This paper discusses the interpretation and use of the results-of mouse painting experiments. An imaginary experiment is proposed in which a steady state is reached by continuously feedinC in fresh mice. In due course the numbers build up until the number of mice dying from all causes per unit time equal the number of mice put into the experiment. Under these conditions the number of healthy mice in the steady population and the number showing tumours per unit time would seem intuitively to be a useful measure of tumorigenic potency. The age distribution in these two classes and the ratio of tumour bearing mice are discussed. It is shown how this data for the imaginary steady state experimen&; can be deduced from the results of a normal bioassay experiment and numerical results are quoted from the measurements given in Day Brit.J. of Cancer [in publicationJ. ON OIN L.Ij BATCo document for Province of British Columbia 5 November 1999 PAINT --XPrT?I' VIATY9TS OF -OM"," I 17r, T 7 -IT Charles Ellis. December 1966 We do not know how smoke condensate causcs tum-ours on the skin of mice and, therefore, we cannot interpret our experiments even in terms of "mouse-skin reaction" except by maRing assumptions. Paigel has referred to this and has suagested that when the action of two different materials is in all respects similar and dose 711 of the first material gives identically the same results as dose "'.2 of the second material vie 6an then say that the carcinogenic potencies are in the ratio This is logically satisfactory but somewhat restrictive. In default of a logical basis on which to interpret the results of experiments ,ue must depend on intuition, and a possible a,pproach iz the followinC. let us consider an imaginary mouse painting expertment where the dosinG rate of introduction of fresh mice of the same initial age, so that 17,Y1 new m ice enter the ex, periment in time (SZ- . Thus, if the experiment started at t ime 7-'~~ 0 then at time 77 there would be inice of all ages from the initial age up to -77 -J. the initial age. If this imWinary ex-aeriment continues for a sufficient length of, time a steady state will ultimately be reached in which there are /1 VM healthy mice without tumours Al? mice with tumours A/C mice with carcinoma etc. I Day and Paige Brit.J.of Cancer [in publication] C7 N 0*1 BATCo document for Province of British Columbia 5 November 1999 2. The number of mice dyine in time 91 f rom all ca-usea will equal the number entering the experiment, that is 4rL -~'Z- . To simplify the discuosion we will restrict ourselves to the consideration of tumours only. We also assvwie that in this imaginary experiment we ''6 ? /-,-7 determine / which is the number of previously healthy mice who develop tumours in t irie The problem now is to decide-whether the best guess for comparing tw o materials i3 to use the stationary ratio or The first alternative looks attractive since it is ratio of similar quantities, but yet the stationary value of A~ depends on a balance between the nnmber joinint-,, the classification in a Civen interval anl the number lezniing it by death or progreGsion to carcinonas. Uno as long as a mouse is alive it is impossible to be certain that it carries only a tumour and that this has not progrezsed to a carcinoma. In contrast the rr.te of occurrence of tumour-bearing mice only involves one phanonenon and is only related to the source of such tumour-bearing mice, that is the healthy mice without tumours. We therefore choose /T// A/ IV ....... 1. as turaori.-enic index, it has the dimensions of time -1. This does not use all the information that CD is available in this imaginary experiment since in ~_n C7% addition we can presume to know the aCe distribution - in these two classes. CD U- CX11 C-r BATCo document for Province of British Columbia 5 November 1999 3. The general form of these distributions will be A3 e A Age distribution in the steady state among healthy mice Age di3tribution in the citeady state amorc; the mice showing tumours in a given interval Here 41 1/4 and 010 are the fractions with ages between Aw,4*1,4 . It would seem a priori that the characteristics of these curves would be related to the tumorigenic properties of the substance used in the experiment. For example, even if the same total number of tumours per unit time were produced by a certain dose of a strong chemical carcinogen and also by, say, smoke condensate, it is likely that these distribution curves against age would be different. 