Mutation Research, 119 (1983) 95-102 95 Elsevier Biomedical Press

A microcomputer program for analyzing Ames test data

Dan Moore and James S. Felton

Lawrence Livermore National Laboratory, Biomedical Sciences Division, University o f California, P.O. Box 5507 L-452, Livermore, CA 94550 (U.S.A.)

(Accepted 13 September 1982)

Several methods have been proposed for analysing results f rom the

A m e s / S a l m o n e l l a Mutagen Assay. The analysis is usual ly designed to answer two

quest ions: (1) is the c o m p o u n d under test mutagenic? (2) if the c o m p o u n d is

mutagenic how potent is it? Table 1 summarizes the features of 6 recently proposed

methods which are based on specific mathemat ica l models of the dose - r e sponse

re la t ionship and are designed to answer these quest ions. Fig. 1 shows graphical ly

what each model looks like in a c o m m o n d o s e - r e s p o n s e space. A similar feature of

all the methods is the requi rement for a modera te to large sized compute r for

parameter es t imat ion. Conv inc ing a rguments can be made in suppor t of each model

bu t in most appl icat ions, where there are few replicate measurements made at each

dose level, the da ta are insuff ic ient to dis t inguish a m o n g the models (i.e. any one

of the models provides an adequate fit to the data). Thus , in the interest of simplici-

ty, it is t empt ing to use a simple l inear model , similar to that proposed by Bernstein

et al. (1982) for analysis. The Bernstein method is restricted to fi t t ing points which

are on the initial l inear response par t of the curve and requires m a x i m u m likel ihood

es t imat ion. The Snee and Irr model (1981) also describes a l inear relat ionship bet-

Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract number W-7405-ENG-48 and partially supported by Interagency Agreement (NIEHS 222-Y01-ES-10063) between the National Institute of Environmental Health Sciences and the Department of Energy.

Disclaimer: This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial products, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government thereof, and shall not be used for advertising or product endorsement purposes.

0165-7992/83/0000-0000/$ 03.00 © Elsevier Biomedical Press

96

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Fig. 1.6 models for analyzing Ames/Salmonella assay results. Each model was required to pass through the 2 points (0, 10) and (100, 50). From top to bottom the models are: Chu et al., Margolin et al., Stead et al. and the linear models of Bernstein et al., Snee and Irr and Myers et al. (see Table I for descriptions). In this plot exponential toxicity has been set equal to zero for those models which include a term for it.

ween dose and response; the exponent is used to transform the data during fitting

so that the variances are equal. In this letter we describe a method which is based on simple least-squares linear

regression. This greatly simplifies estimation of the model parameters since only one iteration is required while all other methods require several iterations. This means

that the method can be efficiently programmed to run on a microcomputer. Thus, data analysis can be more readily available to the many small laboratories using the

Ames/Salmonella test. The fitting program is interactive and has graphical display

enabling the user to decide for himself which points to include and whether or not the linear fit is acceptable. Use of this user-oriented, least-squares linear regression program will allow better quantitative comparison of Ames/Salmonella test results

between laboratories and more quantitative decisions on when to repeat experiments at lower doses because of excess toxicity at doses tested. In our laboratory the

microcomputer has been linked directly to a Biotran II automatic counter (New Brunswick Sci.)so that scanning of culture plates and analysis can be accomplished

rapidly and easily (Slezak, 1981).

Program description In this section we describe briefly the microcomputer program used for data

analysis. The program fits the simple linear regression equation

Y = /~o + /~zX

to the data. In this equation Y is the number of revertants and X is the dose of the

98

mutagen under test. The program performs the fit by minimizing the weighted sum of squared residuals

S = ~;wi -1 (Yi - Go - ~1 X) 2

A variety o f weighting schemes are available including equal weights, Poisson weights and observed variance weights. If it is believed that the data came from a

OBSERVED VARIANCE WEIGHTS STEAD SAMPLE TA9E3-

DOSE PLATE COUNTS M E A N S.D. LINEAR MODEL PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INTERCEPT = 27 .2921 0 29 I~ 18 20 8 . 1 9 SLOPE = . I 0 9 8 ( 9 . 2 E - 0 3 ) bO 30 37 41 3b 5 . 5 7

