Given the questions below, provide clear answers

Question 3.18 You want to use Cox regression to estimate the force of mortality for a group of endowment assurance policyholders. You propose using a model that takes account of duration (ie the time that has elapsed since the policy was issued) and the age and sex of the policyholder. You start by investigating the model: U(x, 21, 22) = Mo(x)eBIZI+By Zz where x denotes the age of the policyholder, 0 if the duration is less than 1 year Z1 = if the duration is at least 1 year 0 for males for females You have estimated the values of the parameters , and By , and have obtained the following results: Covariate Parameter Standard error Duration 0.416 0.067 Sex -0.030 0.017 (i) State the class of policyholders to which the baseline hazard refers. [1] (ii) Explain whether the duration covariate is significant in determining mortality. [3] (iii) Compare the force of mortality for a new female policyholder to that of a male policyholder of the same age, who took out a policy 2 years ago. [2] [Total 6]Question 3.17 A medical researcher is investigating the time it takes for their symptoms to disappear after patients start taking a particular drug. The results of a pilot study of 6 men and 8 women were as follows: Day on which symptoms disappeared Males: 3, 2, 6, 15, 6, 2 Females: 5, 2, 2, 3, 7, 2, 6, 6 The researcher is using the following proportional hazards model to describe the hazard rate at time & (measured in days from commencement of treatment) for the ith individual: 2;(t) = 1(1) xk Here 1(t) denotes the baseline hazard rate at time z and x; encodes the sex of the ith individual, with x; =0 for a male and x; =1 for a female. (i) Without carrying out any calculations, state how the sample mean and standard deviation of the times taken for symptoms to disappear could be used to gauge whether the baseline hazard rate is approximately constant. [2](ii) (iii) {iv} (V) Shotsr that the partial log-likelihood function can be written in the form: 31k} = Slog k IS log(.?5 + it} 21og(.8 +it} 51og(l + it} +eonstant [4] An initial estimate of if, the maximum likelihood estimate of it , is 1.4. Use one iteration of the Newton-Raphson method to obtain an improved estimate of if . [3] fine vaton-Rapns'on method area the fact that if x is a good initiair approximation to a root of the equation f(x}={], than 35*: 3;- if?) 1'5 x nsna y a batter approximation. Assuming that your estimate obtained in (iii) is accurate, evaluate 8'13?) and hence can}: out an approximate test to determine whether the rates rut} are different for males and females. [4] On the assumption that the hazard rates do not differ according to sex, estimate the median time until symptoms disappear using the Nelson-Aalen method. [3] [Total 16]