Relationship between adiposity and body size reveals limitations of BMI

The aims of this study were to assess 1) whether the stature-adjusted body mass index (BMI) is a valid proxy for adiposity across both athletic and nonathletic populations, and 2) whether skinfold measurements increase in proportion to body size, thus obeying the principle of geometric similarity. The research design was cross-sectional, allowing the relationship between skinfold calliper readings (at eight sites and between specific athletic and nonathletic groups, n = 478) and body size (either mass, stature, or both) to be explored both collectively, using proportional allometric MANCOVA, and individually (for each site) with follow-up ANCOVAs. Skinfolds increase at a much greater rate relative to body mass than that assumed by geometric similarity, but taller subjects had less rather than more adiposity, calling into question the use of the traditional skinfold-stature adjustment, 170.18/stature. The best body-size index reflective of skinfold measurements was a stature-adjusted body mass index similar to the BMI. However, sporting differences in skinfold thickness persisted, having controlled for differences in body size (approximate BMI) and age, with male strength- and speed-trained athletes having significantly lower skinfolds (32% and 23%, respectively) compared with controls. Similarly, female strength athletes had 29% lower skinfold measurements compared to controls, having controlled for body size and age. These results cast serious doubts on the validity of BMI to represent adiposity accurately and its ability to differentiate between populations. These findings suggest a more valid (less biased) assessment of fatness will be obtained using surface anthropometry such as skinfolds taken by experienced practitioners following established procedures.     

Dynamic analysis of recurrent event data using the additive hazard model

We propose a method for analysis of recurrent event data using information on previous occurrences of the event as a time-dependent covariate. The focus is on understanding how to analyze the effect of such a dynamic covariate while at the same time ensuring that the effects of treatment and other fixed covariates are unbiasedly estimated. By applying an additive regression model for the intensity of the recurrent events, concepts like direct, indirect and total effects of the fixed covariates may be defined in an analogous way as for traditional path analysis. Theoretical considerations as well as simulations are presented, and a data set on recurrent bladder tumors is used to illustrate the methodology.     

High‐Dimensional Cox Models: The Choice of Penalty as Part of the Model Building Process

The Cox proportional hazards regression model is the most popular approach to model covariate information for survival times. In this context, the development of high‐dimensional models where the number of covariates is much larger than the number of observations ( $p \,{\gg }\, n$ ) is an ongoing challenge. A practicable approach is to use ridge penalized Cox regression in such situations. Beside focussing on finding the best prediction rule, one is often interested in determining a subset of covariates that are the most important ones for prognosis. This could be a gene set in the biostatistical analysis of microarray data. Covariate selection can then, for example, be done by L₁‐penalized Cox regression using the lasso (Tibshirani ( 1997 ). Statistics in Medicine 16 , 385–395). Several approaches beyond the lasso, that incorporate covariate selection, have been developed in recent years. This includes modifications of the lasso as well as nonconvex variants such as smoothly clipped absolute deviation (SCAD) (Fan and Li ( 2001 ). Journal of the American Statistical Association 96 , 1348–1360; Fan and Li ( 2002 ). The Annals of Statistics 30 , 74–99). The purpose of this article is to implement them practically into the model building process when analyzing high‐dimensional data with the Cox proportional hazards model. To evaluate penalized regression models beyond the lasso, we included SCAD variants and the adaptive lasso (Zou ( 2006 ). Journal of the American Statistical Association 101 , 1418–1429). We compare them with “standard” applications such as ridge regression, the lasso, and the elastic net. Predictive accuracy, features of variable selection, and estimation bias will be studied to assess the practical use of these methods. We observed that the performance of SCAD and adaptive lasso is highly dependent on nontrivial preselection procedures. A practical solution to this problem does not yet exist. Since there is high risk of missing relevant covariates when using SCAD or adaptive lasso applied after an inappropriate initial selection step, we recommend to stay with lasso or the elastic net in actual data applications. But with respect to the promising results for truly sparse models, we see some advantage of SCAD and adaptive lasso, if better preselection procedures would be available. This requires further methodological research.     

Analysis of a potential trigger of an acute illness

Sometimes certain short-term risk exposures are postulated to act as a trigger for the onset of a specific acute illness. When the incidence of the illness is low it is desirable to investigate this possible association using only data on cases detected during a specific observation period. Here we propose an analysis for such a study based on a model expressed in terms of the probability that the exposure triggers the illness and a random delay from a triggered illness until its diagnosis. Both the natural hazard rate for the illness and the probability that the exposure triggers the illness are assumed to be small and possibly dependent on age and covariates such as sex and duration or severity of the exposure. The method of analysis is illustrated with a study of the association between long flights and hospitalization for venous thromboembolism.     

