Colleen Kelly

Monotone smoothing with application to dose-response curves and the assessment of synergism.

A spline-based procedure for monotone curve smoothing is proposed and is illustrated by application to dose-response curves. It is then shown how such smoothing can be applied to assess possible synergism or antagonism of two drugs.

Correcting for Regression to the Mean in Behavior and Ecology

If two successive trait measurements have a less‐than‐perfect correlation, individuals or populations will, on average, tend to be closer to the mean on the second measurement (the so‐called regression effect). Thus, there is a negative correlation between an individual’s state at time 1 and the change in state from time 1 to time 2. In addition, whenever groups differ in their initial mean values, the expected change in the mean value from time 1 to time 2 will differ among the groups. For example, birds feeding nestlings lose weight, but initially heavier birds lose more weight than lighter birds, a result expected from the regression effect. In sexual selection, males who remain unmated in the first year are, on average, less attractive than mated males. The regression effect predicts that these males will increase their attractiveness in the second year more than mated males. In well‐designed experiments, changes in the experimental and control groups would be compared. In observational studies, however, no such comparison is available, and expected differential effects must be accounted for before they can be attributed to external causes. We describe methods to correct for the regression effect and assess alternative causal explanations.

Tests for homogeneity of the risk ratio in a series of 2×2 tables

We often apply the risk ratio to measure the strength of a causal relationship between a suspected risk factor and a disease of interest. In this paper we consider testing the homogeneity of risk ratio over a series of 2x2 tables. In addition to the classical weighted least squares (CWLS) test procedure, we consider two test procedures using simple transformations of the CWLS statistic and develop three other asymptotically weighted test procedures. On the basis of Monte Carlo simulation, we conclude that the commonly-used CWLS test procedure is generally conservative, especially when the number of 2x2 tables is large and the mean group size per table is moderate or small. We further find that two of the test procedures discussed here can not only generally outperform the CWLS test procedure, but also perform well in a variety of situations considered in this paper. Finally, we illustrate the use of these testing procedures with an example of six randomized trials that assess the effects of aspirin on the prevention of death in post-myocardial infarction patients.

A Test of the Markovian Model of DNA Evolution

The Markov model of molecular evolution has recently received a significant amount of interest because its statistical nature allows for the testing of a number of evolutionary hypotheses. Here we propose a test which assesses whether data from two species sharing a common ancestor will fit a general Markovian model. We illustrate the test with two examples of data which appear at first glance not to fit a Markov model.

A note on interval estimation of kappa in a series of 2 × 2 tables

When there are confounders in reliability studies, failing to stratify data to account for these confounding effects may produce a misleading estimate of the interrater agreement. In this paper, we focus discussion on interval estimation of kappa for measuring agreement between two raters with stratified data. Using Monte Carlo simulation, we compare four asymptotic interval estimators of kappa for stratified data: estimator (1), a weighted average of the stratum-specific kappa estimates with weights equal to the inverse of the estimated asymptotic variances of these estimates; the two estimators, (2) and (3), with use of the logarithmic and the square root transformations, respectively, and a principle similar as used in estimator (1); estimator (4), a weighted average of the stratum-specific kappa estimates with weights equal to stratum sizes. We find that while the coverage probability of the first three interval estimators (1)-(3) can often be less than the desired confidence level, the fourth interval estimator (4) consistently performs well in all the situations considered here. We further find that when the underlying kappa is moderate (0.30</=kappa</=0.50), we can substantially improve the performance of the first three estimators by using a point estimator recently proposed elsewhere for kappa in estimation of weights. Because interval estimator (4) outperforms the other three estimators in a variety of situations, we recommend this estimator for general use.

Estimation of the transmission probability of Lyme borreliosis

Whether physicians should prophylactically treat tick bites in areas endemic for Lyme disease has been debated. The high rates of tick infection (10–50%) found in Lyme disease-endemic areas suggest that tick bites should be treated; conversely, the low rates of Lyme disease (1–4%) found in recent clinical trials of untreated tick-bite victims suggest caution in treatment. Medical advice given from Lyme-disease World Wide Web sites is equally contradictory, ranging from suggesting that all tick bites should be treated to suggesting that no tick bites be treated. To clarify this issue, we estimate the transmission probability of the causative agent of Lyme disease, Borrelia burgdorferi, for different durations of tick attachment. The data used to estimate this transmission probability is obtained from previously published animal studies. The accuracy of these estimates is assessed by comparing model predictions of the number of Lyme disease cases to that actually observed in clinical studies of Lyme disease. Our results suggest that tick bites should be treated only when it is known that the duration of tick attachment is longer than 48 hours.

Using James–Stein Estimators in Homogeneity Tests of the Risk Difference

ABSTRACT In multi-center clinical trials in which the success/failure of two treatments are measured, 2 × 2 × K contingency data are obtained, where K is the number of centers in the study. In this context, the risk difference may be preferred (over the odds ratio or relative risk) as a measure of the efficacy of the new treatment. To summarize the risk difference across centers, the estimated risk difference for each center must be comparable. Although several weighted least squares (WLS) tests of homogeneity of the risk difference have been proposed for the sparse data situation (1,2), none of these tests perform satisfactorily when each center has small samples. In the sparse data situation, the weights given to each centers risk difference estimate are imprecise and may be undefined. James–Stein estimates have been shown to be more precise (in terms of mean squared error) than their maximum likelihood counterparts. In this article, we investigate the use of James–Stein estimates for these weights. These estimates shrink the individual risk estimates towards the overall center mean and thus avoid problems encountered when risk estimates are zero or one. We use Monte Carlo simulations to show that using these estimates in the WLS test of homogeneity of risk differences improves their performance in terms of Type I error.

An improved method for predicting duration of blacklegged tick (Ixodes scapularis) attachment

Abstract Risk of infection with most tick-borne pathogens depends directly on the duration of tick attachment. To determine the duration of attachment of nymphal and adult female Ixodes scapularis Say, previous studies have used polynomial regression to model tick engorgement with a fixed time of initial tick attachment. We studied the impact of the time of day of initial tick attachment on engorgement rates in the nymphal stage, and found that ticks attaching early in the photophase engorged at significantly slower rates than ticks attaching later. We propose an improved method of predicting duration of tick attachment that incorporates this variability in tick engorgement rates. A graphical method is presented to facilitate prediction.