# SPSS - Binary logistic regression: classification cutoff

Let's say I want to evaluate the predictive value of a continuous variable in the prediction of malignancy (event/status) of a tumour.

Malignant = 1 Nonmalignant = 0

In SPSS, I can run a binary logistic regression model to do so. It allows me to set a cutoff value for classification. My question is: SPSS assumes equal pretest chances and odds in both groups, and proposes a cutoff value of 0.5. However, research has shown that malignant tumours are 70 % of all tumours, and nonmalignant tumours are 30 % of all tumours. Hence, a priori, there is a chance of 70 % for a tumour to be malignant. There is, however, no way to include an a priori chance in SPSS (at least, not by my knowledge). Am I instead allowed to change the cutoff value to 0.5/(0.7/0.5)?

The rationale is that the probability for malignancy is 0.7/0.5 times larger than 0.5, and thus that, instead of changing pretest probabilities, the posttest probability could be reduced by a factor 0.7/0.5.

Is this correct, or not?

• Check the sensitivity and specificity at the different cut-off point (between 0 to 1). ROC curve is helpful. Then find the best cut-off point. Commented Oct 13, 2018 at 21:13
• Maybe a duplicate: stats.stackexchange.com/questions/212228/… Also stats.stackexchange.com/questions/67091/… Commented Oct 13, 2018 at 21:31
• @a_statistician the problem with that is that that would be based on my sample, which consists of only about 30 patients. In my sample, there's about an even number of persons with a malignant tumour and persons with a benign tumour. We're not talking about a cutoff value of the variable, but in logistic regression, the cutoff point of the probability for malignancy: a tumour has a probability for malignancy ranging from 0 to 100 %, and the cutoff is somewhere in between: when there is an even amount of malignant and benign tumours in the population, that would be 50 %. But ... Commented Oct 13, 2018 at 22:34
• ... here the cutoff of the probability cannot be 50 %, since there are more malignant tumours in the population than benign tumours. And although that is not the case in my sample, we need to account for that fact. We need to incorporate a 70 % a priori probability for malignancy, rather than 50 %; and since this is not directly possible in SPSS, I was wondering whether I could instead change the malignancy probability cutoff: Commented Oct 13, 2018 at 22:38
• SPSS: "PrTP = 0.50" or "PrTO = 1.00" || PrTO * ARG = PoTO || SPSS: 1.00 * ARG = PoTO || SPSS: if 1.00 * ARG > 1.00 then MAL || 2 options to incorporate true pretest probability: (1) Increase PrTP or PrTO such that PrTO * ARG > CUTO (impossible in SPSS) (2) Decrease CUTO such that PrTO * ARG > CUTO || REAL: PrTP = 0.70 | PrTO = 2.33 || REAL: 2.33 * ARG = PoTO || REAL: if 2.33 * ARG > 1.00 then MAL || ((1) Increase PrTO: 2.33 * ARG > 1.00) || (2) Decrease CUTO: 1.00 * ARG > 0.43 NEW CUTO: 0.43 ~ P = 30 % Commented Oct 13, 2018 at 23:14