11/26/07: Is there increased parity in the NFL (Has Paul Tagliabue’s dream come true)?

Joseph Koopmeiners

The 1999 St. Louis Rams shocked the football world winning Super Bowl XXXIV
a year after going 4-12. Two years later, the New England Patriots completed a similar worst-to-first turnaround winning Super Bowl XXXVI a year after going 5-11. These surprising results lead football fans and sports writers to speculate that the NFL had entered a new era of parity due to the implementation of the salary cap and free agency before the 1994 season. Economists have written extensively on competitive balance in professional sports. Larsen et al. (2006) examined the effect of the salary cap and free agency on competitive balance in the NFL and found no significant difference in the standard deviation of team winning percentages before and after the 1994 season. The analysis of Larsen et al. has two primary limitations. First, using the standard deviation of team winning percentages as the outcome ignores that game results are the result of paired comparisons and therefore not all winning percentages are created equal. Second, Larsen et al. do not account for changes in year-to-year autocorrelation over time that could explain rapid improvements such as the 1999 Rams or 2001 Patriots.

We model NFL team strengths using a Bayesian state-space model that treats
game results as paired comparisons and allows for the comparison of the
standard deviation and autocorrelation of NFL team strengths by decade. The
year-to-year autocorrelation in NFL team strengths has decreased steadily
from .781 in the 1970s (95% CI: .665, .871) to .566 in the 2000s (.350,
.755). The standard deviation of NFL team strengths has decreased from .862
in the 1970s (.708, 1.07) to .731 in the 2000s (.589, .914) but there has
been little change since the 1980s (.737, 95% CI: .603, .923).

No seminar this week

11/12/07: Bayesian modeling of the dependence between two longitudinal processes with application to a smoking cessation trial

Prof. Mike Daniels, University of Florida

Joint models for the association of a longitudinal binary and
a longitudinal continuous process are proposed for situations where
their association is of direct interest. The models are parameterized
such that the dependence between the two processes is
characterized by unconstrained regression coefficients. Bayesian
variable selection techniques are used to parsimoniously model
these coefficients. An MCMC sampling algorithm is developed for
sampling from the posterior distribution, using data augmentation
steps to handle missing data. Several technical issues are
addressed to implement the MCMC algorithm efficiently. The models
are motivated by, and are used for, the analysis of a smoking
cessation clinical trial in which an important question of interest
was the effect of the (exercise) treatment on the relationship
between smoking cessation and weight gain.
Joint with Xuefeng Liu and Bess Marcus

11/05/07: An underlying framework for estimating a volume-outcome association

Ben French

A volume-outcome study is typically used to evaluate whether patients
treated by high-volume health care providers (e.g. surgeons or hospitals)
have better post-treatment outcomes than those treated by low-volume
providers. Previous methodological literature does not provide definitive
guidance on appropriate methods for a volume-outcome analysis. To provide a unified framework I explore a recurrent marked point process and examine the use of existing longitudinal analysis methods in the context of disaggregate volume-outcome data. Results from a simulation study indicate that generalized estimating equations and linear mixed models may provide a biased estimate of the volume-outcome association. However, an independence
estimating equation provides an unbiased estimate with nominal confidence
interval coverage. In this talk I will review the analysis of typical
longitudinal data. I will then describe the recurrent marked point process
setting and discuss implications for a volume-outcome analysis.