Analyzing Incomplete Data Subject to a Threshold using Empirical Likelihood Methods: An Application to a Pneumonia Risk Study in an ICU Setting

Summary .  The initial detection of ventilator-associated pneumonia (VAP) for inpatients at an intensive care unit needs composite symptom evaluation using clinical criteria such as the clinical pulmonary infection score (CPIS). When CPIS is above a threshold value, bronchoalveolar lavage (BAL) is performed to confirm the diagnosis by counting actual bacterial pathogens. Thus, CPIS and BAL results are closely related and both are important indicators of pneumonia whereas BAL data are incomplete. To compare the pneumonia risks among treatment groups for such incomplete data, we derive a method that combines nonparametric empirical likelihood ratio techniques with classical testing for parametric models. This technique augments the study power by enabling us to use any observed data. The asymptotic property of the proposed method is investigated theoretically. Monte Carlo simulations confirm both the asymptotic results and good power properties of the proposed method. The method is applied to the actual data obtained in clinical practice settings and compares VAP risks among treatment groups.     

Testing equality of survival functions based on both paired and unpaired censored data

We introduce two test procedures for comparing two survival distributions on the basis of randomly right-censored data consisting of both paired and unpaired observations. Our procedures are based on generalizations of a pooled rank test statistic previously proposed for uncensored data. One generalization adapts the Prentice-Wilcoxon score, while the other adapts the Akritas score. The use of these particular scoring systems in pooled rank tests with randomly right-censored paired data has been advocated by several researchers. Our test procedures utilize the permutation distributions of the test statistics based on a novel manner of permuting the scores. Permutation versions of tests for right-censored paired data and for two independent right-censored samples that use the proposed scoring systems are obtained as special cases of our test procedures. Simulation results show that our test procedures have high power for detecting scale and location shifts in exponential and log-logistic distributions for the survival times. We also demonstrate the advantages of our test procedures in terms of utilizing randomly occurring unpaired observations that are discarded in test procedures for paired data. The tests are applied to skin graft data previously reported elsewhere.     

Platelet lumiaggregation testing: Reference intervals and the effect of acetylsalicylic acid in healthy adults

BackgroundLight transmission aggregometry with lumiaggregometry are methods commonly recommended as a first-line test in platelet dysfunction diagnostic work-up. They are poorly standardized and usually performed in specialized laboratories. For proper interpretation, each laboratory should establish its own diagnostic approach in order to recognize abnormal aggregation patterns. The aim of this study was to measure plasma lumiaggregometry with basic agonists to establish the analyzer-reagent reference intervals (RI) for adults and to test the method response to aspirin.MethodsThe Chrono-Log Model 700 lumiaggregometer using Chrono-Par and Chrono-lume reagents (Chrono-Log Corp., Havertown, PA, USA) was used to measure the maximal aggregation and adenosine triphosphate release using adenosine diphosphate (2 μmol/L), collagen (2 μg/mL), arachidonic acid (1 μmol/L), epinephrine (5.5 μmol/L) and ristocetin (1.25 mg/mL), and thrombin (1 U/mL). The effect of aspirin on platelet aggregation and granule release was inspected.ResultsRIs derived from 40 healthy adults were calculated using the non-parametric approach. Wider intervals and low lower limits were determined for weak agonist as well as absence or impaired aggregation in up to one of 7 healthy controls. The response of platelets to aspirin shows response comparable to previously reported study.ConclusionsLocally established RI in our study enable us to investigate platelet function in patients with a high probability of bleeding disorders. Values are agonist and equipment specific. The variability of the method can be reduced by considering standardized preanalytical and analytical variables. Pathological results must be interpreted in the context of other hemostasis test results and clinical findings.     

Hypothesis testing in semiparametric additive mixed models

We consider testing whether the nonparametric function in a semiparametric additive mixed model is a simple fixed degree polynomial, for example, a simple linear function. This test provides a goodness-of-fit test for checking parametric models against nonparametric models. It is based on the mixed-model representation of the smoothing spline estimator of the nonparametric function and the variance component score test by treating the inverse of the smoothing parameter as an extra variance component. We also consider testing the equivalence of two nonparametric functions in semiparametric additive mixed models for two groups, such as treatment and placebo groups. The proposed tests are applied to data from an epidemiological study and a clinical trial and their performance is evaluated through simulations.     

Comparing treatments in the presence of crossing survival curves: an application to bone marrow transplantation

Summary .   In some clinical studies comparing treatments in terms of their survival curves, researchers may anticipate that the survival curves will cross at some point, leading to interest in a long-term survival comparison. However, simple comparison of the survival curves at a fixed point may be inefficient, and use of a weighted log-rank test may be overly sensitive to early differences in survival. We formulate the problem as one of testing for differences in survival curves after a prespecified time point, and propose a variety of techniques for testing this hypothesis. We study these methods using simulation and illustrate them on a study comparing survival for autologous and allogeneic bone marrow transplants.     

Sequential Analysis of Longitudinal Data in a Prospective Nested Case–Control Study

Summary The nested case–control design is a relatively new type of observational study whereby a case–control approach is employed within an established cohort. In this design, we observe cases and controls longitudinally by sampling all cases whenever they occur but controls at certain time points. Controls can be obtained at time points randomly scheduled or prefixed for operational convenience. This design with longitudinal observations is efficient in terms of cost and duration, especially when the disease is rare and the assessment of exposure levels is difficult. In our design, we propose sequential sampling methods and study both (group) sequential testing and estimation methods so that the study can be stopped as soon as the stopping rule is satisfied. To make such a longitudinal sampling more efficient in terms of both numbers of subjects and replications, we propose applying sequential sampling methods to subjects and replications, simultaneously, until the information criterion is fulfilled. This simultaneous sequential sampling on subjects and replicates is more flexible for practitioners designing their sampling schemes, and is different from the classical approaches used in longitudinal studies. We newly define the σ‐field to accommodate our proposed sampling scheme, which contains mixtures of independent and correlated observations, and prove the asymptotic optimality of sequential estimation based on the martingale theories. We also prove that the independent increment structure is retained so that the group sequential method is applicable. Finally, we present results by employing sequential estimation and group sequential testing on both simulated data and real data on children's diarrhea.     

Asynchronous functional linear regression models for longitudinal data in reproducing kernel Hilbert space

Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite-sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).     

On the use of the variogram in checking for independence in spatial data

The variogram is a standard tool in the analysis of spatial data, and its shape provides useful information on the form of spatial correlation that may be present. However, it is also useful to be able to assess the evidence for the presence of any spatial correlation. A method of doing this, based on an assessment of whether the true function underlying the variogram is constant, is proposed. Nonparametric smoothing of the squared differences of the observed variables, on a suitably transformed scale, is used to estimate variogram shape. A statistic based on a ratio of quadratic forms is proposed and the test is constructed by investigating the distributional properties of this statistic under the assumption of an independent Gaussian process. The power of the test is investigated. Reference bands are proposed as a graphical follow-up. An example is discussed.