1. Based on the fitted equation, write the formula, and calculate the estimated hazard ratio comparing the risk of death for a patient 75 years-old to that of a patient 65 years-old (reference), assuming the following:

C1) Both patients had high disease volume and received the standard treatment.

Relevant Info below:

Table 1 columns B and C report the estimates of parameters and their standard errors of a fitted multivariable Cox proportional hazards model for overall survival, The analyzed data is from randomized phase 2 clinical trial in 860 patients with metastatic castration-resistant prostate cancer, with patients assigned in a 1:1 allocation ratio to receive testosterone suppression plus either open-label enzalutamide ((ENZA) or a standard nonsteroidal antiandrogen therapy (Standard, control group). Overall survival was defined as the elapsed time from date of recurrent disease diagnosis to date of death or date last known to be alive (censored observations). Table 1. Multivariable Cox proportional hazards regression analysis of overall survival. A B C D E F G H Reg Std Wald Wald 2-sided Hazard 95% CI Prognostic factor coeff error z-value 02-value p-value Ratio LE UB Treatment arm ENZA vs. Standard (referent) -0.412 0.137 -3.007 9.044 0.003 0.049 -0.681 -0.143 Disease Volume High vs. Low (ref.) 1.234 0.356 3.466 12.015 0.001 3.435 0.536 1.932 Age (in years) 1-year increase 0.071 0.023 3.087 9.529 0.002 1.074 0.026 0.116 5-year increase Write the corresponding fitted Cox model equation expressing the hazard function or risk of dying at time t. . The fitted Cox model equation is given by: b(t, X) = ho(t) exp(-0.412 TREAT + 1.234 VOL + 0.071 + AGE) . ho(t) is the baseline hazard function; TREAT= 1 (ENZA), 0 (Standard - referent); VOL= 1 (High), 0 (Low - Ref); Age in years (1 year increase, 5 year increase). From the estimated coefficient b = -0.412, we obtain the estimated hazard ratio comparing ENZA v. Standard (ref.) as follows: HR = h(t, X=1) / h(t, X=0) = exp(b)= exp(-0.412) = 0.049. From the estimated coefficient b = 1.234, we obtain the estimated hazard ratio comparing high v. low (ref.) as follows: HR = exp(b) = exp(1.234) = 3.435. . From the estimated coefficient b = 0.071, we obtain the estimated hazard ratio comparing age as follows: HR = exp(b) = exp(0.071) = 1.074