AI for Medical Prognosis Week 4 Quiz Answers!

Question 1) Person 1 has hazard hi(t) = 1, and Person 2 has hazard h2(t) = 2. What is the probability of dying within the first year for each patient?

Hint: The survival function S(t) in terms of the hazard function is:

• 0.63, 0.86 

• 0.5, 0.6 

• 0.37, 0.14

Question 2) Let T >0.

For patient 1, let the survival function be Si(t) and the hazard function be hi(t).

For patient 2, let the survival function be S2(t) and the hazard function be h2(t)

You see that S(T) > S2(T). The survival probability of patient 1 at time T is higher than the survival probability of patient 2 at time T.

Which of the following is true about the hazard of patient 1 and 2 at time T?

Hint: 

• h_1(T)>h_217) 
• h_1(1) <h_2(1)
• h_1(T) = h_2(1)
• None of the above

Question 3) Now assume that the hazards for patient 1, hy and for patient 2. h2 are proportional to each other. Also assume that Si(T) > S2(T) for some T>0.

Then which of the following is true about the hazards?

• h_1(1) = h_201) 
• h_1(1)<h_2(1)
• h_1(T)>h_2(1)

Question 4) You've fit a Cox model on 2 features: age and smoking status.

• 0.36
• 2.64 
• 2.7

Question 5) You've fit a cox model and have the following coefficients:

Which of the following interpretations is most correct?

• All other things held equal, having lower age increases your risk
• All other things held equal, having higher BP decreases your risk
• All other things held equal, being a female decreases your risk

Question 6) Assume h_1(t) = t, and h_2(t) = 1.0. At which time T> 0 does 5_1(T) = 5_2(T)?

• 
  
• 2 
• 1
• 0.5
• None of the above

Question 7) Using the Nelson-Aalen estimator estimate H(7), the value of the cumulative hazard at t=7 for this dataset.

The Nelson-Aalen estimator is:

• 7/12
• 8/11
• 519

Question 8) Which risk assignments would make this pair concordant?

• 0.3, 0.8 
• 0.5, 0.3 
• 0.5, 0.5
• The pair is not permissible

Question 9) Compute the Harrell C-index for the following dataset and risk scores:

Step 1: Find all the permissible pairs

Step 2: of the permissible pairs, determine which ones are concordant.

Step 3: of the permissible pairs, determine which ones are risk ties.

• 1.0
• 0.8
• 0.7