I00 3b 41 39 3 8 . 7 2 . 5 2 DOSE MEAN PRED RESID 200 49 55 55 53 ~ .4& 0 20 2 7 . 2 9 - 7 . 2 9 &O0 85 99 87 9 0 . 3 7 . 5 7 60 36 3 3 . 8 8 2 . 1 2 I000 90 90 0 IO0 3 8 . 6 7 3 8 . 2 7 . 4

200 53 4 9 . 2 5 3 . 7 5 OBSERVED VARIANCE WEIGHTS 600 9 0 . 3 3 9 3 . 1 5 - 2 . 8 2

LINEAR MODEL PARAMETERS A N 0 V A INTERCEPT = 3 0 . 2 5 9 5 SLOPE = .0~38 ( 9 . 8 E - 0 3 ) SOURCE S.S. D.F. M.S.

REGRESS 5 3 4 7 . 1 6 1 5 3 4 7 . 1 6 DOSE MEAN RRED RESID ABT REG 194 .42 3 6 4 . 8 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . WTN GRP 2 9 2 . 9 9 10 2 9 . 3 0 2D 3 0 . 2 b - 1 0 . 2 6 T O T A L 5 8 3 4 . 5 6 14 4 1 6 . 7 5 60 36 3 5 . 2 9 .71 100 3 8 . 6 7 3 8 . 6 4 .()3 TEST FOR LINEARITY 200 53 47 .01 5 . 9 9 F = 2 . 2 1 WITH ( 3 , 1 0 ) D .F . (P = . 1 4 9 2 } 600 9 0 . 3 3 8 0 . 5 2 9 .81 1000 90 114 .03 - 2 4 . 0 3 TEST FOR ZERO SLOPE

F = 182.51 WITH ( I , l O > D.F. (P = O)

A N 0 V A

SOURCE S.S. D.F. M. S. 1 00 t I / ÷ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

REGRESS 6 0 4 2 . 2 5 i &042 .25 8 0 ABT REG 8 5 5 . 6 3 4 213 .91 WTN GRP 301. 19 10 30. 12 G 8 + T O T A L 7 1 9 9 . 0 7 15 4 7 9 . 9 4 . ~

4 8

TEST FOR LINEARITY F = 7 .1 WITH ( 4 , 1 0 ) D .F . (R = 6E-03) 2 0 '

WARNING! MODEL DOES NOT F IT DATA 0 8 Z80 4 8 0 SO0

TEST FOR ZERO SLOFE DOSE, l~O F = 200.bI WITH (1.10) D.F. (R = O)

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Fig. 2. Results of fits to data from Stead et al. The left panel shows a fit of the linear model Y = B0 + ~l X t o all 6 dose points; there is significant lack of fit due to the response at 1000 #g. A refit to the first 5 doses produces an acceptable fit and significant slope indicating mutagenicity.

99

Poisson- l ike d is t r ibut ion , characterized by the spread of the response da ta being

p ropor t iona l to the mean response of the data, Poisson weighting will lead to more

precise parameter estimates. I f it is believed that the data may con ta in 'out l ie rs ' (i.e.

a few values widely discrepant f rom the ma in body of data possibly due to poor

plat ing technique, con t amina t i on , etc.) observed var iance weighting will cause these

values to have relatively smaller inf luence on the fit.

The fit p rogram also allows the user to remove dose points interactively to see the

effects on the fit. I f toxicity appears to be causing the dose - r e sponse to bend over

f rom its initial l inear t ra jectory, high dose points may be e l iminated in subsequent

refits of the same data. A graph of the da ta and the l inear fit is shown on the screen

after each fit and a table giving the s tandard regression analysis o f var iance

(ANOVA) is pr inted. The pr in ted analysis also includes a test for l ineari ty that may

be used to decide which subset o f data points best describe the init ial l inear dose

response. Mutagenic i ty may be decided on the basis o f the test for significance of

the slope (i.e. a s ignif icant slope implies mutagenici ty) .

