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\section*{Theories for chemical carcinogenesis}
Prevention of environmentally-induced cancers is a health issue of
unquestionable importance.  Almost every sphere of human activity in
an industrialised society faces potential chemical hazards of some
form.  It is estimated that nearly 100,000
chemicals are in use in large amounts every day. A further 500--1000
are added every year.  Only a small fraction of these chemicals have
been evaluated for toxic effects like carcinogenicity. The U.S.
National Toxicology Program  contributes to this enterprise
by conducting standardised chemical bioassays -- exposure of rodents
to a range of chemicals -- to help identify substances that may have
carcinogenic effects on humans.  However, obtaining empirical evidence
from such bioassays is expensive and usually too slow to cope with the
number of chemicals that can result in adverse effects on human
exposure.  This has resulted in an urgent need for models that propose
molecular mechanisms for carcinogenesis.

The data here come from tests conducted by the NTP.
These have  so far resulted in a data base of more
than 300 compounds that have been shown to be carcinigenic or otherwise
in rodents. Amongst other criteria, the chemicals have been selected
on the basis of their carcinogenic potential
-- for example, positive mutagenicity tests -- and on
evidence of substantial human exposure.
Using rat and mouse strains (of both genders) as predictive surrogates
for humans, levels of evidence of carcinogenicity are obtained from
the incidence of tumors on long-term (two years) exposure to the chemicals.
The NTP assigns the following levels of evidence: CE, clear evidence;
SE, some evidence; E, equivocal evidence; and NE, no evidence.
For the experiments here, we are concerned only with overall
levels of activity: +, if CE or SE; or -, otherwise.

A complete listing of all chemicals tested
is available at the NTP Home Page {\em http://ntp-server.niehs.nih.gov\/}.
The diversity of these compounds present a general problem to many
conventional SAR techniques. Most of these, such as the regression-based
techniques under the broad category called Hansch Analysis
can only be applied to model compounds that have similar
mechanisms of action. This ``congeneric'' assumption does not hold for the
chemicals in the NTP data base, thus limiting the applicability of such
methods. The Predictive Toxicology Evaluation project undertaken by
the NIEHS aims to obtain an unbiased comparison of prediction methods
by specifying compounds for blind trials. One such trial, PTE-1, is now
complete. Complete results of NTP tests for compounds in the second trial, PTE-2,
will be available by mid 1998.

ILP experiments with this data use Progol to predict
carcinogenic activity for compounds in PTE-1 and PTE-2.
These experiments use the obvious generic description of compounds
consisting of atoms and their bond connectivities.
These two predicates follow the same representation as used by us earlier
in predicting the mutagenic activity of nitro-aromatic compounds.
The background knowledge thus available for the ILP program was as follows.

\begin{description}
\item[Atom-bond description.] These are ground facts representing
        the atom and bond structures of the compounds. The
        representation first introduced in our mutagenesis experiments is retained.
        These are Prolog translations of the output of the molecular
        modelling package QUANTA. Bond information consist of facts of the form
        {\it bond(compound,atom1,atom2,bondtype)\/} stating that
        {\em compound\/} has a bond of {\em bondtype\/} between the atoms
        {\em atom1\/} and {\em atom2\/}. Atomic structure consists of facts
        of the form {\em atm(compound,atom,element,atomtype,charge)\/},
        stating that in {\em compound\/}, {\em atom\/} has element
        {\em element\/} of {\em atomtype\/} and partial charge {\em charge\/}.
\item[Generic structural groups.] This represents generic structural
        groups (methyl groups, benzene rings etc.) that can be defined
        directly using the atom and bond description of the compounds.
        Here we use definitions for $29$ different structural
        groups, which expands on the $12$ definitions
        used in the mutagenesesis studies.
        We pre-compute these structural
        groups for efficiency. An example fact that
        results is in the form {\em methyl(compound,atom\_list)\/},
        which states that the list of atoms
        {\em atom\_list\/} in {\em compound\/} form
        a methyl group. Connectivity amongst groups is
        defined using these lists of atoms.
\item[Genotoxicity.] These are results of short-term assays
        used to detect and characterize chemicals that may
        pose genetic risks. These assays include
        the {\em Salmonella\/} assay, in-vivo tests for the
        induction of micro-nuclei in rat and mouse bone marrow etc.
        A full report available at the NTP Home Page
        lists the results from such tests in one of $12$ types.
        Results are usually $+$ or $-$ indicating positive or negative response.
        These results are encoded into Prolog facts of the form
        {\em has\_property(compound,type,result)\/}, which states
        that the {\em compound\/} in genetic toxicology {\em type\/}
        returned {\em result\/}. Here {\em result\/} is one of $p$
        (positive) or $n$ (negative).
        In cases where more than 1 set of results are available for
        a given type, we have adopted the position of returning the
        majority result. When positive and negative results are returned
        in equal numbers, then no result is recorded for that test.
\item[Mutagenicity.] Progol rules from the earlier experiments on
        obtaining structural rules for mutagenesis are
        included. Mutagenic chemicals
        have often been found to be carcinogenic
        and we use all the rules found with Progol.
\item[Structural indicators.] We have been able to encode some of
        the carcinogenic structural alerts from the literature. At the
        time of writing this paper, the NTP proposes to make available
        nearly $80$ additional structural attributes for the chemicals.
        Unfortunately, this is not yet in place for reuse in experiments here.
\end{description}

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