Linear measurement error models with restricted sampling

The relationship between nutrient consumption and chronic disease risk is the focus of a large number of epidemiological studies where food frequency questionnaires (FFQ) and food records are commonly used to assess dietary intake. However, these self-assessment tools are known to involve substantial random error for most nutrients, and probably important systematic error as well. Study subject selection in dietary intervention studies is sometimes conducted in two stages. At the first stage, FFQ-measured dietary intakes are observed and at the second stage another instrument, such as a 4-day food record, is administered only to participants who have fulfilled a prespecified criterion that is based on the baseline FFQ-measured dietary intake (e.g., only those reporting percent energy intake from fat above a prespecified quantity). Performing analysis without adjusting for this truncated sample design and for the measurement error in the nutrient consumption assessments will usually provide biased estimates for the population parameters. In this work we provide a general statistical analysis technique for such data with the classical additive measurement error that corrects for the two sources of bias. The proposed technique is based on multiple imputation for longitudinal data. Results of a simulation study along with a sensitivity analysis are presented, showing the performance of the proposed method under a simple linear regression model.     

Accuracy and power in fluctuating asymmetry studies: effects of sample size and number of within-subject repeats

This paper presents results from simulations investigating the effect of sample size, number of within-subject repeats and relative degree of measurement error on the power and accuracy of test for fluctuating asymmetry (FA). These data confirm that sampling variation of population-level FA-estimates is large and that high sample size is required to obtain reasonably high power when testing for FA or comparing FA levels between populations. The results also clearly show that increasing the number of within-subject repeats can dramatically increase accuracy and power when measurement error is relatively high.     

Adaptive Modifications of Hypotheses After an Interim Analysis

It is investigated how one can modify hypotheses in a trial after an interim analysis such that the type I error rate is controlled. If only a global statement is desired, a solution was given by Bauer (1989). For a general multiple testing problem, Kieser , Bauer and Lehmacher (1999) and Bauer and Kieser (1999) gave solutions, by means of which the initial set of hypotheses can be reduced after the interim analysis. The same techniques can be applied to obtain more flexible strategies, as changing weights of hypotheses, changing an a priori order, or even including new hypotheses. It is emphasized that the application of these methods requires very careful planning of a trial as well as a critical discussion of the scientific aims in order to avoid every manipulation.     

On the False Discovery Rate and Expected Type I Errors

The paper is concerned with expected type I errors of some stepwise multiple test procedures based on independent p‐values controlling the so‐called false discovery rate (FDR). We derive an asymptotic result for the supremum of the expected type I error rate(EER) when the number of hypotheses tends to infinity. Among others, it will be shown that when the original Benjamini‐Hochberg step‐up procedure controls the FDR at level α, its EER may approach a value being slightly larger than α/4 when the number of hypotheses increases. Moreover, we derive some least favourable parameter configuration results, some bounds for the FDR and the EER as well as easily computable formulae for the familywise error rate (FWER) of two FDR‐controlling procedures. Finally, we discuss some undesirable properties of the FDR concept, especially the problem of cheating.     

Shrinkage and Pretest Nonparametric Estimation of Regression Parameters from Censored Data with Multiple Observations at Each Level of Covariate

A simple linear regression model is considered where the independent variable assumes only a finite number of values and the response variable is randomly right censored. However, the censoring distribution may depend on the covariate values. A class of noniterative estimators for the slope parameter, namely, the noniterative unrestricted estimator, noniterative restricted estimator and noniterative improved pretest estimator are proposed. The asymptotic bias and mean squared errors of the proposed estimators are derived and compared. The relative dominance picture of the estimators is investigated. A simulation study is also performed to asses the properties of the various estimators for small samples.     

A Note on the Log‐Rank Test in Life Table Analysis with Correlated Observations

Survival data consisting of independent sets of correlated failure times may arise in many situations. For example, we may take repeated observations of the failure time of interest from each patient or observations of the failure time on siblings, or consider the failure times on littermates in toxicological experiments. Because the failure times taken on the same patient or related family members or from the same litter are likely correlated, use of the classical log‐rank test in these situations can be quite misleading with respect to type I error. To avoid this concern, this paper develops two closed‐form asymptotic summary tests, that account for the intraclass correlation between the failure times within patients or units. In fact, one of these two test includes the classical log‐rank test as a special case when the intraclass correlation equals 0. Furthermore, to evaluate the finite‐sample performance of the two tests developed here, this paper applies Monte Carlo simulation and notes that they can actually perform quite well in a variety of situations considered here.     

