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I wanted to find the ability of a numeric continuous variable to predict mortality (dead/alive), and what cut off value to take in the continuous variable.

I wanted to construct an ROC curve and find the cut off value to achieve this.

I did a logistic regression, taking mortality (m) to be the dependent variable, and the continuous variable (v) to be the predictor.

The p value of the coefficient I got for v was 0.19. The study take p value of <0.05 as significant.

Given that the coefficient is not significant, can this model be used for prediction, and ROC curve constructed using this model?

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It can be used as a predictor if you feel that the coefficient you obtained is clinically important, you don't mind a p-value of 0.19, and the sensitivity or specificity is particularly favorable for your diagnostic or prognostic problem.

However, a coefficient with a p-value of 0.19 is unlikely to correctly classify dead/alive status.

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The question of how well something predicts something else is about effect size, not statistical significance. If N is small, then a fairly good predictor might be non-significant. If N is very large, then a very poor predictor might be significant.

However, with small N, our estimates of parameters are usually not very precise, so you will have a lot of doubt about any predictions you make.

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  • $\begingroup$ Thank you, the size in question here is 63 data points. Would you suggest checking AIC for whether to use this model or not? $\endgroup$ – Sudhanva Rao Nov 10 '19 at 12:48
  • $\begingroup$ AIC is only useful for comparing one model to another. I suggest using a measure of effect size. $\endgroup$ – Peter Flom Nov 10 '19 at 16:07

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