OBJECTIVES: Derivation of incremental cost-effectiveness ratios (ICER) is a standard requirement for 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, under the assumption of linearity, which rarely holds. Machine learning (ML) methods through symbolic regression (SR) to improved model fit and estimated mean utilities within each health state was applied. We investigated 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). 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. These were modelled separately for each treatment (Erlotinib and best supportive care) separately. We generated the incremental QALY for the ‘best’ vs 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 higher mean QALYs and better model fit statistics: AIC of 92.4 for a 5 parameter model vs 115.7 for the OLS model). The mean incremental QALY changes 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 compared to standard OLS methods, while ensuring improved goodness of fit. SR, while apparently improving fit and lowering the ICER, is complex and requires further testing in more datasets.