Altern. Animal Test. EXperiment. 5, 39-58 (1998)

Validation Study on Five Cytotoxicity Assays by JSAAE
II.
Statistical Analysis
Takashi Omori1, Kaoru Saijo2, Mayako Kato2, Makoto Hayashi3, Hiroshi Itagaki4,
Satoru Miyazaki5, Tadao Ohno2*, Hideaki Sugawara5, Noriko Teramoto2, Noriho
Tanaka6, Shinobu Wakuri6, and Isao Yoshimura1(The Working Group for data analyses in this validation study)
1

Department of Management Science, Faculty of Engineering, Science Univeristyof Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162, 2RIKEN Cell Bank, The Institute of Physical and Chemical Research (RIKEN), 3-1-1 Koyodai, Tsukuba Science City, Ibaraki 305, 3Shiseido Safety & Analytical Research Center, 1050 Nippacho, Kohoku-ku, Yokohama-shi 223, 4Division of Genetics and Mutagenesis,
National Institute of Health Sciences, 1-18-1 Kamiyoga, Setagaya-ku, Tokyo 158,
5
Life Science Research Information Laboratory, The Institute of Physical andChemical Research (RIKEN), 2-1 Hirosawa, Wako-shi, Saitama 351-01, 6Hatano
Research Institute, Food and Drug Safety Center, 729-5 Ochiai, Hadano-shi,
Kanagawa 257, Japan
Abstract
The validation study organized by JSAAE (JSAAE study) brought to light
three main statistical problems, namely, (1) how to obtain a reliable estimate of
ED50 from each experiment, (2) how to check the availability of the ED50 estimate obtained from each experiment, and (3) how to evaluate the feasibility of
assays included in the JSAAE study.
To resolve the first problem, the authors devised a computer program (LAPJSAAE) on SAS which incorporated a non-linear least squares method to obtain
estimates of ED50 based on a logistic model for raw measurements. To resolve
the second problem, the authors set several criteria for checking data which had
previously been treated with manual adjustments for trivial errors such as de* Correspondence : The Working Group of JSAAE for the
1st Validation Study on Cytotoxicity Assays, c/o T.
Ohno, RIKEN Cell Bank, 3-1-1 Koyadai, Tsukuba Science City, Ibaraki 305, Japan
Key words: alternatives, chemical irritancy, colony formation assay, crystal-violet staining assay, cytotoxicity assay, Draize eye irritation test, ED50, inter-laboratory validation, LDH release assay, logistic model,
MTT assay, neutral red uptake assay, non-linear leastsquares method

Abbreviations: CF, colony formation; CV, crystal-violet
staining; ED50, 50% effective dose; FRLA, factor forremaining LDH activity; JSAAE, Japanese Society of
Alternatives to Animal Experiments; JSAAE study, thevalidation study organized by JSAAE; LDH, lactate
dehydrogenase release; MTT, 3-(4,5-dimethylthiazol2-yl)2,5-diphenyl tetrazolium bromide; NR, neutral red
uptake; PFD, power for distinction.
Received: July 4, 1997. Accepted: September 10, 1997.

– 39 –

Validation Article II. Statistical analysis

scriptions out of format. They are related to detecting extraordinary large observations, inspecting excessively wide confidence intervals obtained by LAPJSAAE, checking whether observed responses, for at least one dose, are within
the range of 20% and 80%, assessing the lack of fit to the logistic model, and soon. To resolve the last problem, the authors devised the “power-for-distinction”(PFD) which was defined as the ratio of the range of medians to the mean valueof the hinge-spreads for log(ED50), where medians and hinge-spreads are frominter-laboratory variation and the range and the mean are from chemical response
variation.
After establishing the methods, the authors performed data analysis for the
JSAAE study and concluded that the crystal-violet staining assay (CV) with HeLa
S3 (SC) cells and the colony formation assay (CF) with HeLa S3 (SC) cells arereliable in the sense that they give high values of the PFD.

1. Introduction

make some remarks on their application to suchdata as in this study.

