Testing for a change in repeated measures data

Four nonparametric test statistics for the change-point problem with repeated measures data are proposed. In a Monte Carlo simulation study, critical values for the proposed test statistics are simulated and the performances of the proposed tests are compared with the performances of some competitive tests in terms of asymptotic behavior and power. We provide appropriate recommendations for different occurrences of the change-point and illustrate the testing methods using a set of real data.     

Random stopping sets in a sequential analysis of random measures and fields

A random stopping set is defined and some of its properties are proved. Namely, we prove the theorem on the absolute continuity of measures on a σ-algebra F_τ connected with a random stopping set τ, which can be applied to the sequential analysis of random measures and fields.     

Profile parallelism in repeated measures designs

Three statistics are developed to test tor treatment by time interaction after a certain point in repeated measures designs under several covariance matrix configurations, viz., unstructured, spherically symmetric and autoregressive. An example is fully developed.     

Minimal circular strongly balanced repeated measurements designs in periods of three different sizes

Repeated measurements designs (RMD) are widely used in medicine, pharmacology, animal sciences, and psychology. If there is a restriction on the total number of treatments, some experimental units can receive on the total length of time while some experimental units can remain in the trial, then RMD in periods of unequal sizes should be used. In this article, some infinite series are developed to generate the minimal circular strongly balanced RMD in periods of three different sizes p₁, p₂, and p₃, where 2 ≤ p₃ < p₂ ≤ 10.     

Some new construction of circular weakly balanced repeated measurements designs in periods of two different sizes

Abstract

Balanced repeated measurements designs (RMDs) balance out the residual effects. Williams Latin square designs work as minimal combinatorial balanced as well as variance balanced for RMDs for p (period sizes) = v (number of treatments). If minimal balanced RMDs cannot be constructed for the situations where p must be less than v then weakly balanced RMDs should be preferred. In this article, some generators are developed to generate circular weakly balanced RMDs in periods of two different sizes. To obtain the proposed designs, some construction procedures are also described for some of the cases where we could not develop generators.     

Small area estimation under a multivariate linear model for repeated measures data

In this article, small area estimation under a multivariate linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units, and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points, and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study.     

Estimation of proportion ratio in non-compliance randomized trials with repeated measurements in binary data

It is not uncommon to encounter a randomized clinical trial (RCT) in which each patient is treated with several courses of therapies and his/her response is taken after treatment with each course because of the nature of a treatment design for a disease. On the basis of a simple multiplicative risk model proposed elsewhere for repeated binary measurements, we derive the maximum likelihood estimator (MLE) for the proportion ratio (PR) of responses between two treatments in closed form without the need of modeling the complicated relationship between patient’s compliance and patient’s response. We further derive the asymptotic variance of the MLE and propose an asymptotic interval estimator for the PR using the logarithmic transformation. We also consider two other asymptotic interval estimators. One is derived from the principle of Fieller’s Theorem and the other is derived by using the randomization-based approach suggested elsewhere. To evaluate and compare the finite-sample performance of these interval estimators, we apply the Monte Carlo simulation. We find that the interval estimator using the logarithmic transformation of the MLE consistently outperforms the other two estimators with respect to efficiency. This gain in efficiency can be substantial especially when there are patients not complying with their assigned treatments. Finally, we employ the data regarding the trial of using macrophage colony stimulating factor (M-CSF) over three courses of intensive chemotherapies to reduce febrile neutropenia incidence for acute myeloid leukemia patients to illustrate the use of these estimators.     

Informing the selection of futility stopping thresholds: case study from a late-phase clinical trial

In an environment where (i) potential risks to subjects participating in clinical studies need to be managed carefully, (ii) trial costs are increasing, and (iii) there are limited research resources available, it is necessary to prioritize research projects and sometimes re-prioritize if early indications suggest that a trial has low probability of success. Futility designs allow this re-prioritization to take place. This paper reviews a number of possible futility methods available and presents a case study from a late-phase study of an HIV therapeutic, which utilized conditional power-based stopping thresholds. The two most challenging aspects of incorporating a futility interim analysis into a trial design are the selection of optimal stopping thresholds and the timing of the analysis, both of which require the balancing of various risks. The paper outlines a number of graphical aids that proved useful in explaining the statistical risks involved to the study team. Further, the paper outlines a decision analysis undertaken which combined expectations of drug performance with conditional power calculations in order to produce probabilities of different interim and final outcomes, and which ultimately led to the selection of the final stopping thresholds.     

