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I'm trying to predict a binary outcome - let's call it "Cancer/no cancer" after this example here.

I'm trying to predict a binary outcome - let's call it "Cancer/no cancer" after this example here.

If not, what should I do?

Is it realistic to think there's a model (and associated cost function) that would come up with parameters that directly maximize one of those skill scores I'm interested in? So maybe this hypothetical model would produce probabilities and a threshold, or maybe it would produce probabilities that optimize the skill score when some standard threshold like 0.5 is applied to it, or maybe it would just produce binary forecasts of 0 and 1. I'm completely open to the possibility that such a model is not feasible - but why is it not feasible?

If such a model is unfeasible (or wouldn't work well), what should I do?

Is that feasible? If not, what should I do?

EDIT: Thanks to @deltaiv's answer, I realise I misspoke here - I understand that I'd need to change the model as well as the cost function. Is there some model and cost function that 'matches' a skill score I might be interested in? 

If not, what should I do?