In 1992, the Japanese Society for Alternatives
to Animal Experiments (JSAAE) organized avalidation study, the JSAAE study, to evaluate
the feasibility of five cytotoxicity assays (CF,CV, LDH, MTT, and NR) as a part of alternatives for the Draize eye irritation test (Ohno etal., 1995). The principal results obtained in thisstudy were reported in the preceding article (Validation Article I) in this issue, where the 50% effective dose (ED50) was the index used to assess the toxicity of chemicals.
The authors encountered some statistical issues during the course of data analysis in thisJSAAE study, and accordingly, were forced toaddress them before the completion of data
analysis. Through intensive discussions within
the working group composed of the authors of
this paper, the issues were reduced to the following three problems: (1) how to obtain a reliable estimate of ED50 from each experiment,(2) how to check the availability of the ED50
estimate obtained from each experiment, and (3)how to evaluate the feasibility of assays includedin the JSAAE study.
We devised statistical methods to answer
these problems, and subsequently applied themto analyse the data gathered in the JSAAE study.
The results obtained and conclusions drawn were
described in Validation Article I. In what follows,
we explain these devised methods along withcomputer programs named LAP-JSAAE and2. Data in the JSAAE study
In the JSAAE study, the toxicity of six chemicals, one of which was dupulicated under adouble-mask code to assess the reproducibilityof results, was measured by four cytotoxicity
assays (CF, CV, MTT, and NR) and the LDHrelease assay sub-divided into four assays (LDH1, LDH-2A, LDH-2B, LDH-2C) using two celllines as has been described (see Validation Article I in this issue).
The committee for the JSAAE study specified that one data file for each experiment with achemical in each assay using a cell line be constructed by all laboratories that participated in
the study. Therefore, one value of ED50 was
assumed to have been obtained from each data
file corresponding to one experiment. Each data
file contained various data such as the date of
the experiment, the name of laboratory, and soon. The essential details of raw data from eachassay necessary to estimate ED50 are shown in
Tables 1 through 4. The principal data in the four
assays excluding CF were measurements of optical density (OD) while those in CF were numbers of colonies, reflecting the proportion of survived or damaged cells incubated in the corresponding well.
To formulate the devised methods, it was convenient to express the data by variables. We de-– 40 –

Response(%)

100

pendices A and B. The superscript "A" simply
implies the first sheet, "C", the cell layer, and"S", the supernatant of the solution.
3. ED50 estimation

50

0
ED50

Dose

Fig. 1. Illustration of the relationship between doseresponse curve and ED50

noted the OD measurement or the number ofcolonies by z with subscripts such as i, j, B, N,
and P, corresponding to the i-th dose (or concentration) level di of the test chemical, the j-th
repetition, the blank, i.e., vacant-cell-well, thenegative control, i.e., zero-dose level, and thepositive control, i.e., a toxic chemical specified
in the protocol, respectively. Further, we denoted
the number of dose levels, excluding negative
control, positive control, and blank, by a and thenumber of repetitions of measurement by r. Numeric values of these variables given in Table 1
are such that zB1=0.057, zN1=0.528, d1=0.005,
z11=0.680, z12=0.255, a = 7, r = 6 and, in Table 2,
zN1=0.096, zP1=0.349, d1=0.25, z11=0.101, and soon.
In the case of CF, the number of cells inoculated in each well was also necessary in order toestimate the proportions of survived cells, andhence was denoted by a variable such as sB or si.
Note that they were regarded as error-free values in the data analysis of the JSAAE study because it was believed that their variabilities did
not affect the results. Likewise in case of the
LDH assay, the factor for remaining LDH activity (FRLA) in the i-th dose, i = 1, 2, ... , a isnecessary and hence denoted by ci, the meaningof which is explained in Validation Article VI.
In the case of LDH-2A, 2B, and 2C, threeinterrelated data sheets, which were distinguished by superscripts A, C, and S, were usedin part or simultaneously as is explained in Ap-

3.1 Difficulty inherent in the conventional
ED50 estimation
In this section, we deal only with the case of
the CV assay to explain the problems to be resolved, leaving the case of other assays to Appendices, since the issues in question were essentially the same for all assays.
In the field of in vitro cytotoxicity testing, therelationship of the survived proportion of incubated cells with the applied dose of chemical isreferred to as the dose-response relationship or
the dose-response curve, and the toxicity of thechemical tested is assessed by ED50 which isconceptually defined as the dose inflicting damage on 50% of incubated cells or, in other words,
maintiaining 50% of survived cells as is seen in
Fig. 1. Practically, however, the true dose-response curve as well as ED50 cannot be known
exactly and, therefore, have to be estimated fromexperimental data.
In the case of the CV asssay, the response,
i.e., the survived proportion pi (%) of incubatedcells treated with dose di, is conventionally calculated by Equation (1) where the z refers to themean of the observed z values at each dose (i),blank (B), or negative control (N). Formulaefor other assays are given in Appendix A.

To estimate ED50 from this type of dose-response data {(di, pi); i = 1, 2, ... , a}, it is quite
reasonable to assume a suitable function as thedose-response curve and fit it to the data. The
dose corresponding to 50% response on the fitted function was taken to be the ED50 value. As
for the suitable function and the method of curve
fitting, a probit function, i.e., the cumulative
normal distribution function and a probit analy-– 41 –

Validation Article II. Statistical analysis

Table 1. An example of raw data in a CV assay
zij’s are OD measurements and di’s are doses.
In this case, the number of dose levels is a = 7 and the number of repetition is r = 6. The same
form of data as CV is used in the case of the NR assay.
File: 20CVC7.TXT
Dose (% in W/V)
Blank
Negative control
d1 = 0.005
d2 = 0.01...
d7 = 0.06

OD measurement
Plate 1zB1 = 0.057
zN1 = 0.528
z11 = 0.680
z12 = 0.581
z21 = 0.525
z22 = 0.526...
z71 = 0.060
z72 = 0.059

Plate 2zB2 = 0.052
zN2 = 0.513
z13 = 0.255
z14 = 0.435
z23 = 0.313
z24 = 0.456...
z73 = 0.060