Aligned rank statistics for repeated measurement models with orthonormal design, employing a Chernoff–Savage approach

In this paper, aligned rank statistics are considered for testing hypotheses regarding the location in repeated measurement designs, where the design matrix for each set of measurements is orthonormal. Such a design may, for instance, be used when testing for linearity. It turns out that the centered design matrix is not of full rank, and therefore it does not quite satisfy the usual conditions in the literature. The number of degrees of freedom of the limiting chi-square distribution of the test statistic under the null hypothesis, however, is not affected, unless rather special hypotheses are tested. An independent derivation of this limiting distribution is given, using the Chernoff–Savage approach. In passing, it is observed that independence of the choice of aligner, which in the location problem is well-known to be due to cancellation, may in scale problems occur as a result of the type of score function suitable for scale tests. A possible extension to multivariate data is briefly indicated.     

Sample size estimation for a two-group comparison of repeated count outcomes using GEE

Randomized clinical trials with count measurements as the primary outcome are common in various medical areas such as seizure counts in epilepsy trials, or relapse counts in multiple sclerosis trials. Controlled clinical trials frequently use a conventional parallel-group design that assigns subjects randomly to one of two treatment groups and repeatedly evaluates them at baseline and intervals across a treatment period of a fixed duration. The primary interest is to compare the rates of change between treatment groups. Generalized estimating equations (GEEs) have been widely used to compare rates of change between treatment groups because of its robustness to misspecification of the true correlation structure. In this paper, we derive a sample size formula for comparing the rates of change between two groups in a repeatedly measured count outcome using GEE. The sample size formula incorporates general missing patterns such as independent missing and monotone missing, and general correlation structures such as AR(1) and compound symmetry (CS). The performance of the sample size formula is evaluated through simulation studies. Sample size estimation is illustrated by a clinical trial example from epilepsy.     

Mean-Squared errors of small area estimators under a multivariate linear model for repeated measures data

In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the mean-squared errors (MSE) for the predicted small area means as a measure of precision. At the first stage, we derive the MSE when the covariance matrices are known. At the second stage, a method based on parametric bootstrap is proposed for bias correction and for prediction error that reflects the uncertainty when the unknown covariance is replaced by its suitable estimator.     

Sample size increase during a survival trial when interim results are promising

This paper is to extend Mehta and Pocock (2011 Mehta, C.R., Pocock, S.J. (2011). Adaptive increase in sample size when interim results are promising: a practical guide with examples. Stat Med. 00(00):00–00. [Google Scholar]) to provide a way in doing sample size increase in survival trials. Sample space is divided by observed test statistic at interim into three zones: unfavorable, promising, and favorable, within which sample size (required number of events) has a proper increase if falling into the promising zone and otherwise remains unchanged. Simulations with scenarios in the presence/absence of censoring, with/without adaptation, and allowing fourfolds versus twofolds of increase in sample size are compared.     

Revisiting retesting in the estimation of proportions by group testing

In the estimation of a proportion p by group testing (pooled testing), retesting of units within positive groups has received little attention due to the minimal gain in precision compared to testing additional units. If acquisition of additional units is impractical or too expensive, and testing is not destructive, we show that retesting can be a useful option. We propose the retesting of a random grouping of units from positive groups, and compare it with nested halving procedures suggested by others. We develop an estimator of p for our proposed method, and examine its variance properties. Using simulation we compare retesting methods across a range of group testing situations, and show that for most realistic scenarios, our method is more efficient.     

