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A genetic algorithm for variable selection in logistic regression analysis of radiotherapy treatment outcomes
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Image of FIG. 1.
FIG. 1.

Schematic for genetic algorithm, showing the initialization process, the building of the subsequent generations with genetic operations, the evaluation of the population, and the output of the algorithm.

Image of FIG. 2.
FIG. 2.

Second term of the fitness function: empirical function of the -value for the regression coefficients, rewarding models with statistically significant variables.

Image of FIG. 3.
FIG. 3.

Selection of parents: stochastic uniform sampling using the roulette wheel method. The example shows a population of eight individuals, ranked 1–8 according to their fitness score. The crossover fraction is 0.5, therefore nine parents must be selected. The cursor selects nine locations in equal steps through the wheel, ensuring the individuals with a higher score have a greater probability of being selected.

Image of FIG. 4.
FIG. 4.

Evolution generation after generation of the population’s lowest and mean penalty, for model order 3. “Survival of the fittest” is evidenced by the overall decrease of the mean penalty (final mean penalty 0.719), and the monotonic decrease of the lowest penalty (final lowest penalty 0.341) illustrates the fact that a generation’s best individual always survives into the next generation.

Image of FIG. 5.
FIG. 5.

Penalty score of the best model as a function of model order, for different weight factors , 0.25, 0.5, 0.75, and 1. As the weight of the -value function increases, higher model orders are penalized more because they involve more nonsignificant variables.


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Variables selected by the GA, the baseline, and DREES for the best model at each model order, with the variables’ respective -value, and the model’s AUC, Spearman rank correlation coefficient, and fitness score (using AUC as predicting power and assuming ).

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Univariate analysis of the V30 and the use of tobacco at time of referral: percentage of patients developing RP of grade for each category listed in the first column.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A genetic algorithm for variable selection in logistic regression analysis of radiotherapy treatment outcomes