Abstract
To avoid diagnostic surgery, the probability of nodal involvement of prostate cancer is modeled using the probit link function to determine whether the lymph nodes of a patients are infected. X-ray status and level of acidphosphatase in the blood serum of patients are considered as preoperative explanatory variables with the number of patients having nodal involvement as response variable. Within the framework of the probit regression model, the level of nodal involvement is predicted and the probability of nodal involvement obtained.
Highlights
INTRODUCTIONThe response y is a proxy for a variable that is continuous (Newsom, 2005)
For some dichotomous variables, the response y is a proxy for a variable that is continuous (Newsom, 2005)
A regression analysis that predicts the underlying latent variable is called the probit regression. It is characterized by the probit link function defined as the inverse of the standard cumulative normal distribution
Summary
The response y is a proxy for a variable that is continuous (Newsom, 2005). Z is the level of non-involvement of the lymph nodes of cancer patients. Probit regression is employed to determine the level of non-involvement of prostate cancer using acid phosphatase in the blood serum and X-ray status as preoperative explanatory variables. The level of non-involvement is the unobserved variable whose values are obtained by the probit model. Group 2: Patients with Acid PH < 60, positive X-ray status Probit (p2) = Φ-1(p2) = Z2 = 2.1176 – 2.0772 = 0.0404 p2 = prob (y = 0 | x1 < 60, x2 positive) p2 = Φ(Z2) = Φ (0.0404) = 0.5160 probability of involvement for group 2 is equal to 0.484. These values of probabilities can be compared with the proportions of non-involvement to check the accuracy of the fitted probability values as follows: Group 1: Group 2: Group 3: Group 4: Proportion of non-involvement
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