Fall 2013 Seminars
- Pythagorean Triples: from here to Infinity?
Marvin Gamble (USD)
December 4, Arts & Sciences Room 105, 4 p.m. - 5 p.m.
Are there an infinite number of primitive Pythagorean triples? Using number theory I will show the answer to this question and how to find these triples. I will prove what numbers can and cannot be used in the triples and prove the method that will be demonstrated.
This should be an interest to all secondary math education
majors and next semesters number theory students.
- Approximating the Baseline Hazard Function by Taylor Series for Interval-Censored Time-to-Event Data
Yuhlong Lio (USD)
October 2, Arts & Sciences Room 107, 4 p.m. - 5 p.m.
In many oncology clinical trials, time-to-event data are generated from scanning for cancer within a specific interval, resulting in interval-censoring along with complete-time and right/leftcensored time-to-event data. A common practice in analyzing data from this type of trials is to impute the interval-censored event time using the midpoint or right endpoint (i.e. the first observed time) of the interval so that well-known statistical methods developed for rightcensored time-to-event data, such as Cox regression, may be used for the requisite analyses. This may introduce bias and lead to erroneous conclusions. In this paper, a Taylor series is proposed to approximate the log baseline hazard function in Cox proportional hazards regression to mitigate the bias arising from analyzing the imputed time-to-event data. With this formulation, the likelihood ratio test can be used to select an appropriate order for this Taylor series approximation and maximum likelihood techniques used to estimate model parameters and provide statistical inference; e.g., on treatment effect. The application of this novel method is demonstrated by a simulation study and application to data from a breast cancer clinical trial