TABLE 2

COMPARISON BETWEEN LEAST SQUARES AND MAXIMUM LIKELIHOOD FITS OF LINEAR MODEL TO DATA a

Strain Number of LS Slope ML e Intercept _+ $9 dose points LSF d

used/total

LS b ML c LS LSF ML

TA98- 5/6 3/6 0.11"* 0.18"* 0.20 27.3 22.1 20.7 TA98 + 5/6 4/6 0.28** 0,32** 0.32 42.4 40.1 40.2

TAI00- 6/6 5/6 0.05* 0.21"* 0.21 79.4 73.9 73.6 TAI00+ 3/6 3/6 1.45"* 1.45"* 1.44 119 119 119

TA1535 - 6/6 6/6 0.00 0,00 0.00 21.0 21,0 20.9 TA1535+ 7/7 6/7 0.00 0.01 0.01 16.3 15,7 16.1

TA1537- 5/7 3/6 0.21"* 0,26** 0.26 8.2 7,3 7.2 TA1537+ 4/6 4/6 0.16"* 0.16"* 0.17 11.3 11,3 11.8

TA1538- 5/6 5/6 0.20** 0.27** 0.27 20.9 18,1 18.2 TA1538 + 3/5 3/5 3.09** 3.09** 3.26 17.9 17,9 21.6

* Slope significant at P < 0.05. **Slope significant at P < 0.01. a Data from Stead et al. (1981). b LS, Least-squares method as described in this paper. Dose points are deleted sequentially as long as

the linearity test fails at the 0.05 level of significance. c ML, maximum likelihood method described in Bernstein et al. (1982). d L S F , Least-squares forced to use the same doses as the ML method. • Significance of slope not reported by Bernstein et al. (1982).

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Examples and comparison of results An example print-out obtained by applying this program to data presented by

Stead et al. (1981) is shown in Fig. 2. The first panel shows that the fit to all 6 doses by the linear model is unsatisfactory. There is a very large residual (observed

CHU DATA TAIO0+

DOSE PLATE COUNTS M E A N S.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

OBSERVED VARIANCE WEIGHTS

LINEAR MODEL PARAMETERS INTERCEPT = 117.3516

0 131 117 101 116.3 15.01 SLOPE = .0269 ( .019) . 3 95 82 90 89 6 . 5 6 1 102 131 122 118.3 14.84 DOSE MEAN PRED RESID 3 . 3 1 2 6 1 2 0 1 0 4 1 1 6 . 7 1 1 . 3 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 96 79 113 96 17 0 116.33 117.35 - 1 . 0 2 33 .3 97 125 133 118.3 18.9 1 118.33 117.38 .95 !00 127 141 102 123.3 19.76 3 . 3 116.67 117.44 - . 7 7 333 .3 131 122 125 126 4 . 5 8 33 .3 118.33 118.25 .09

I00 123.33 120.04 3 . 2 9 OBSERVED VARIANCE WEIGHTS 333 .3 126 126.32 - . 3 2

LINEAR MODEL PARAMETERS A N 0 V A INTERCEPT = 105.9973 SLOPE = .0641 ( .0263) SOURCE S.S. D.F. M.S.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

DOSE MEAN PRED RESID REGRESS 262 .8 1 262 .8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AST REG 25 .16 4 6 . 2 9 0 116.33 106 10.34 WTN GRP 2066.3 12 172.19 . 3 89 106.02 - 1 7 . 0 2 TOTAL 2354.26 17 138.49 1 118.33 106.06 12.27 3.'3 116.67 106.21 10.46 TEST FOR LINEARITY 10 96 106.64 --10.64 F = .04 WITH (4 ,12 ) D .F . (P = 1) 33 .3 118.33 108.13 10.2 100 123.33 112.41 10.92 TEST FOR ZERO SLOPE 333 .3 126 127.38 - 1 . 3 8 F = 1 .53 WITH (1 ,12 ) D.F. (P = .2391)

A N O V A

SOURCE S.S. D.F. M.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

REGRESS 1548.72 1 1548.72 ABT REG 3361.04 6 560 .17 WTN GRP 2380.17 16 148.76 TOTAL 7289.93 23 316 .95

TEST FOR LINEARITY F = 3 . 7 7 WITH (6 ,16 ) D.F. (P = .0157)

