I have nine variables, age, bmi, duration of disease, fasting blood glucose, diastolic blood pressure, systolic blood pressure, cholesterol, triglyceride, and HbA1c. Using these variables I want to predict the prevalence of an event (outcome: 1=yes, 0=no) related to this specific disease. I applied logistic regression using stepwise backward elimination.
I got fasting blood glucose, diastolic and systolic blood pressure, cholesterol and triglyceride as non significant variables. The regression coefficients for the remaining variables are:
Next, I want to calculate the probabilities of the event for each patient by the formula $$ p = \exp(B_o+B_1X_1+\dotso+B_nX_n)/(1+\exp(B_o+B_1X_1+\dotso+B_nX_n)) $$ Out of the total patients that were included in the study only 8% had the event. I don't know why but all the probabilities are coming out to be 1 or approximately 1 for every case.
Neither the regression coefficients nor the variable values are too high. Even with 92% negative events, why is the probability prediction always 1? Is overfitting the reason? If so, how to detect and solve overfitting? My question is why are my probabilities always 1 and how can I fix it? Is there any other method to calculate probabilities?
I am stuck in my research at this point and will be highly grateful to anyone who assists me with this problem.