Adjusting for regression effect in uncontrolled studies

When clinical studies require enrolled patients to have abnormal assays, the natural tendency of repeat measurements to regress toward the mean can lead to a false assessment of effectiveness of therapy. We propose a method to more accurately estimate the true effect of therapy by adjusting for a component of improvement that can be attributed to regression effect. The model we use allows for a combination of additive and/or multiplicative effects of the therapy.     

Craniodental body mass estimators in the dwarf bushbaby (Galagoides)

This study reports data on 17 craniodental body mass estimators in a sample (n = 38) of dwarf galagos (Galagoides). Correlation coefficients (r) range from a high of 0.64 for bizygomatic breadth and body mass to a low of 0.10 for M(3) length and body mass. Of the 17 variables studied, 7 exhibit significant (P < 0.05) correlation coefficients, with 5 of the 7 being multitooth (i.e., tooth row) or cranial variables. In contrast to the correlation coefficients of greater than 0.90 (e.g., Martin [1980] Z Morphol Anthropol 71:115-124; Steudel [1981] Int J Primatol 2:81-90; Gingerich et al. [1982] Am J Phys Anthropol 58:81-100; Conroy [1987] Int J Primatol 8:115-137) published for higher taxonomic level analyses (i.e., all-primate or prosimian) for many of the same variables studied here, the current data indicate weaker relationships when analyzed at the generic level. Possible explanations for the contrast in correlation coefficients between the current and many previous studies include the following: 1) individual variation due to a geographically dispersed sample, 2) individual body mass fluctuations due to seasonal food availability, and 3) individual variation within the sample due to variation in life-history parameters. Because the overall size range of the individuals in a specific or generic level analysis is smaller than that in an ordinal or subordinal sample, the individual variation normally masked when using species means represents a larger proportion of the total variation in a more limited sample. This may then be a cause of these weaker correlations.     

A hierarchical Bayesian model to predict the duration of immunity to Haemophilus influenzae type b

A hierarchical Bayesian regression model is fitted to longitudinal data on Haemophilus influenzae type b (Hib) serum antibodies. To estimate the decline rate of the antibody concentration, the model accommodates the possibility of unobserved subclinical infections with Hib bacteria that cause increasing concentrations during the study period. The computations rely on Markov chain Monte Carlo simulation of the joint posterior distribution of the model parameters. The model is used to predict the duration of immunity to subclinical Hib infection and to a serious invasive Hib disease.     

Statistical inference for serial dilution assay data

Serial dilution assays are widely employed for estimating substance concentrations and minimum inhibitory concentrations. The Poisson-Bernoulli model for such assays is appropriate for count data but not for continuous measurements that are encountered in applications involving substance concentrations. This paper presents practical inference methods based on a log-normal model and illustrates these methods using a case application involving bacterial toxins.     

Kriging with nonparametric variance function estimation

A method for fitting regression models to data that exhibit spatial correlation and heteroskedasticity is proposed. It is well known that ignoring a nonconstant variance does not bias least-squares estimates of regression parameters; thus, data analysts are easily lead to the false belief that moderate heteroskedasticity can generally be ignored. Unfortunately, ignoring nonconstant variance when fitting variograms can seriously bias estimated correlation functions. By modeling heteroskedasticity and standardizing by estimated standard deviations, our approach eliminates this bias in the correlations. A combination of parametric and nonparametric regression techniques is used to iteratively estimate the various components of the model. The approach is demonstrated on a large data set of predicted nitrogen runoff from agricultural lands in the Midwest and Northern Plains regions of the U.S.A. For this data set, the model comprises three main components: (1) the mean function, which includes farming practice variables, local soil and climate characteristics, and the nitrogen application treatment, is assumed to be linear in the parameters and is fitted by generalized least squares; (2) the variance function, which contains a local and a spatial component whose shapes are left unspecified, is estimated by local linear regression; and (3) the spatial correlation function is estimated by fitting a parametric variogram model to the standardized residuals, with the standardization adjusting the variogram for the presence of heteroskedasticity. The fitting of these three components is iterated until convergence. The model provides an improved fit to the data compared with a previous model that ignored the heteroskedasticity and the spatial correlation.     

Empirical Bayes estimation of random effects parameters in mixed effects logistic regression models

We extend an approach for estimating random effects parameters under a random intercept and slope logistic regression model to include standard errors, thereby including confidence intervals. The procedure entails numerical integration to yield posterior empirical Bayes (EB) estimates of random effects parameters and their corresponding posterior standard errors. We incorporate an adjustment of the standard error due to Kass and Steffey (KS; 1989, Journal of the American Statistical Association 84, 717-726) to account for the variability in estimating the variance component of the random effects distribution. In assessing health care providers with respect to adult pneumonia mortality, comparisons are made with the penalized quasi-likelihood (PQL) approximation approach of Breslow and Clayton (1993, Journal of the American Statistical Association 88, 9-25) and a Bayesian approach. To make comparisons with an EB method previously reported in the literature, we apply these approaches to crossover trials data previously analyzed with the estimating equations EB approach of Waclawiw and Liang (1994, Statistics in Medicine 13, 541-551). We also perform simulations to compare the proposed KS and PQL approaches. These two approaches lead to EB estimates of random effects parameters with similar asymptotic bias. However, for many clusters with small cluster size, the proposed KS approach does better than the PQL procedures in terms of coverage of nominal 95% confidence intervals for random effects estimates. For large cluster sizes and a few clusters, the PQL approach performs better than the KS adjustment. These simulation results agree somewhat with those of the data analyses.     

Selection models and pattern-mixture models for incomplete data with covariates

Most models for incomplete data are formulated within the selection model framework. This paper studies similarities and differences of modeling incomplete data within both selection and pattern-mixture settings. The focus is on missing at random mechanisms and on categorical data. Point and interval estimation is discussed. A comparison of both approaches is done on side effects in a psychiatric study.