Plate 3zB3 = 0.064
zN3 = 0.582
z15 = 0.592
z16 = 0.444
z25 = 0.494
z26 = 0.455...
z75 = 0.060

z74 = 0.059

z76 = 0.061

Table 2. An example of raw data in a MTT assay
zij’s are OD measurements and di’s are doses.
In this case, the number of dose levels is a = 12 and the number of repetition is r = 3.
File: 3MH3.TXT
Dose (% in W/V)
Negative control
Positive control
d1 = 0.25
d2 = 0.10...
...
d10 = 0.01
d11 = 0.001
d12 = 0.0001

OD measurement
Plate 1zN1 = 0.096
zP1 = 0.349
z11 = 0.101
z21 = 0.555...
...
z101 = 0.465
z111 = 0.525
z121 = 0.529

Plate 2zN2 = 0.076
zP2 = 0.419
z12 = 0.057
z22 = 0.547...
...
z102 = 0.480
z112 = 0.480z122 = 0.472

sis method have been conventionally used as
specified in the initial protocol for each assay.
Applying the protocol to collected data, however, we found that reasonable estimates of ED50
could not be obtained in some cases such as
shown in Fig. 2; in one case, the applied method

Plate 3zN3 = 0.050
zP3 = 0.701
z13 = 0.063
z23 = 0.684...
...
z103 = 1.128
z113 = 0.737
z123 = 0.720

did not yield any estimate and in another case,the acquired estimate was far from a reasonablevalue in the sense that it deviated from the visually plausible one as is shown in Fig. 3. Aftersome examinations and discussions, we understood that the failure resulted from the inappro-– 42 –

Table 3. An example of raw data in a CF assay
zij’s are number of colonies, di’s are doses, and si’s are number of seeds.
In this case, the number of dose levels is a = 6 and the number of repetition is r = 4.
File: 40CH6-3.TXT

Number of colonies
Seed

Dose (% in W/V)
Negative control sN = 100
d1 = 0.012
s1 = 100d2 = 0.011
s2 = 100d3 = 0.010
s3 = 100
d4 = 0.009
s4 = 100
d5 = 0.008
s5 = 100
d6 = 0.007
s6 = 100

Dish 1zN1= 92z11 = 0z21 = 0z31 = 3z41 = 49z51 = 61z61 = 83

Dish 2zN2 = 77z12 = 0z22 = 2z32 = 2z42 = 38z52 = 69z62 = 84

Dish 3zN3 = 100z13 = 0z23 = 1z33 = 3z43 = 56z53 = 67z63 = 81

Dish 4zN4 = 106z14 = 0z24 = 1z34 = 2z44 = 53z54 = 58z64 = 80

Table 4. An example of raw data in a LDH-1 assay
zij’s are OD measurements, di’s are doses, and ci’s are factors of remaining LDH activity.
In this case, the number of dose levels is a = 6 and the number of repetition is r = 6. The formof data in LDH-A, B and C is the same as this one.
File: 46AH1-2.TXT
Dose (% in W/V)
Blank

Factor

Negative control
Positive control
d1 = 0. 200

1.0
1.0
c1 = 1.43

d2 = 0.125

c2 = 1.42... ...
d6 = 0.050...
c5 = 1.41

OD measurement
Plate 1zB1 = 0.189
zN1 = 0.190
zP1 = 0.665
z11 = 1.195
z12 = 1.129
z21 = 1.161
z22 = 1.078... ...
z61 = 0.427
z62 = 0.659

priateness of the adopted method for the collecteddata.
As is well known (Finney, 1971, 1985a), theprobit analysis method comprises a variety ofalgorithms for practical use, a typical one being
the maximum likelihood method based on the

Plate 2

Plate 3zB2 = 0.309
zN2 = 0.300
zP2 = 0.781
z13 = 1.335
z14 = 1.258
z23 = 1.297
z24 = 1.201

zB3 = 0.245
zN3 = 0.252
zP3 = 0.676
z15 = 1.271
z16 = 1.192
z25 = 1.235
z26 = 1.115

z63 = 0.555
z64 = 0.739

z65 = 0.474
z66 = 0.695

assumption of binomial distribution and anotherone being the graphical method such as the
Litchfield-Wilcoxon method (Litchfield &Wilcoxon, 1949). All of them, however, have acommon feature in that they are essentially basedon the line fitting with proper weight on the re-– 43 –

Validation Article II. Statistical analysis
CF 13ch2

120

Fig. 2. An example of data file on which a probit
analysis method failed to yield ED50 estimate.

110
100
90

Rate(%)

80
70
60
50
40
30
20
10
0
-2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2 -1.9 -1.8 -1.7 -1.6 -1.5log(Dose)

CV 2cvc3-2

250

Fig. 3. An example of data file with which estimated ED50 by a probit analysis method is far different from a visually-obtained estimate.
The log(ED50) estimated by a probit analysis
method is -12.6.