'Ve guess, therefore, that it might be instructive to compare the average age of the mice showing tumours to the average age of the healthy mice. BATCo document for Province of British Columbia 5 November 1999 4. At this stage we must make the point that v.,ere it possible to carry out the steady state experiment it would be easily interpretable and, froza an intuitive standpoint, would lead directly to concliisions that would be likely to belp towards a understanding of the phenomenon. We have instanced two types of data that we *think the investiCator would be interested in obtaining from such an experiment. They are firstly the tumorigenic index, that is the ratio of the rate of occurrence of tumour-bearing mice to the number of healthy non twaour-bearing mice and secondly, the age distribution of the healthy mice and of the mice shoviii-4; tumours in a Given interval. Quite obviously it is not possible to carry out a "steady state" experiment, but on the other hand it is simple to deduce from the results of a normal bio-assay experiment what would be the outcome of a "steady state" experiment. The attitude of this paper, therefore, ic not to suggest the consideration of the "steady state" as a kind of trick on which to base a formula for a tiunorigenic index, but on the contrary, to propose such an experiment as the loCical ba3is by which to compare the carcinogenic potencies of different materials. We look then at the usual bioassay experiment, not as an end in itself, but as a measurement which enables us to synthesise the "steady state" experiment. ON ON BATCO document for Province of British Columbia 5 November 1999 5. 2. We first relate the characteristics of the stationary state to the properties of the groups of mice which constitute it. Suppose the experiment started at time r- 0 and consider the group of mice 4" a~~ in number entering this imaginary experiment betvreen and 1---4- FZ- . At a later time they will have been for time in the exneriment and we write the numbers of healthy mice surviving as /V - = 4-k7 rz- 1-16 rl- 2 0 3 is the mortal*t If ction The total number 7 of healthy mice 7-/-"7 at t ime is, -7 ezj The stationary value of /V is thus C) CX) BATCO document for Province of British Columbia 6 November 1999 6. Novi consider the stationary state durine an interval z-'A T . The total number AR of healthy mice present is made up by mice of all age groups, that of age 4& being in number Ile t A P-represent the probability o a healthy mouse of this age e developing a tumour in time then the number of mice from the Group of age Z- which will develop tumours. in time A is -7 7, 71 ;1 C) Z- and therefore the total number of tumours produced per unit time ZI '77 5. The first tumorigenic index is, therefore, alz- 6. BATCo document for Province of British Columbia 5 November 1999 7. It will now be clear that the age distribution in the stationary state of the healtly mice which has been given the symbol *t ?X) is just the function defined above. Purther, the function V showing the oFe distribution among the mice developing tumours in unit time is the product of functions 21 ~ anti The average P-,-e of the population of the healthy mic.e without tumours is ,4 "Ce and the average age of the mice developing tumours in unit time is "a A P h/ I J-71 7 0- BATCo document for Province of British Columbia 5 November 1999 11 lu The task that now remains is to show how these two functions - and w"ich describe the "steady state', can be obtained from a real, conventional, bioassay ex-:)eriment. If the results of the bioassay e=eriment are shown as /1/, mice initially 0 healthy mice.surviving at the beginning of A/ successive 4 - weekly periods number of previously /J healthy mice showing 0 tumours in the course of the 4 - weeks period then in term of the "steady state" functions and /V 12- V), r-7 9 Thus the Tumorigenic Index is L DIr A0 0 Oc &I Oc Z-) P jr BATCo document for Province of British Columbia 5 November 1999 9. The numerator is just the sum of all the tumour-bearing mice which occur during the experiment, the denominator depends on the mortality curve of healthy mice. If in two experiments to be compared this factor does not vax-j greatly then the Tumorigenic Indices are simply in the ratio of the aggregate number of tumour-bearing mice. This assumption haz frequently been made in the past, but without proDer examination of its reliability. It may be of interest to 'see the value of the factor in the denominator for some cases of the exneriment described by Day [loc cit5l. The integration is carried to the 116th week. TA711P I. 6 The factor ~Wz for some cases Pxneriment Pactor X 10-4 PASH 0.869 PAS*.' 