WARNING! MODEL DOES NOT F I T DATA

TEST FOR ZERO SLOPE F = 10.41 WITH (1 ,16) D.F. (P = 5 .4E-03 ) 2ooj

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Fig. 3. Results of fits to data from Chu et al. The left panel shows a fit of the linear model to all 8 dose points; there is significant lack of fit due to the response at 0.3 #g. When this point is deleted a refit indicates a lack of fit due to the response at l0 pg (analysis not shown). A refit to the rtTnaining 6 dose points gives a good fit with a non-significant slope.

101

m e a n - predicted value) at the highest dose and the test for linearity fails with P = 0.006. The second panel shows that discarding the highest dose and refitting to the first 5 doses is satisfactory. The test for linearity is acceptable with P = 0.15. Since the slope is also significant, the compound under test would be labeled mutagenic and, judging from the initial slope derived from doses in the 0-600/~g range, we can calculate a potency of roughly 11 revertants per 100/zg of compound.

Table 2 compares the results from our program with those reported by Bernstein et al. (1982) who analyzed all of the Stead et al. (1981) examples. In running our program we deleted high dose points sequentially whenever the test for linearity failed at P < 0.05. This usually resulted in retaining more dose points than Bernstein et al., but they used a likelihood ratio test with a p < 0.25 criterion for dose point rejection. The estimates for the slope and intercept parameters suggest that there is no significant loss in accuracy by using least-squares analysis in place of the maximum likelihood method. The 2 methods also agree on classifying agents as mutagenic or non-mutagenic. In these examples all results except those on strain TA1535 were judged mutagenic by both methods as well as by the method of Stead et al.

The ease with which inconsistencies in the data can be detected is illustrated by Fig. 3 which shows the result of using this program on data reported by Chu et al. (1981). They reported that these data were classified as negative by a consensus panel of biologists but were statistically positive according to 2 statistical tests. When our model is fit to all 8 doses there is significant lack of linearity (see left panel where P = 0.0157). Examination of the residuals suggests that the response at dose 0.3 ttg is unexpectedly low (residual = - 17.02). When this dose is removed and the model is fit to the remaining 7 doses, there is still a significant lack of linearity (P = 0.0272). This time it is caused by a low response at 10 #g. When this dose is also removed we get P -- 1.0 for linearity (implying a good fit o f the model to the data) and a non-significant slope indicating that the compound is non-mutagenic.

Program availability This program is written in BASIC and is currently running on an Apple computer.

The program should run on any microcomputer with minor changes to the graphic display routines. A program listing is available upon request to the first author.

References

Bernstein, L., J. Kaldor, J. McCann and M.C. Pike (1982) An empirical approach to the statistical analysis of mutagenesis data from the Salmonella test, Mutation Res., 97, 267-281.

Chu, K.C., K.M. Patel, A.H. Lin, R.E. Tarone, M.S. Linhart and V.C. Dunkel (1981) Evaluating statistical analyses and reproducibility of microbial mutagenicity assays, Mutation Res., 85, 119-132.

Margolin, B.H., N. Kaplan and E. Zeiger (1981) Statistical analysis of the Ames Salmonella/microsome test, Proc. Natl. Acad. Sci. (U.S.A.), 78, 3779-3783.

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Myers, L.E., N.H. Sexton, L.I. Southerland and T.J. Wolff (1981) Regression analysis of Ames test data, Environ. Mutagen., 3, 575-586.

Slezak, T. (1981) Interfacing for economical data gathering and processing, T.H.E. Journal, 8, 59-60. Snee, R.D., and J.D. Irr (1981) Analysis of Salmonella histidine reversion data, paper presented at the

NIEHS workshop on Statistical Analysis of In Vitro Tests for Mutagenicity, Chapel Hill, NC, 20-23 April 1981.

Stead, A.G., V. Hasselblad, J.P. Creason and L. Claxton (1981) Modeling the Ames test, Mutation Res., 85, 13-27.