A Generalized Class of Synthetic Estimators with Application to Crop Acreage Estimation for Small Domains

This paper defines and discusses a generalized class of synthetic estimators for small domains, using auxiliary information, under simple random sampling and stratified random sampling schemes. The generalized class of synthetic estimators, among others, includes the simple, ratio and product synthetic estimators. The proposed class of synthetic estimators gives consistent estimators if the synthetic assumption holds. Further, it demonstrates the use of the generalized synthetic and ratio synthetic estimators for estimating crop acreage for small domains and also compare their relative performance with direct estimators, empirically, through a simulation study.     

Group Sequential Monitoring with Arbitrary Inspection Times

The classical group sequential test procedures that were proposed by Pocock (1977) and O'Brien and Fleming (1979) rest on the assumption of equal sample sizes between the interim analyses. Regarding this it is well known that for most situations there is not a great amount of additional Type I error if monitoring is performed for unequal sample sizes between the stages. In some cases, however, problems can arise resulting in an unacceptable liberal behavior of the test procedure. In this article worst case scenarios in sample size imbalancements between the inspection times are considered. Exact critical values for the Pocock and the O'Brien and Fleming group sequential designs are derived for arbitrary and for varying but bounded sample sizes. The approach represents a reasonable alternative to the flexible method that is based on the Type I error rate spending function. The SAS syntax for performing the calculations is provided. Using these procedures, the inspection times or the sample sizes in the consecutive stages need to be chosen independently of the data observed so far.     

Inter- and intra-rater reliability of 3D kinematics during maximum mouth opening of asymptomatic subjects

Previous studies evaluated 3D human jaw movements using kinematic analysis systems during mouth opening, but information on the reliability of such measurements is still scarce. The purpose of this study was to analyze within- and between-session reliabilities, inter-rater reliability, standard error of measurement (SEM), minimum detectable change (MDC) and consistency of agreement across raters and sessions of 3D kinematic variables during maximum mouth opening (MMO). Thirty-six asymptomatic subjects from both genders were evaluated on two different days, five to seven days apart. Subjects performed three MMO movements while kinematic data were collected. Intraclass correlation coefficient (ICC), SEM and MDC were calculated for all variables, and Bland-Altman plots were constructed. Jaw radius and width were the most reproducible variables (ICC > 0.81) and demonstrated minor error. Incisor displacement during MMO and angular movements in the sagittal plane presented good reliability (ICC from 0.61 to 0.8) and small errors and, consequently, could be used in future studies with the same methodology and population. The variables with smaller amplitudes (condylar translations during mouth opening and closing and mandibular movements on the frontal and transversal planes) were less reliable (ICC < 0.61) and presented larger SEM and MDC. Although ICC, SEM and MDC showed less between-session reproducibility than within-session and inter-rater, the limits of agreement were larger in inter-rater comparisons. In future studies care must be taken with variables collected on different days and with mandibular movements in the frontal and transversal planes.     

Accuracy map of an optical motion capture system with 42 or 21 cameras in a large measurement volume

Optical motion capture is commonly used in biomechanics to measure human kinematics. However, no studies have yet examined the accuracy of optical motion capture in a large capture volume (>100 m³), or how accuracy varies from the center to the extreme edges of the capture volume. This study measured the dynamic 3D errors of an optical motion capture system composed of 42 OptiTrack Prime 41 cameras (capture volume of 135 m³) by comparing the motion of a single marker to the motion reported by a ThorLabs linear motion stage. After spline interpolating the data, it was found that 97% of the capture area had error below 200 μm. When the same analysis was performed using only half (21) of the cameras, 91% of the capture area was below 200 μm of error. The only locations that exceeded this threshold were at the extreme edges of the capture area, and no location had a mean error exceeding 1 mm. When measuring human kinematics with skin-mounted markers, uncertainty of marker placement relative to underlying skeletal features and soft tissue artifact produce errors that are orders of magnitude larger than the errors attributed to the camera system itself. Therefore, the accuracy of this OptiTrack optical motion capture system was found to be more than sufficient for measuring full-body human kinematics with skin-mounted markers in a large capture volume (>100 m³).