OBJECTIVES: Derivation of incremental cost-effectiveness ratios (ICER) is a standard requirement for some decision makers. A key part of methodology used requires estimating utilities, generated within pre-defined discrete health states, typically achieved through modelling utilities as functions of health states, often under the assumption of linearity, which may not hold. We tested the application of machine learning (ML) methods through symbolic regression (SR) to investigate model fit and mean utilities within each health state. We evaluated the performance of ML algorithms on the ICERs and quality adjusted life years (QALYs).

METHODS: We used data from a previous published trial (TOPICAL) in non small cell lung cancer (NSCLC) that compared Erlotinib with placebo. Health states were defined as progression free (PF), progressive disease (PD) and Dead through a standard 3 state partitioned survival Markov model. Utilities were modelled (linear and non linear) as functions of health states. Mathematica® was used to generate 2000 models (within 3 minutes) of varying complexity and performance. The 'best' model fit (using e.g. AIC,R²) was used, to generate the incremental QALY and compare with the linear (OLS) model.

RESULTS: The observed mean utilities for each of PFS and PD were 0.566 and 0.474, respectively. Models using SR resulted in improved model fit: AIC of 92.4 (5 parameter model) vs 115.7 (OLS model). The mean incremental QALY changed from 0.035 to 0.049 when using more complex models, thereby reducing the ICER from £202,571 (OLS) to £144,673 (5 parameter) - around 30% decrease.

CONCLUSIONS: The use of ML through SR was shown in this case to improve model fit and lower the ICER as compared to standard OLS methods, while ensuring improved goodness of fit. SR, appears to improve model fit, however, is complex and requires further testing in more datasets.