Logistic Regression A predictor of whether throat cancer has metastasized to the lymph nodes is the size of the tumor. Here's the log odds regression equation predicting the probability of metastasis from the size of the tumor measured in cm from a hypothetical study of a 100 patients. In 음 = -2 + 0.8 x Size a. Use the above equation to estimate the odds of a metastasis for a patient with a tumor of 10 cm. odds = (Hint: First calculate the In(odds), then exponentiate to get the odds) Submit Answer Tries 0/4 b. Use the equation to estimate the probability of a metastasis for a patient with a tumor of 10 cm. Submit Answer Tries 0/4 c. How much do the estimated odds of metastasis change if the tumor increases in size by 1 cm? In other words what the Odds Ratio for Size? Submit Answer Tries 0/4 d. Compare the odds of metastasis for 2 patients whose tumor sizes differs by 3 cm. The odds of metastasis for the patient with the larger tumor is times the odds of metastasis of the patient with the smaller tumor. Submit Answer Tries 0/4 e. How does the estimated probability of metastasis change if the tumor increases in size by 1 cm? It changes by a fixed additive amount regardless of the tumor size. (.e., there's a constant slope in the probability vs size plot) It changes by a fixed multiplicative factor Neither of the above, you can't describe how the probability changes with either an additive or multiplicative constant since probability is bounded between 0 and 1 (think of the "S" shaped curve.) f. How large does the tumor have to be for the estimated probability of metastasis to be 50%, how about 90%? (Answer by filling in the chart below) Tumor Size in cm In(odds) odds p 10 Submit Answer Tries 0/3 Submit Answer Tries 0/3 Submit Answer Tries 0/3 0.5 Submit Answer Tries 0/3 Submit Answer Tries 0/3 Submit Answer Tries 0/3 0.9 Submit Answer Tries 0/3 Submit Answer Tries 0/3 Submit Answer Tries 0/3
