Chapter 18
Comparison of In Vivo and In Vitro Toxicity Tests from Co-inertia Analysis 1
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James Devillers and Daniel Chessel 1
Centre de Traitement de l'Information Scientifique, 21 rue de la Bannière, 69003 Lyons, France Université Lyons-I, Unité de Recherche Associée, Centre National de la Recherche Scientifique 1451, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France 2
Co-inertia analysis is a multivariate method allowing to find the co-structure between two data tables from powerful statistical and graphical tools. It was used to compare toxicity results obtained with the rabbit eye test in vivo to those obtained with the in vitro eye organ test.
The aim of toxicity testing is to allow the prediction of the effects that chemicals are likely to have in man by the extrapolation of the effects observed in experimental animals or other biological systems. Safety testing is performed either to assure the safety in use of a medicine, food or consumer product, or to estimate the extent of the occupational hazard presented by an industrial chemical (7). Over the last decade, there has been an increasing pressure to reduce animal experimentation and develop in vitro methods in pharmacotoxicology (2,5). However, before any in vitro toxicity test can be used with any degree of reliability, a validation exercise is needed (4). Usually, in vitro data are compared with in vivo data by means of regression analysis (e.g.; 5, 6). Even if this simple statistical analysis generally gives some interesting results, it is not sufficient to estimate the relevance of these different test systems, to select adequate endpoints, and to derive valuable structure-activity relationships. This study is designed to stress the usefulness of co-inertia analysis (7) to overcome these different problems. 0097-6156/95/0589-0250$12.00/0 © 1995 American Chemical Society In Computer-Aided Molecular Design; Reynolds, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.
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Sample a n d Research Methodology
During the past several years, considerable research effort has been directed towards the development of alternatives in vitro to the rabbit eye test in vivo (8-12). Indeed, rabbit eye test in vivo (13) has frequently been criticized due to methodological, economical, and ethical problems (72,14,15). Under these conditions, a wide variety of in vitro techniques for predicting eye irritancy has been described in the literature (8,10,11,16). Among them, the enucleated eye test (17, 18) based on the measurement of the change in corneal thickness that follows exposure of the eye to an irritant chemical is regularly cited in the literature as an attractive alternative in vitro method. Indeed, although enucleated eyes are required, the animals are humanely killed before use. Two eyes are available from each rabbit, when in vivo only one eye is used. Eyes may be taken from rabbits that have been used for skin irritation and that are due to be killed on the completion of that test. Complex and expensive tissue culture techniques are not required and after the initial outlay on the equipment, the running costs are minimal. The in vitro eye organ test can be used to examine insoluble powders and acid or alkali solutions that cannot, or cannot readily, be assayed in cell cultures (79-27). In a recent article, Jacobs and Martens (22) estimated in a first time the corneal swelling in vivo and in vitro for 34 substances. The corneal swelling data obtained in vivo after 4, 24, 48, and 72 hours of exposure were then compared with the corneal swelling data obtained in vitro after 0.5, 1, 2, and 4 hours of exposure by means of simple regression analyses. Since their data appeared insufficiently exploited, we have tried to extract more information from their matrices by means of the co-inertia analysis (7). Co-inertia analysis can be viewed as a generic multivariate method to find the co-structure between two data tables (Figure 1). These two data matrices arefirstconsidered independently. They can be analyzed by means of different multivariate approaches such as principal components analysis (PCA), correspondence factor analysis (CFA), or multiple correspondence factor analysis (MCFA). These separate analyses underline the basic structure of the two data tables. In a second step, a matching analysis is performed in order to detect a costructure between the two data matrices. This second analysis is based on the research of co-inertia axes maximizing the covariance between the coordinates of the projections of the rows of each data table. The mathematical model of this analysis can be formulated as follows: Let (X, Dp, D ) and (Y, D , D ) be two statistical triplets; Table X is thefirstdata set (after an initial transformation); D contains the n
q
n
p
In Computer-Aided Molecular Design; Reynolds, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.
COMPUTER-AIDED MOLECULAR DESIGN
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chemicals
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chemicals
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η
γ
η in vivo
in vitro
in vitro
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MAXIMAL COVARIANCE BETWEEN IN VIVO AXIS AND IN VITRO AXIS in vitro
• a^i MAXIMAL » CORRELATION 7
MAXIMAL STANDARD DEVIATION
in vivo
axis
MAXIMAL STANDARD DEVIATION Figure 1. General principle of co-inertia analysis.
In Computer-Aided Molecular Design; Reynolds, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.
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In Vivo and In Vitro Toxicity Tests
weights associated with the columns of Table X; D contains the weights associated with the rows of Table X. Table Y is the second data set (after an initial transformation); D contains the weights associated with the columns of Table Y; D contains the weights associated with the rows of Table Y. Thefirststatistical triplet (X, D , D ) defines an inertia analysis of η points in a multidimensional space noted R and of ρ points in a multidimensional space noted R . After diagonalization, r principal axes are kept and the matrices R , C , N are generated. R contains the scores of the η rows on the r axes. C contains the scores of the ρ columns on the r axes. Ncontains the eigenvalues (vi...v ). The second statistical triplet (Y, Dq, D ) defines an inertia analysis of η points in a multidimensional space noted R and of q points in a multidimensional space noted R . After diagonalization, s principal axes are preserved and the matrices R , C , M are generated. R contains the scores of the η rows on the s axes. C contains the scores of the q columns on the s axes. M contains the eigenvalues (μι...μ ). Let u and ν be a pair of vectors. The former is normalized by matrix Dp in the multidimensional space R and the latter is normalized by matrix D in the multidimensional space R . The projection of the multidimensional space associated with Table X onto vector u generates η coordinates in a column matrix: n
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r
r
r
r
r
r
r
n
q
n
s
s
s
s
s
s
δ
p
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q
ξ =Χ ϋ
(1)
ρ ΰ
The projection of the multidimensional space associated with Table Y onto vector ν generates η coordinates in a column matrix: \|f = Y D v
(2)
q
Co-inertia associated with the pair of vectors u and ν is equal to: H(u,v)= ξ ί ϋ η ψ
(3)
If the initial Tables X and Y are centered, then the co-inertia is the covariance between the two new sets of scores: Cov (ξ,ψ) = (Ineri (u))l/2 (Iner (v))l/2 Corr (ξ,ψ) 2
(4)
with Ineri (u) as the projected inertia onto vector u (i.e.; the variance of the new scores on u), Iner2 (v) as the projected inertia onto vector ν (i.e.; the variance of the new scores on v), and Corr (ξ,ψ) as the
In Computer-Aided Molecular Design; Reynolds, C., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1995.
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correlation between the two coordinate systems. Note that the square of the latter entity Corr (ξ,ψ) is maximized via canonical correlation analysis. To obtain co-inertia axes, one diagonalizes the following matrix: W = Dpl/2 Xt D Y D Y* D X D l/2 n
q
n
(5)
p
Let U be the matrix containing thefirstζ normalized eigenvectors of W and Λ ζ be the matrix containing the first ζ corresponding eigenvalues (noted Xk, l