225
200

Rate(%)

175
150
125
100
75
50
25
0
-5

-4.5

-4

-3.5
log(Dose)

-3

-2.5

sponse values obtained through a transformationsuch as the probit transformation. This common
feature, without doubt, brought us the abovementioned difficulty because some of response
values were outside the range of 0% and 100%,
although they were assumed to be within thisrange. If we would apply the probit method tothe collected data ignoring this feature, we shouldhave removed such measurements ignoring therisk of biases in estimation. In reality, however,it was not acceptable and, accordingly, we wereforced to devise another method to obtain reasonable ED50 estimates.
3.2 Proposed method of ED50 estimation
3.2.1 Logistic model on the raw data
Since the basic concept of the proposed
method is essentially the same in all assays, we
explained our idea using the case of the CV assay with a logistic function exemplified by thedose-response curve, leaving the details in othercases to Appendix B.
The difficulty mentioned above was obviously due to the improper recognition of errors

such that the measurements, especially for theblank and control, are not affected at all, or at
most in negligibly small orders, by measurement
errors and, therefore, responses calculated by theformula (1) can neither be less than 0% nor
greater than 100%.
In reality, however, they are affected by manysources of errors such as the number of cells incubated, time duration of processing, diluting of
the concentration of the test chemical, measurement of OD, etc. Their influence is not at all
negligible. Actually, the variability of measurements within the same dose is rather large, andthe assumption of small errors is not correct as
is seen in Fig. 2 and 3. Consequently, it became
necessary to construct a suitable model on measurements incorporating the errors such as theone characterized above.
As a suitable model, we decided to use a logistic model, not on responses p, but on raw measurements z as Equation (2) through (5), where
β1, β2, correspond to a location and a scale parameter; β3 and β 4 are parameters corresponding to a blank and a negative control, respec-– 44 –

tively, and ε's represent random errors. In thismodel, the log ED50 and ED50 are defined asby Equation (6) or Equation (7).
Note that, although the models for the otherassays should have been modified from the above
modeling according to the definition of responses
explained in Appendix A, the function f(di; β1,β2) was assumed to be common for all assays
and, therefore, the estimation procedure in otherassays was essentially the same as the one for
CV except for the modification given in Appendix B.
3.2.2 Non-linear least squares method for
ED50 estimation
Since there were various sources of measurement error which were thought to be additiveand continuous in nature, it was reasonable toassume a normal distribution of errors. We decided to use the method of non-linear leastsquares to estimate parameters b1, b2, b3 and b4,
i.e., to use as estimates of b's the values of themwhich minimize Q defined by Equation (8).

Without doubt, it is natural to estimate ED50
by inserting acquired estimates of β1 and β2 into
the definition of ED50 given by the formula (7),which is the proposed method of ED50 estimation.
3.2.3 Delta method for constructing the confidence interval
The precision of the ED50 estimate obtained
from each experiment should be evaluated using a confidence interval for ED50. Three methods, namely, 1) the delta method (D-method), 2)
the Fieller's method (F-method), and 3) the likelihood ratio method (L-method), can be considered for constructing the confidence interval,
among which we adopted the D-method due tothe reason discussed later in Chapter 8.
Let the estimates of β1 and β2 obtained by the
proposed method be b1 and b2, respectively. Thenthe logarithm of the estimate of ED50, say
logED, can approximately be expanded as Equation (9), which yields an approximate formulafor the variance of logED as Equation (10).

– 45 –

Validation Article II. Statistical analysis

By obtaining estimates of the variance andcovariance of b1 and b2 through linear approximation in the non-linear least squares method(cf. SAS manual), an estimate of var(logED), say
S2, can be calculated by inserting them into theabove formula. From it, we can obtain an approximate 95% confidence interval of logED50
as Equation (11), subsequently yielding the confidence interval of ED50 as Equation (12).
4. The method of data check
Before evaluating assays based on ED50s
obtained from collected data files, we were compelled to check whether each data file should bedeleted or not. This is because, even after careful cleaning and correction of data as describedin Validation Article III in this issue, there remained some files with abnormal behavior,
which led us to a suspicion that some data files
might have been obtained through inappropriate experimentation. Since the existence of data
files from inappropriate experimentation does
not reflect the capability of the assay as alternatives to animal experiments but the impracticability of the assay, we excluded such data files
from the evaluation of the capability of assays.
Consequently, we decided to provide criteria for
exclusion of data files as a “data check” in the
JSAAE study after the correction of trivial errors such as mis-recording or out-of- format description of measurements.
Based on intensive discussions, we reduced
the possible inappropriateness of experimenta-– 46 –

tion using to the following checkpoints:

