Direct search methods in the optimisation of cancer chemotherapy regimens

Current cancer chemotherapy regimens may involve 20-30 or more independent variables, each affecting therapeutic response and toxicity. With standard response surface modelling methods, finding the optimum combination with as few as 10 variables entails testing over 1,000 combinations, so these methods do not provide a feasible approach to such problems. However, they may be tackled by direct search methods (DSM), i.e. stepwise searches of the response surface. Experiments were carried out in advanced L1210 leukaemia treated with combinations of adriamycin with cyclophosphamide, isophosphamide with acetylcysteine and methotrexate with leucovorin. Two established DSM (Nelder-Mead and Box) were used, and a new method was designed to find consistent search paths in spite of wide biological variation. With methotrexate and leucovorin, DSM located combinations prolonging mean survival to 40-50 days (compared with 10.4 in controls) and giving high proportions of long-term survivors. These results were achieved with single injections of drugs given 7 days after injection of 10(6) leukaemic cells, i.e. 2-3 days before deaths began in untreated mice, and appear to be unprecedented with these agents. Searching for optimal combinations of established agents may be at least as rewarding as searching for new agents, and thus DSM may prove a powerful tool for improving the results of combination cancer chemotherapy.