-age-standardized anti-HBs positive rate for whole population of Korea was estimated by 18.7% (Table 8). (5) As for the sex differentials in age specific HBsAg positive rate, the female's rates were relatively lower than those of males in the age group of 40 years or less which agree with our general notion. However, it was rather peculiar to find that the pattern turned out to be reversed, that is, the female's rates were higher than those of males after 40 years of age (Table 5). A similar pattern could be observed in age specific anti-HBs positive rates. Whether or not this pattern might be simply due to a random variation need to be explored further.
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