NR 35nn7-1

120

Check point expressed as Code-B
If the correction factor is greater than 2.0 orless than 0.1 in case of LDH, we regarded it asevidence of inappropriate experimentation andexcluded the corresponding data file from theevaluation of assays, because then the correction of the observed LDH activity to the original
LDH activity is essentially meaningless as explained in Validation Article VI. Note that thischeckpoint is applied only to the LDH assay.
Check point expressed as Code-C
In the above-mentioned model, q’s in Equation(13), where the β3 and β4 replaced with theirestimates, were observed responses corresponding to pi in Equation (1), and, therefore, in thispaper we refer to their average within the same
dose di as the observed mean response.
If there was no dose, at which the observed
mean response was within the range of 20% and80%, we regarded it as evidence of inappropriate choice of doses in the experiment and excluded the corresponding data file from theevaluation of assays, outputting in Code-C, thenumber of doses with the mean response within
this range. Note that, although the initial protocol had required the selection of doses in eachexperiment so as to hold, at least, three doseswith observed mean response within this range,
it was difficult maintaining this strict require-

110
100
90
80
Rate(%)

Check point expressed as Code-A
If LAP-JSAAE failed to yield any ED50
value, we regarded it as evidence of experiment
failure, denoting with “FAILED” in Code-A,
otherwise with “MET”. A typical example, inwhich LAP-JSAAE outputs “FAILED” is shownin Fig. 3. We excluded the data files with“FAILED” output from the evaluation of assays.
Note that, even when ED50 is obtained, the data
file was excluded when the estimated value ofb2 was negative, because it was theoreticallyunacceptable in case of CV as well as other assays except LDH; in case of LDH, the data file
was deleted when the estimated value of β2 waspositive.

70
60
50
40
30
20
10
0
-10
-4.5

-4

-3.5

-3

-2.5
-2
log(Dose)

-1.5

-1

-0.5

Fig. 4 An example of data file with no observed
mean response within the range of 20% and 80%
The log(ED50) estimated by a probit analysis
method is -12.6.

ment. We therefore relaxed the restriction in order to utilize more data files, and prepared a
new condition of keeping at least one dose inthis range, which was required because an inappropriate ED50 was obtained when this condition was violated as is shown in Fig. 4.
Check point expressed as Code-D
If the maximum observed response wasgreater than 200% in a given dose in an experiment, we regarded it as evidence of excessive
errors in measurement and excluded the corresponding data file from the evaluation of assays,
expressing it with “X” in Code-D, otherwise with
“OK”.
Check point expressed as Code-E
If the width of the induced 95% confidence
interval of ED50 was excessive, i.e., the upper
confidence limit was greater than the lower limit
by 100 times, we regarded it as evidence of inappropriate experimentation and excluded thecorresponding data file from the evaluation of
assays.
Check point expressed as Code-F
If the root-mean-square error (RMS) after fitting the logistic function was too large, i.e., RMS
is greater than 10%, we regarded it as evidence
of inappropriateness of the assumed dose-response curve or the logistic model and excluded– 47 –

Validation Article II. Statistical analysis

the corresponding data file from the evaluationof assays, although it might occur in exceptional
cases discussed later in Chapter 8. Here, RMS
is formally expressed by Equation(14), where
the parameters are replaced by their estimates.
It is clear that RMS is an index which indicatesthe degree of deviation of the observed dose-response curve from the logistic model. In otherwords, a large value of RMS implies lack of fitof the logistic model to the data.
5. Criteria to evaluate the validity of assays
Three points were considered to be important in the evaluation of validity of each assay.
Firstly, the result obtained by the assay must be
effective in predicting the result of the in vivo
animal experiment. In other words, ED50s measured through the assay must be highly correlated with Draize test scores on a variety ofchemicals to be assessed. Secondly, ED50 values for the same assay must be reproducible, that
is, almost the same values should be obtained
regardless of which laboratory performed theassay. This is expected to allow only inter-laboratory variations among laboratories. Thirdly, theassay must be robust in the sense that there
should rarely be room for misoperation in the
conduct of the assay, which is assured by thesimplicity of operation and realized by the number of files available to estimate ED50 values in
the JSAAE study.
It was quite disadvantageous to evaluate thepredictability of in vivo results from each assay
where only six chemicals were included in the
JSAAE study and half of them were non-irritant. For such small numbers of chemicals, thecorrelation coefficient was not a good measureof predictability of each assay even when therank correlation instead of Pearson correlation
was used. Therefore we had to devise anotherindex for the evaluation.
As is clearly seen from dose-response curves
shown in Validation Articles VI - VIII in this issue, the distribution of ED50 estimates on eachassay, cell line, and chemical was not a normalone; outliers in both larger and smaller sides frequently appeared even after data cleaning anddata check. This suggested the use of such statistical tools as the box-and-whisker plot proposed by Tukey (Tukey, 1977) to analyse datain this JSAAE study. Along this line of thought,
we decided to use medians instead of means andhinge-spreads instead of standard deviations toevaluate the central tendency and the reproducibility of ED50 values in each assay, where thehinge-spread is defined by the difference of theupper quartile and the lower quartile.
Using these statistics, we devised an index toevaluate the capability of assays as alternatives
to animal experiments, being the ratio of therange of medians among the chemicals over themean hinge-spread taken on all chemicals. It isformally defined in Equation(15), and referred
to as the “power-for-distinction (PFD)” index in
the present study.

