Examples of possible questions to the oral exam

The list is not exclusive; it only gives examples of questions.

Several questions will be posed to each student.

Some of the questions may be supplemented with computer output and graphs.

 

�         Explain what is meant by a counting process and its intensity process. Illustrate with examples.

�         Explain how a martingale may be derived from a counting process. What are the predictable and optional variation processes of the martingale?

�         Explain what is meant by a stochastic integral with respect to a counting process martingale, and why the stochastic integral is itself a martingale. What are the predictable and optional variation processes of the stochastic integral?

�         Explain what is meant by independent right censoring.

�         Explain what is meant by the multiplicative intensity model for counting processes and give examples of situations that may be described by the multiplicative intensity model.

�         Give a motivation for the Nelson-Aalen estimator for the multiplicative intensity model for counting processes and show that the estimator is approximately unbiased. Derive an estimator for its variance.

�         Show that the Nelson-Aalen estimator is approximately normally distributed and use this to derive a log-transformed confidence interval for the cumulative hazard.

�         How are the survival function and the (cumulative) hazard rate defined for the continuous case, and how are they related? How can the relations be generalized to general distributions?

�         Give a motivation for the Kaplan-Meier estimator and describe how it may be used to estimate quartiles of the survival distribution. How can one derive confidence limits for the quartiles?

�         Explain the relation between the Kaplan-Meier and Nelson-Aalen estimators.

�         Show that the Kaplan-Meier estimator is approximately normally distributed and use this to derive a log-log-transformed confidence interval for the survival function.

�         Give a motivation for the logrank test for two samples, and describe alternative tests.

�         Describe Cox's regression model and discuss the model assumptions.

�         Derive Cox's partial likelihood and Breslow's estimator for the cumulative baseline hazard.

�         Describe Aalen's additive regression model and give a motivation for the estimator for the cumulative regression functions.

�         Describe situations where occurrence/exposure rates apply, derive the occurrence/exposure rates and discuss their statistical properties.

�         Describe situations where Poisson regression applies, and describe how the model fit may be performed by "standard software"

�         Explain what is meant by the proportional gamma frailty model. Derive the population survival function and population hazard rate and interpret the results.