Exercises for Mon Oct 15

1. On Mon Oct 8 I went through more on Cox regression and also Aalen's linear hazard rate regression model. For those having wished for more time and more details we had 45 extra minutes in UE 32, with a bit on martingales, etc.

2. I've uploaded com18a (on the pornoscope data) and com21c (on Cox regression for the Australian drug users) to the website. The latter also has my simple code for the log-partial-likelihood, for this dataset, finding the same beta estimates and standard errors as the "coxph" command in R's "survival" package.

3. Next week I do more with the Aalen linear model, and round off Ch 4. I also start Ch 5, which should contain non-surprising material, partly in the category of "similar, but simpler, than Ch 4".

4. For the n = 238 Australian drug users, do *both* semiparametric Cox regression *and* two parametric versions, with (i) the Weibull \theta s^\gamma and (ii) the Gomertz \theta \exp(\gamma s) for the baseline hazard. These two models have five parameters (two for the baseline and three \beta for the three covariates). For each of the two models, compute ML estimates, the standard errors, and also the maximised log-likelihood values. Which of these two models is best?

5. Try to fit the linear Aalen model to the Australian dataset, computing estimates of the cumulative functions B_0, B_1, B_2, B_3.

6. I've now uploaded an updated version of the Nils Collection of Exercises and Lecture Notes (now version 0.69, as of 9-x-2018, comprising 36 exercises, 52 pages).