6. LAP-JSAAE
We developed a computer program named the“logistic analysis program by the Japanese Society of Alternatives to Animal Experiments(LAP-JSAAE)", which works on SAS, a widely– 48 –

**************************************************************;*CV̲V6.SAS*;*
LAP-JSAAE Ver.6.2 *;*9/5/1996 *;**************************************************************;OPTIONS LINESIZE=90 PAGESIZE=40 NODATE;FILENAME FI̲IN 'a:¥6cvh1.out';
DATA YOMI1;YOMIGYO=2;
CALL SYMPUT('YOMI',YOMIGYO);%INCLUDE 'a:¥cv̲61.sas';
PROC PLOT DATA=IN12 HPCT=90 VPCT=90 NOLEGEND;
PLOT PLATE*LOG̲DOSE;%INCLUDE 'a:¥cv̲62.sas';
PROC PLOT DATA=PARA3 HPCT=90 VPCT=90 NOLEGEND;
PLOT P̲PRED*LOG̲DOSE='P' P̲RATIO*LOG̲DOSE='Y'/ OVERLAY VREF=0 50 100;
PROC PRINT DATA=ED9 NOOBS LABEL;VAR F̲NAME N P CODE̲A CODE̲C CODE̲D CODE̲E CODE̲F
ED50 LOW̲ED50 UP̲ED50 ;RUN;Fig. 5 Initial control program for LAP-JSAAE on SAS
The log(ED50) estimated by a probit analysis method is -12.6.

used statistical software package. The source
program of LAP-JSAAE for which copyright isjointly held by Takashi Omori and JSAAE, together with an operation manual in Japanese, canbe acquired upon request.
The LAP-JSAAE essentially consists of threeparts, namely, 1) the ED50 estimation, 2) the data
check, and 3) the graphic representation, and is
optionally controlled with an initial setting as
shown in Fig. 5. (see SAS manuals for specificoptions.)
An example of output with an input is shownin Fig. 6. In this output, “File” is the data filename to be analyzed which is given by the user,“N” is the total number of measurements in thedata, and “P” is the number of dose levels included in the experiment excluding the negativeand positive controls and blank. “A”, “C”, etc.
are the output of check codes. The values in“LOW_ED50” and “UP_ED50” are the lower
and upper limit of the 95% confidence intervalof ED50, respectively. The value in “Code_F”
is the value of RMS as already explained.
7. Results of statistical analysis
The collected data files were processed following the flow chart given in Fig. 7 (also shown– 49 –

Validation Article II. Statistical analysis

Fig. 6. An example of input and output of LAP-JSAAE– 50 –

Submission of the worksheet

Step 1

No

Is it strictly keeping the protocol ?
Yes

Step 2

Were both data files on
chemical #1 and #7 submitted ?

Discard all the data files ofchemical #1 - #7 on thespecific assay.

No

Yes
Step 3

Analysis on LAP-JSAAE program

Step 4Is the check code "OK" on data filesof chemical #1 and #7 ? A checkcode will appear in the order of A,
B, C, D, E, F, then "OK".

No

Yes
Step 5Is the ratio of log ED50 of chemical #1 tothat of chemical #7, or its reciprocal, lessthan 5 ?

No

Reject all the data files ofchemical #1 - #7 on thespecific assay.

Yes
Step 6Is the check code "OK" on data filesof chemical #2 - #6 ? A check code
will appear in the order of A, B, C,
D, E, F, then "OK".

No

Reject the specific data file

Yes
Step 7

Box-whisker plot analysis

Fig. 7. Data file processing in the present study
Definitions of check codes are as follows:
Code-A : Calculation of ED50 values failed because of wide variation of data.
Code-B : In the LDH-release assay, LDH activity is directly inhibited or stimulated by the test chemicalwith the correction factor of below 0.1 or above 2.0, respectively. With these factors, correction of
the observed LDH activity to the original LDH activity in a sample is essentially meaningless.
Code-C : No observed point between 20-80% of the maximum effect was found in the data file.
Code-D : Data included response of 200% or more (negative controls set at 100%).
Code-E : Of the 95% confidence limits of ED50, the upper limit was over 100 times that of the lower
limit.
Code-F : RMS is 10 or more. RMS indicates the degree of deviation of observed dose-response relationship from the logistic model. See details in the following Validation Article II in this issue.