Repeated Confidence Intervals Under Fractional Brownian Motion in Long-Term Clinical Trials

Repeated confidence interval (RCI) is an important tool for design and monitoring of group sequential trials according to which we do not need to stop the trial with planned statistical stopping rules. In this article, we derive RCIs when data from each stage of the trial are not independent thus it is no longer a Brownian motion (BM) process. Under this assumption, a larger class of stochastic processes fractional Brownian motion (FBM) is considered. Comparisons of RCI width and sample size requirement are made to those under Brownian motion for different analysis times, Type I error rates and number of interim analysis. Power family spending functions including Pocock, O'Brien-Fleming design types are considered for these simulations. Interim data from BHAT and oncology trials is used to illustrate how to derive RCIs under FBM for efficacy and futility monitoring.     

A comparison of univariate and multivariate multilevel models for repeated measures of use of antenatal care in Uttar Pradesh

Summary.  We compare two different multilevel modelling approaches to the analysis of repeated measures data to assess the effect of mother level characteristics on women's use of prenatal care services in Uttar Pradesh, India. We apply univariate multilevel models to our data and find that the model assumptions are severely violated and the parameter estimates are not stable, particularly for the mother level random effect. To overcome this we apply a multivariate multilevel model. The correlation structure shows that, once the decision has been made regarding use of antenatal care by the mother for her first observed birth in the data, she does not tend to change this decision for higher order births.     

Planning the duration of a survival group sequential trial with a fixed follow-up time for all subjects

To explore the operation characteristics of survival group sequential trials with a fixed follow-up period, the accrual time and total trial duration to ensure power and type I error rate requirements are explained and investigated for hazard ratios ranging from 1.3 to 3.0, with slow or high accrual rate, and in the presence or absence of censoring. Impacts of hazard rate, accrual rate, and competitive censoring on accrual time and subsequently on total trial duration are carefully illustrated. Real time for interim analyses, needed number of events, and recruited number of subjects at time of interim analyses are also tabulated.     

Adaptive wavelet estimation of a function from an m-dependent process with possibly unbounded m

The estimation of a multivariate function from a stationary m-dependent process is investigated, with a special focus on the case where m is large or unbounded. We develop an adaptive estimator based on wavelet methods. Under flexible assumptions on the nonparametric model, we prove the good performances of our estimator by determining sharp rates of convergence under two kinds of errors: the pointwise mean squared error and the mean integrated squared error. We illustrate our theoretical result by considering the multivariate density estimation problem, the derivatives density estimation problem, the density estimation problem in a GARCH-type model and the multivariate regression function estimation problem. The performance of proposed estimator has been shown by a numerical study for a simulated and real data sets.     

Asymptotic optimality of a two-stage procedure in Bayes sequential estimation

The problem of sequential estimation of the mean with quadratic loss and fixed cost per observation is considered within the Bayesian framework. Instead of fully sequential sampling, a two-stage sampling technique is introduced to solve the problem. The proposed two-stage procedure is robust in the sense that it does not depend on the distribution of outcome variables and the prior. It is shown to be asymptotically not worse than the optimal fixed-sample-size procedures for the arbitrary distributions, and to be asymptotically Bayes for the distributions of one-parameter exponential family.     

Early stopping by using stochastic curtailment in a three-arm sequential trial

Summary. Interim analysis is important in a large clinical trial for ethical and cost considerations. Sometimes, an interim analysis needs to be performed at an earlier than planned time point. In that case, methods using stochastic curtailment are useful in examining the data for early stopping while controlling the inflation of type I and type II errors. We consider a three-arm randomized study of treatments to reduce perioperative blood loss following major surgery. Owing to slow accrual, an unplanned interim analysis was required by the study team to determine whether the study should be continued. We distinguish two different cases: when all treatments are under direct comparison and when one of the treatments is a control. We used simulations to study the operating characteristics of five different stochastic curtailment methods. We also considered the influence of timing of the interim analyses on the type I error and power of the test. We found that the type I error and power between the different methods can be quite different. The analysis for the perioperative blood loss trial was carried out at approximately a quarter of the planned sample size. We found that there is little evidence that the active treatments are better than a placebo and recommended closure of the trial.