The occurrence of ochratoxin A in dust collected from a problem household

Accumulated dust samples were collected from the heating ducts in a household where signs resembling ochratoxin poisoning in animals occurred. Several Penicillium spp. and Aspergillus ochraceous had been identified previously from air samples taken from this house. A composite sample from six collected samples was examined by HPLC, and it was determined that 58 ppb of ochratoxin A was present in this sample. A second set of six samples was collected and determinations were made by HPLC of the ochratoxin content in each sample. All samples, including one sample of dirt from a crawl space, yielded at least a trace of ochratoxin A; however, one sample of dust collected from the heating ducts yielded over 1500 ppb of ochratoxin A, and another sample of dust from a different heating duct yielded 306 ppb of ochratoxin A. Ochratoxin A was confirmed in all samples by LC-MS, and ochratoxin was evident in the samples by TLC analysis. This is believed to be the first report of finding ochratoxin inhouse dust. This revised version was published online in June 2006 with corrections to the Cover Date.     

A marginal mixed baseline hazards model for multivariate failure time data

In multivariate failure time data analysis, a marginal regression modeling approach is often preferred to avoid assumptions on the dependence structure among correlated failure times. In this paper, a marginal mixed baseline hazards model is introduced. Estimating equations are proposed for the estimation of the marginal hazard ratio parameters. The proposed estimators are shown to be consistent and asymptotically Gaussian with a robust covariance matrix that can be consistently estimated. Simulation studies indicate the adequacy of the proposed methodology for practical sample sizes. The methodology is illustrated with a data set from the Framingham Heart Study.     

Adaptive regression splines in the Cox model

We develop a method for constructing adaptive regression spline models for the exploration of survival data. The method combines Cox's (1972, Journal of the Royal Statistical Society, Series B 34, 187-200) regression model with a weighted least-squares version of the multivariate adaptive regressi on spline (MARS) technique of Friedman (1991, Annals of Statistics 19, 1-141) to adaptively select the knots and covariates. The new technique can automatically fit models with terms that represent nonlinear effects and interactions among covariates. Applications based on simulated data and data from a clinical trial for myeloma are presented. Results from the myeloma application identified several important prognostic variables, including a possible nonmonotone relationship with survival in one laboratory variable. Results are compared to those from the adaptive hazard regression (HARE) method of Kooperberg, Stone, and Truong (1995, Journal of the American Statistical Association 90, 78-94).     

Regression analysis of doubly censored failure time data with applications to AIDS studies

In many epidemiological studies, the survival time of interest is the elapsed time between two related events, the originating event and the failure event, and the times of the occurrences of both events are right or interval censored. We discuss the regression analysis of such studies and a simple estimating equation approach is proposed under the proportional hazards model. The method can easily be implemented and does not involve any iteration among unknown parameters, as full likelihood approaches proposed in the literature do. The asymptotic properties of the proposed regression coefficient estimates are derived and an AIDS cohort study is analyzed to illustrate the proposed approach.     

A parametric model for studying organism fitness using step-stress experiments

We propose a method based on parametric survival analysis to analyze step-stress data. Step-stress studies are failure time studies in which the experimental stressor is increased at specified time intervals. While this protocol has been frequently employed in industrial reliability studies, it is less common in the life sciences. Possible biological applications include experiments on swimming performance of fish using a step function defining increasing water velocity over time, and treadmill tests on humans. A likelihood-ratio test is developed for comparing the failure times in two groups based on a piecewise constant hazard assumption. The test can be extended to other piecewise distributions and to include covariates. An example data set is used to illustrate the method and highlight experimental design issues. A small simulation study compares this analysis procedure to currently used methods with regard to type I error rate and power.     

A causal proportional hazards estimator for the effect of treatment actually received in a randomized trial with all-or-nothing compliance

Survival data from randomized trials are most often analyzed in a proportional hazards (PH) framework that follows the intention-to-treat (ITT) principle. When not all the patients on the experimental arm actually receive the assigned treatment, the ITT-estimator mixes its effect on treatment compliers with its absence of effect on noncompliers. The structural accelerated failure time (SAFT) models of Robins and Tsiatis are designed to consistently estimate causal effects on the treated, without direct assumptions about the compliance selection mechanism. The traditional PH-model, however, has not yet led to such causal interpretation. In this article, we examine a PH-model of treatment effect on the treated subgroup. While potential treatment compliance is unobserved in the control arm, we derive an estimating equation for the Compliers PROPortional Hazards Effect of Treatment (C-PROPHET). The jackknife is used for bias correction and variance estimation. The method is applied to data from a recently finished clinical trial in cancer patients with liver metastases.