– 51 –

Validation Article II. Statistical analysis
LDH1 9l1h5

1250

200

1000

150

750

50

250

0

-5

-4.5
-4
log(Dose)

-3.5

-50
-3

-3

Fig. 8. An example data file deleted at the check point B

-2.6

-2.4
log(Dose)

-2.2

-2

-1.8

NR
3nn6

120
110

90

100

80

90

70

80

Rate(%)

60
50
40

70
60
50
40

30

30

20

20

10
0
-2.5

-2.8

Fig. 9. An example data file deleted at the checkpoint D

LDH1 3l1h1

100Rate(%)

100

500

0
-5.5

LDH1 7l1h3

250

Rate(%)

Rate(%)

1500

10

-2

-1.5

-1

-0.5
log(Dose)

0

0.5

1

0
-5

1.5

-4.5

-4

-3.5

-3

-2.5 -2
log(Dose)

-1.5

-1

-0.5

0

Fig. 10. An example data file deleted at the checkpoint E

Fig. 11. An example data file deleted at the checkpoint F

as Fig. 1 in Validation Article I. in this issue). As
explained in Validation Article III, much laborious work had been done during this study to inspect and correct trivial mistakes. We applied
LAP-JSAAE to data which had been subjected
to such cleaning and summarized the results inTable 5 (The same table shown in Validation
Article I. in this issue, Table 5). Typical examplesof data files excluded from the evaluation of assays are shown in Figs. 8 - 11.
Table 5 shows that the CV assay with HeLa
S3 (SC) cells achieved the best score in PFD andin the number of data files available for the evaluation of assays; the second best score was for
the MTT assay with HeLa S3 (SC) cells.

8.1 PROC PROBIT for in vivo bioassay and
LAP-JSAAE
Although the proposed method realized in the
LAP-JSAAE uses a logistic function as the doseresponse curve in place of a probit curve in theconventional probit analysis, the difference is no
more essential than the difference between LAPJSAAE and the probit analysis (Finney, 1985b).
In fact, we can assume a logistic function as thedose-response curve for any in vivo bioassay andapply PROC PROBIT in SAS to the data entirely in the same manner as in the case of a probit
curve, obtaining, in most cases, quite similar results on the same data.
The essential difference between the two
methods lies in the estimation procedure; a nonlinear least squares method is used in LAPJSAAE, whereas a maximum likelihood method

8. Discussion– 52 –

Table 5. Number of files rejected or finally accepted by the logistic analysis program, LAP-JSAAE.
Candidate
files

Assay

Rejected files

Finally
accepted
files

Ratio
Chemical of ED50
Chemical #2 - #6 with**#1 or #7 of #1/#7
with Code (#7/#1) is Code A Code B Code C Code D Code E Code F $A* ~ F 5 or more

Cells

HeLa S3 (SC)BALB/3T3
A31-1-1CV
HeLa S3 (SC)CHL
LDH-1 HeLa S3 (SC)SQ-5
LDH-2A HeLa S3 (SC)SQ-5
LDH-2B HeLa S3 (SC)SQ-5
LDH-2C HeLa S3 (SC)SQ-5
MTT
HeLa S3 (SC)SQ-5
NR
HeLa S3 (SC)
NRCE

116
149

0
7

6&
4

2
3

7
7

0
0

1
0

0
2

100
126

84
83
57
50
54
39
41
34
54
40
95
89
126
132

7
0
7
14
21
7
21
14
14
7
0
0
7
7

0
0
0
5&
0
0
0
0
0
0
0
0
7
7

1
2
2
1
2
1
0
0
6
2
2
2
0
0

1
1
6
4
1
3
0
0
3
0
2
4
3
5

0
1
1
0
0
0
0
0
0
0
0
0
0
3

0
0
0
0
0
0
0
0
2
1
0
0
0
3

0
1
1
1
2
0
2
0
2
5
2
0
1
4

75
78
39
25
26
28
18
20
26
25
89
83
108
103

Total files

1243

133

29

26

47

5

7

23

969

CF

1
0
2
0
0
0
1
0

4

* Code A. Calculation of an ED50 value failed because of wide variation of data.
** Calculation met the requirement by the logistic analysis program LAP-JSAAE but with the code B, D, E, orF.
Code B indicates that, in the LDH-release assay, LDH activity is directly stimulated or inhibited by the test
chemical with the correction factor of over 2.0 or under 0.1, respectively. With these factors, correction of
the observed LDH activity to the original LDH activity in a sample is essentially meaningless.
Code-C indicates that no observed point was found between 20-80% of the maximum effect in the data file.
Note that the numbers in this column do not contain the files which have been rejected under the check code
A and B, therefore they are different from the number of data files shown in Table 4.
Code D indicates that data include response of 200% or more where that of negative control was 100%.
Code E indicates that, of the 95% confidence limits of ED50, the upper limit is over 100 times the lower limit.
$ Code F indicates that RMS was 10 or more. On the difinition of RMS, see the subsequent article on statisticalanalyses and LAP-JSAAE.
& The data file set on this assay did not include files on one or two of chemicals #2 - #6.

based on the assumption of binomial distribution or a modified version of it is used in the
probit analysis. The reason why we adopted a
non-linear least squares method for LAP-JSAAE
lies in the characteristic of random variations ormeasurement errors in observed data. They arereasonably regarded to be normally distributed,
being affected by many sources of variation incontinuous type such as time setting, dilution ofsolution, volume measurement by pipette, OD
measurement and so on. For data with such typesof variation, the appropriate method is not a
maximum likelihood method based on the bino-

mial distribution as is usually assumed for in vivo
assays, but a non-linear least squares method
based on the normal distribution. The adoptionof the latter automatically removed the difficultyof the probit analysis method which came frompossible responses outside of the range of 0%
and 100%.
8.2 Appropriateness of the logistic model
Although an ogive curve such as a probit
curve or logic function is widely used as the doseresponse curve, it should not be admitted without validation. In fact, some assays eventually– 53 –

