Bootstrap applications in proportional hazards models

Experiments in which the measured responses are times until events occur are common in a variety of fields. When only one response is measured on each subject, the proportional hazards model of Cox (1972) is often used to assess the effects of one or more explanatory variables on the event times. Two new resampling plans are introduced for bootstrapping estimators from this model when explanatory variables are fixed by design. One method resamples from the Uniform (0,1) distribution of the probability integral transformation corresponding to the conditional failure time distribution, and it is easily adapted to a wide variety of censoring schemes. The other method is an analog to the residual-resampling method for regression introduced by Efron (1979), and it admits random censoring from a class of distributions which includes the Koziol-Green model;Multivariate extensions of resampling methods are developed for situations where multiple event times are monitored on individual subjects. Marginal models are fit using an independence working model approach. Resampling procedures are then applied to the joint distribution of the multiple responses or residuals to make bias corrections to the parameter estimates, estimate covariance matrices, and construct confidence intervals. Simulation studies indicate that each of the proposed methods provides substantial improvements in mean squared errors over existing techniques for estimation of model parameters. The proposed methods also provide better estimates of standard errors and more reliable confidence intervals for model parameters than existing methods which rely largely on asymptotic approximations. These methods are demonstrated through applications to data sets available in the literature

ANALYZING BINOMIAL DATA IN A SPLIT-PLOT DESIGN: CLASSICAL APPROACHES OR MODERN TECHNIQUES?

Binomial data are often generated in split-plot experimental designs in agricultural, biological, and environmental research. Modeling non-normality and random effects are the two major challenges in analyzing binomial data in split-plot designs. In this study, seven statistical methods for testing whole-plot and subplot treatment effects using mixed, generalized linear, or generalized linear mixed models are compared for the size and power of the tests. This study shows that analyzing random effects properly is more important than adjusting the analysis for non-normality. Methods based on mixed and generalized linear mixed models hold Type I error rates better than generalized linear models. Whole-plot tests tend to be conservative in some cases, but these tests can be improved by removing the lower bound of zero from variance parameter estimation or by increasing the number of whole-plot replications. Mixed model methods tend to have higher power than generalized linear mixed models when the sample size is small. However, they perform equally well as the sample size becomes large

Joint Identification of Location and Dispersion Effects in Unreplicated Two-Level Factorials

Most procedures that have been proposed to identify dispersion effects in unreplicated factorial designs assume that location effects have been identified correctly. Incorrect identi- fication of location effects may impair subsequent identification of dispersion effects. We develop a model for joint identification of location and dispersion effects that can reliably identify active effects of both types. The joint model is estimated using maximum likelihood, and hence effect selection is done using a specially derived information criterion. An exhaustive search through a limited version of the space of possible models is conducted. Both a single-model output and model averaging are considered. The method is shown to be capable of identifying sensible location-dispersion models that are missed by methods that rely on sequential estimation of location and dispersion effects

Statistical Modeling of Discrete Percentage Measurements With Application to Construction of Acceptance Bounds for Wood Failure in Structural Adhesive Testing

The goals of this paper are: (1) to provide a statistical analysis approach that is appropriate for data from an interlaboratory study where responses are measured in discrete percentages and are subject to multiple sources of random variability, and (2) to apply this model to data on wood-failure percentages from block-shear tests on structural wood adhesives. We treat percentage responses measured in 5-point intervals as having arisen from observing 20 independent binary responses on different parts of the observed wood blocks. The overdispersion that is likely to result from the practical inadequacy of this assumption is overcome empirically by the inclusion of a random effect for blocks. We propose an analysis based on a parametric bootstrap to provide sampling distributions for statistics that regulators might wish to use in setting standards for acceptance of wood adhesives. Similar computational methods are developed to assess the fit of the model. This model is shown to provide a reasonably good fit or actual data in many of the cases to which it was applied

Endpoint temperature, cooking method, and marbling degree have different effects on Warner-Bratzler shear force of beef strip loin, bottom round, and brisket muscles

Our objective was to determine the effects of endpoint temperature, cooking method, and marbling on Warner-Bratzler shear force (WBSF; an objective method for determining tenderness) of three beef muscles. Eighteen subprimals of a muscle containing low content of connective tissue, longissimus lumborum (strip loin), and two muscles containing a high content of connective tissue, biceps femoris (bottom round) and deep pectoralis (brisket), were selected from USDA Select and Choice (Certified Angus Beef) carcasses. After 14 days of aging, subprimals were frozen, fabricated into steaks, and stored frozen until cooking. Steaks were assigned to one of two cooking methods, the Magikitch’n® electric belt grill (a rapid conduction method) or a water bath (a slower, convection method); and one of nine endpoint cooking temperatures, 104, 113, 122, 131, 140, 149, 158, 167, or 176°F. According to WBSF results, optimum tenderness for the strip loin occurred around 131°F. Higher marbling protected tenderness at higher endpoint temperatures. Tenderness increased in bottom round and brisket muscles as endpoint temperature increased from 104 to 140°F, then tenderness decreased as endpoint temperature rose from 149 to 176°F. Endpoint temperature was the only significant factor affecting bottom round tenderness. Steaks cooked in the water bath had higher WBSF and, therefore, were less tender than those cooked on the belt grill. This was true for both the strip loin and brisket. The effect of increasing endpoint temperature on WBSF of the strip loin was different than for the bottom round and brisket

Cardiovascular Responses to Orthostasis and Their Association With Falls in Older Adults

Background Orthostatic hypotension (OH) refers to a marked decline in blood pressure when upright. OH has a high incidence and prevalence in older adults and represents a potential intrinsic risk factor for falls in these individuals. Previous studies have not included more recent definitions for blood pressure responses to orthostasis, including initial, delayed, and recovery blood pressure responses. Furthermore, there is little research examining the relationships between cerebrovascular functioning and falling risk. Therefore, we aimed to: (i) test the association between different blood pressure responses to orthostatic stress and retrospective falling history and; (ii) test the association between cerebrovascular responses to orthostatic stress and falling history. Methods We tested 59 elderly residents in long term care facilities who underwent a passive seated orthostatic stress test. Beat-to-beat blood pressure and cerebral blood flow velocity (CBFV) responses were assessed throughout testing. Risk factors for falls and falling history were collected from facility records. Cardiovascular responses to orthostasis were compared between retrospective fallers (≥1 fall in the previous year) and non-fallers. Results Retrospective fallers had larger delayed declines in systolic arterial pressure (SAP) compared to non-fallers (p  = 0.015). Fallers also showed poorer early (2 min) and late (15 min) recovery of SAP. Fallers had a greater decline in systolic CBFV. Conclusions Older adults with a positive falling history have impaired orthostatic control of blood pressure and CBFV. With better identification and understanding of orthostatic blood pressure impairments earlier intervention and management can be implemented, potentially reducing the associated risk of morbidity and mortality. Future studies should utilize the updated OH definitions using beat-to-beat technology, rather than conventional methods that may offer less accurate detection

EXPERIMENTAL ERROR IN AGRONOMIC FIELD TRIALS

Agronomic experiments often summarize work carried out in trials run in several locations over several years, referred to generically as environments. The appropriate statistical analyses for these experiments depend on definitions used for experimental error. The results of one such experiment, in which identical designs were used in each environment, illustrate the commonalities and differences in analyses that can result from using different definitions of experimental error