0.998 PASL 1.126 1.112 NFL 1.085 CO11TU 1.130 CO RA 1.145 It will be noticed that the factor in these comparable experiments varies by a factor of 1.3 Which is not negliGible. If the comparison had been between a slow acting carcinoGen like smoke condensate and a quick acting one like benzpyrene the factor might be still more important. BATCO document for Province of British Columbia 5 November 1999 10. Evaluation of the first tumorigenic index has been carried out for the Harrogate FAS and N.F. exDeriments. The detailed results for 116 weeks were used and a correction, which proved to be of the order of at most 2 - 3 per cent, made*to extrapolate to week 140 which dbes in practice represent infinity. A correction for the naturally occurring tumours was applied by subtracting the average of CONU and COTTA, that is 0.03 x 10-2 weeks -1. TA TT. Tumorigenic Index X 100 [weeks 117 FASI-17 H 2.30 1.39 1.66 I-G3 0.79 2.07 L o.69 0.34 2.05 COW 0.106 CONA 0.053 The main uncertainty in these figures arises from the statistical fluctuations of the occurrence of tumours. The number of these varied from about 200 for FASTI to 46 for "TIT,. Taking 100 as a mean fieure and treating the occurrence of each tumour as an independent event we might expect a probable error of 10 per cent, that is 95 per cent litaits of about 30%. It is, therefore, not'possible to decide BATCo document for Province of British Columbia 5 November 1999 11. from these results whether the dose response curve is linear up to the high dose of 100 mg or whether there is some -ohenomenon analogous to saturation comiric in. For the moment ve average each material by dividiA,,, by the amount of mg in the treatment and obtain the specific tumorigenic index. I TII Specific Tumorigrenic Index x 104 [,.-.-eeks -1 1-mg -lj PAS 2.77 TTF 1.44 Ratio 1.9 + 304 ,,, and Paige Eloc.citJ usir,--,g detailed statistical -ay analysis and a different model for calculation concluded f that at the 95'/'. confidence limit this ratio lay somewhere between 1.5 and 2.1. It may be of interest to show what would be the everare a!~e of the mice in "steady state" experiments ,=--sr 4-ifferent t--e!--tz-en-z. These have tesm ca-1c,.;2zled from the Harroc-a-te results using equations 7. AveraEe "'Iteady Alive vlitliDut tumours Age of *,.'.ice in State" - weeks PA. 1H 35.8 ~T! 138 .9 CO!TU 42.6 Showine tumours PASH 62.4 in rperiod of PA')"j 70.3 4 - weeks PASL 70.6 tTr-11I 72.3 !TF':, 80.0 1 T 76.7 cz:~ (-n ON c::> BATCo document for Province of BritiSh Columbia 5 November 1999 12. It will be seen that the tumorigenic potency of the different treatments is clearly reflected by the average age of the mice showing tumours, it increases as the dose decreases and is hi,r~her for the less potent TIP than for F,A,S. The different toxic effects of the treatments is also brought out clearly, there being more healthy mice of advanced age under CONTJ than under rTFU, and least under the more toxic PAS. It is not clear at this stage whether the "average a5ell concept will prove useful in assessiAG different naterials. On the above results the ra-tio of the average life of the tumour showing class to the healthy mice class is virtually the same for ri~mi - [1.741 as for M - [1.86J. Perhaps more infor--iation will appear when the results for a quicker acting carcinogen such as benzpyrene are available. We may finally examine the help of the "stead7 state" experiment in assessing the value of tumour/carcinoma ratio. Prom the population of living mice the only data that is available and can be uniquely identified concern the he.-Llthy mice without tiimours and the mice per unit time who show tumours. We can only get information about carcinomas from post-mortem histological examination. If 91h S'Z mice are fed into the erperi!jent in time 65 Z- then the same number must leave the experiment by death in time CD U-4 BATCo document for Province of British Columbia 5 November 1999 13. Of these be healthy