Validation Article II. Statistical analysis

90
80

Freequency

70
60
50
40
30
20
10
0
-------000000 -------000000 -------000000
0000000...... 0000000...... 0000000......
.......000111 .......000111 .......000111
1110000257025 1110000257025 1110000257025
5207520505050 5207520505050 5207520505050
050505005050500505050
Delta

FiellerLR

Fig. 12. Frequency distribution of the length of confidence intervals
Although there is no remarkable difference between the histograms of interval
length, the number of data files which did not yield confidence intervals within areasonable time was one for D-method, nine for F-method, and twenty five for Lmethod.

show a dose-response curve with a peak in a low
dose region for some kinds of chemicals, examples of which are shown by Wang et al. (Wanget al., 1995). If such a phenomenon occurs, thecorresponding data file would be improperly excluded from the evaluation of assays through data
check by the checkpoint F. We investigated thepossibilities of this kind of erroneous action of
the JSAAE study and confirmed that the RMS
criterion did not encounter such errors.
8.3 Three methods to construct confidence
intervals
There are three available methods in literature to construct a confidence interval for ED50
from a data file. They are the delta method (Kotz& Johnson, 1985), the method proposed by
Fieller (1967), and the method based on the likelihood ratio test (Williams, 1986), which are referred to as the D-method, the F-method, andthe L-method, respectively. Although all of these
are asymptotically equivalent as is well known,
their behavior is different in small sample sizes
such as in our study. Williams (1986) and Alhoand Valtonen (1995) compared their nature
through a simulation study based on the binomial distribution, leading to the conclusion that
the L-method is superior in the sense that, inmany cases, it leads to shorter intervals keeping
nominal confidence levels. We, however, examined their differences by applying the three methods to our data which were not binominally distributed; the results are summarized in Fig. 12.
This demonstrated the superiority of the Dmethod, because the confidence interval was easily obtained in all cases, whereas the other two
methods failed to reach rapid convergence of iteration in some cases and the length of acquired
intervals did not show any remarkable tendency
as was asserted by Williams (1990). Thus, we– 54 –

implemented the D-method into LAP-JSAAE as
the method to construct confidence intervals.
8.4 Homoscedasticity and sources of variability
In some cases, the variability among measurements on the same dose looks greater for low
doses. This is probably due to the lack of required
fineness of manipulation with low doses. In otherwords, if this is true, the homoscedasticity is violated. The criterion Q in the least squares method
must be modified so that different weights canbe multiplied on each term of squares, which subsequently creates a problem of how to determine
the optimum weighting. This problem is difficult to answer and is left for future studies.
In any assay, each experiment required morethan one plate because there are possible sourcesof bias commonly affecting wells in the sameplate. In the data analysis in this study, however,these biases were ignored as a whole as long as
the data file was accepted after the data check.
The modification of the method to incorporate
plate-depnedent biases will be considered in future studies.
Acknowledgments
This study was supported in part by funds
from JSAAE, a Special Coordination Funds from
Promoting Science and Technology from The
Science and Technology Agency of Japan, and
the Grant-in-Aid for Scientific Research
C07680327 of the Ministry of Education, Science, Sports, and Culture of Japan.

References
Alho J. M. and Valtonen E. (1995): Interval estimation of
inverse dose-response. Biometrics, 51, 491-501.
DeGroot M. H., Ferber R., Frankel M. R., Seneta E., andWatson G. S. (1985): Encyclopedia of Statistics. John
Wiley & Sons, New York.
Fieller E. C. (1940): The biological standardization of insulin. JRSS Supplement, VII, 1-45.
Fieller E. C. (1954): Some problem in interval estimation. JRSS B, 16, 175-185.
Finney, D. J. (1971): Probit Analysis, 3rd edition, Cambridge University Press.
Finney, D. J. (1985a): The median lethal dose and its estimation, Archives of Toxicology, 56, 215-218.
Finney, D. J. (1985b): The estimation of the ED50 for alogistic response curve. Sankhya, 12, 121-136.
Litchfield J. T.Jr. and Wilcoxon F. (1949): A simplified
method of evaluating dose-effect experiment, Journalof Pharmacology and Experimental Therapeutics, 96,
99-114.
Ohno T., Itagaki H., Tanaka N., and Ono H. (1995): Validation study on five different cytotoxicity assays inJapan - An intermediate report. Toxicology in vitro, 9,571-576.
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Tukey T. W. (1977): Exploratory data analysis. AddisonWesley.
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T. (1995): In vitro cytotoxicity of 20 MEIC chemicals
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Williams D. A. (1986): Interval estimation of the medianlethal dose. Biometrics, 42, 641-645.

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Validation Article II. Statistical analysis

Appendix for Validation Article II.

– 56 –

– 57 –

Validation Article II. Statistical analysis– 58 –