On the use of multi-objective evolutionary algorithms for survival analysis

A genetic programming approach to development of clinical prediction models: A case study in symptomatic cardiovascular disease

Background

Genetic programming (GP) is an evolutionary computing methodology capable of identifying complex, non-linear patterns in large data sets. Despite the potential advantages of GP over more typical, frequentist statistical approach methods, its applications to survival analyses are rare, at best. The aim of this study was to determine the utility of GP for the automatic development of clinical prediction models.

Methods

We compared GP against the commonly used Cox regression technique in terms of the development and performance of a cardiovascular risk score using data from the SMART study, a prospective cohort study of patients with symptomatic cardiovascular disease. The composite endpoint was cardiovascular death, non-fatal stroke, and myocardial infarction. A total of 3,873 patients aged 19–82 years were enrolled in the study 1996–2006. The cohort was split 70:30 into derivation and validation sets. The derivation set was used for development of both GP and Cox regression models. These models were then used to predict the discrete hazards at t = 1, 3, and 5 years. The predictive ability of both models was evaluated in terms of their risk discrimination and calibration using the validation set.

Results

The discrimination of both models was comparable. At time points t = 1, 3, and 5 years the C-index was 0.59, 0.69, 0.64 and 0.66, 0.70, 0.70 for the GP and Cox regression models respectively. At the same time points, the calibration of both models, which was assessed using calibration plots and the generalization of the Hosmer-Lemeshow test statistic, was also comparable, but with the Cox model being better calibrated to the validation data.

Conclusion

Using empirical data, we demonstrated that a prediction model developed automatically by GP has predictive ability comparable to that of manually tuned Cox regression. The GP model was more complex, but it was developed in a fully automated way and comprised fewer covariates. Furthermore, it did not require the expertise normally needed for its derivation, thereby alleviating the knowledge elicitation bottleneck. Overall, GP demonstrated considerable potential as a method for the automated development of clinical prediction models for diagnostic and prognostic purposes.

Double-blind evaluation and benchmarking of survival models in a multi-centre study

Accurate modelling of time-to-event data is of particular importance for both exploratory and predictive analysis in cancer, and can have a direct impact on clinical care. This study presents a detailed double-blind evaluation of the accuracy in out-of-sample prediction of mortality from two generic non-linear models, using artificial neural networks benchmarked against a partial logistic spline, log-normal and COX regression models. A data set containing 2880 samples was shared over the Internet using a purpose-built secure environment called GEOCONDA (www.geoconda.com). The evaluation was carried out in three parts. The first was a comparison between the predicted survival estimates for each of the four survival groups defined by the TNM staging system, against the empirical estimates derived by the Kaplan-Meier method. The second approach focused on the accurate prediction of survival over time, quantified with the time dependent C index (C(td)). Finally, calibration plots were obtained over the range of follow-up and tested using a generalization of the Hosmer-Lemeshow test. All models showed satisfactory performance, with values of C(td) of about 0.7. None of the models showed a systematic tendency towards over/under estimation of the observed survival at tau=3 and 5 years. At tau=10 years, all models underestimated the observed survival, except for COX regression which returned an overestimate. The study presents a robust and unbiased benchmarking methodology using a bespoke web facility. It was concluded that powerful, recent flexible modelling algorithms show a comparative predictive performance to that of more established methods from the medical and biological literature, for the reference data set.