Medical Statistics

Joint modelling of longitudinal and survival data in Stata

by Michael Crowther

The joint modelling of longitudinal and survival data has received remarkable attention in the methodological... more The joint modelling of longitudinal and survival data has received remarkable attention in the methodological literature over the past decade; however, the availability of software to implement the methods lags behind. The most common form of joint model assumes that the association between the survival and longitudinal processes are underlined by shared random effects. As a result, computationally intensive numerical integration techniques such as adaptive Gauss-Hermite quadrature are required to evaluate the likelihood. We describe a new user written command, stjm, which allows the user to jointly model a continuous longitudinal response and the time to an event of interest. We assume a linear mixed effects model for the longitudinal submodel, allowing flexibility through the use of fixed and/or random fractional polynomials of time. Four choices are available for the survival submodel; namely the exponential, Weibull or Gompertz proportional hazard models, and the flexible parametric model (stpm2). Flexible parametric models are fitted on the log cumulative hazard scale which has direct computational benefits as it avoids the use of numerical integration to evaluate the cumulative hazard. We describe the features of stjm through application to a dataset investigating the effect of serum bilirubin level on time to death from any cause, in 312 patients with primary biliary cirrhosis.

Comparison of generalized estimating equations and quadratic inference functions using data from the National Longitudinal Survey of Children and Youth (NLSCY) …

by Dillon T. Browne

Variations in posttonsillectomy haemorrhage rates are scale-invariant

by Thomas Ward

Co-authored with J. Phillips and P. Q. Montgomery

Background: Scale invariance is a property of scientific laws or objects that change in a prescribed fashion if... more Background: Scale invariance is a property of scientific laws or objects that change in a prescribed fashion if measurements are scaled, and is often represented by a power-law relationship. Power laws suggest that events of a large magnitude will be rare, while small events will be much more common, and that a simple mathematical law relates severity with frequency. Scale invariance has been demonstrated in scientific fields including physics, social science, and economics. The authors use the complication of a posttonsillectomy hemorrhage to test whether this property is a feature of surgical complications.
Methods: Non-identifiable data were obtained regarding posttonsillectomy hemorrhage and subcategorized by calendar month, and the percentage rate of posttonsillectomy hemorrhage was calculated. The data were then transformed using a logarithmic function. This transformed data were plotted and a linear regression analysis was performed.
Results: The 13-year period studied included 6,381 tonsillectomy procedures. The logarithm of the frequency of a given rate range of posttonsillectomy hemorrhage (y) was linearly related to the logarithm of the geometric mean of the rate range (x). The best-fit straight line was y = -1.3996× + 2.0624 with R2 = 0.851, n = 10, r = 0.922, and P < .001.
Conclusions: The authors found that the incidence of posttonsillectomy hemorrhage is scale invariant. The practical implication is that the observation of rare incidences of large hemorrhage rates may not be due to a unique circumstance or a particular operative fault. To reduce the incidence of extreme rates of postoperative hemorrhage, a review of the entire process of tonsillectomy would be required. Scale-invariance analysis may represent a novel tool that should be considered when reviewing surgical complications.

Calculating and graphing within-subject confidence intervals for ANOVA

by Thom Baguley

Official/complete version:

Baguley, T. (2012). Calculating and graphing within-subject confidence intervals for ANOVA. Behavior Research Methods, 44, 158-175.

The psychological and statistical literature contains several proposals for calculating and plotting confidence... more The psychological and statistical literature contains several proposals for calculating and plotting confidence intervals for within-subject (repeated measures) ANOVA designs. A key distinction is between intervals supporting inference about patterns of means (and differences between pairs of means in particular) and those supporting individual means. It is argued that the former are best accomplished by adapting intervals proposed by Cousineau (2005) and Morey (2008) so that non-overlapping confidence intervals for individual means correspond to a confidence for their difference that does not include zero. The latter can be accomplished by fitting a multilevel model. In situations where both types of inference are of interest, the use of a two-tiered CI is recommended. Free open-source, cross-platform software for these interval estimates and plots (and for some common alternatives) is provided in the form of R functions for one-way within-subject and two-way mixed ANOVA designs. These functions provide an easy to use solution to the difficult problem of calculating and displaying within-subject confidence intervals.

The application of circular statistics to psychophysical research.

by Pearl S. Guterman

International Society for Psychophysics, Co-authored with Robert S. Allison and Hugh McCague, 2009

Directional data arising from psychophysical studies requires careful processing due to its cyclical nature. Unlike... more Directional data arising from psychophysical studies requires careful processing due to its cyclical nature. Unlike linear variables such as response time and intensity, directions can be represented as angles or vectors on a circle, may have no natural zero-point or magnitude, and are defined on a periodic circle rather than an infinite line. Because of these unique features, directional data necessitates the use of circular statistical methods; however, unfamiliarity and limited availability of software that support circular data analysis have largely led to its under-use and misapplication. Here the implications of using linear statistics for circular data were explored by submitting data from a behavioural study to both circular and linear statistical analysis.

No Category Specificity In Alzheimer's Disease: A Normal Aging Effect

by Keith Laws

The authors examined category effects on tasks of picture naming, naming to definition, and word–picture matching in... more The authors examined category effects on tasks of picture naming, naming to definition, and word–picture matching in 38 patients with Alzheimer’s disease (AD) and 30 elderly controls. Each task was matched across category on all “nuisance” variables known to differ across domains. Standard analyses
revealed significant category disadvantages for classifying living things in AD patients but also for elderly controls on each task. To overcome the ceiling effect in controls, the authors conducted 1,000 bootstrap analyses of covariance, with control performance as a difficulty index covariate. These covariate analyses eliminated the category effect in AD patients on all 3 tasks. Indeed, the authors report that control performance accounted for 64% (picture naming), 49% (naming to description), and 42% (word–picture matching) of variance in AD performance. This suggests that, although category effects in AD patients do not reflect intrinsic variables, the size and direction of the category effect are not different from those in elderly controls.