Power analysis of longitudinal studies with piecewise linear growth and attrition

In longitudinal research, the development of some outcome variable(s) over time (or age) is studied. Such relations are not necessarily smooth, and piecewise growth models may be used to account for differential growth rates before and after a turning point in time. Such models have been well developed, but the literature on power analysis for these models is scarce. This study investigates the power needed to detect differential growth for linear-linear piecewise growth models in further detail while taking into account the possibility of attrition. Attrition is modeled using the Weibull survival function, which allows for increasing, decreasing or constant attrition across time. Furthermore, this work takes into account the realistic situation where subjects do not necessarily have the same turning point. A multilevel mixed model is used to model the relation between time and outcome, and to derive the relation between sample size and power. The required sample size to achieve a desired power is smallest when the turning points are located halfway through the study and when all subjects have the same turning point. Attrition has a diminishing effect on power, especially when the probability of attrition is largest at the beginning of the study. An example on alcohol use during middle and high school shows how to perform a power analysis. The methodology has been implemented in a Shiny app to facilitate power calculations for future studies

Власть и управление

В современных условиях все больше внимания уделяется поискам оптимальной управленческой структуры. В статье рассматриваются общие и особенные моменты власти и управления; в частности, рассматриваются проблемы управления человеческими ресурсами предприятия.У сучасних умовах усе більше уваги приділяється пошукам оптимальної управлінської структури. У статті розглядаються загальні й особливі моменти влади і керування; зокрема, розглядаються проблеми керування людськими ресурсами підприємства.In modern conditions of more and more attention it is given searches of optimum administrative structure. In this article the general and especial moments of authority and management are considered; in particular, problems of management are considered by human resources of the enterprise

Power analysis for cluster randomized trials with continuous co-primary endpoints

Pragmatic trials evaluating health care interventions often adopt cluster randomization due to scientific or logistical considerations. Previous reviews have shown that co-primary endpoints are common in pragmatic trials but infrequently recognized in sample size or power calculations. While methods for power analysis based on $K$ ($K\geq 2$) binary co-primary endpoints are available for CRTs, to our knowledge, methods for continuous co-primary endpoints are not yet available. Assuming a multivariate linear mixed model that accounts for multiple types of intraclass correlation coefficients (endpoint-specific ICCs, intra-subject ICCs and inter-subject between-endpoint ICCs) among the observations in each cluster, we derive the closed-form joint distribution of $K$ treatment effect estimators to facilitate sample size and power determination with different types of null hypotheses under equal cluster sizes. We characterize the relationship between the power of each test and different types of correlation parameters. We further relax the equal cluster size assumption and approximate the joint distribution of the $K$ treatment effect estimators through the mean and coefficient of variation of cluster sizes. Our simulation studies with a finite number of clusters indicate that the predicted power by our method agrees well with the empirical power, when the parameters in the multivariate linear mixed model are estimated via the expectation-maximization algorithm. An application to a real CRT is presented to illustrate the proposed method

A comparison of the multilevel MIMIC model to the multilevel regression and mixed ANOVA model for the estimation and testing of a cross-level interaction effect: A simulation study

When observing data on a patient-reported outcome measure in, for example, clinical trials, the variables observed are often correlated and intended to measure a latent variable. In addition, such data are also often characterized by a hierarchical structure, meaning that the outcome is repeatedly measured within patients. To analyze such data, it is important to use an appropriate statistical model, such as structural equation modeling (SEM). However, researchers may rely on simpler statistical models that are applied to an aggregated data structure. For example, correlated variables are combined into one sum score that approximates a latent variable. This may have implications when, for example, the sum score consists of indicators that relate differently to the latent variable being measured. This study compares three models that can be applied to analyze such data: the multilevel multiple indicators multiple causes (ML-MIMIC) model, a univariate multilevel model, and a mixed analysis of variance (ANOVA) model. The focus is on the estimation of a cross-level interaction effect that presents the difference over time on the patient-reported outcome between two treatment groups. The ML-MIMIC model is an SEM-type model that considers the relationship between the indicators and the latent variable in a multilevel setting, whereas the univariate multilevel and mixed ANOVA model rely on sum scores to approximate the latent variable. In addition, the mixed ANOVA model uses aggregated second-level means as outcome. This study showed that the ML-MIMIC model produced unbiased cross-level interaction effect estimates when the relationships between the indicators and the latent variable being measured varied across indicators. In contrast, under similar conditions, the univariate multilevel and mixed ANOVA model underestimated the cross-level interaction effect

Sample size determination for Bayesian ANOVAs with informative hypotheses

Researchers can express their expectations with respect to the group means in an ANOVA model through equality and order constrained hypotheses. This paper introduces the R package SSDbain, which can be used to calculate the sample size required to evaluate (informative) hypotheses using the Approximate Adjusted Fractional Bayes Factor (AAFBF) for one-way ANOVA models as implemented in the R package bain. The sample size is determined such that the probability that the Bayes factor is larger than a threshold value is at least η when either of the hypotheses under consideration is true. The Bayesian ANOVA, Bayesian Welch's ANOVA, and Bayesian robust ANOVA are available. Using the R package SSDbain and/or the tables provided in this paper, researchers in the social and behavioral sciences can easily plan the sample size if they intend to use a Bayesian ANOVA

Enhancing the effect of psychotherapy through systematic client feedback in outpatient mental healthcare:A cluster randomized trial

Objective: Systematic client feedback (SCF), the regular monitoring and informing of patients’ progress during therapy to patient and therapist, has been found to have effects on treatment outcomes varying from very positive to slightly negative. Several prior studies have been biased by researcher allegiance or lack of an independent outcome measure. The current study has taken this into account and aims to clarify the effects of SCF in outpatient psychological treatment. Method: Outpatients (n = 1733) of four centers offering brief psychological treatments were cluster randomized to either treatment as usual (TAU) or TAU with SCF based on the Partners for Change Outcome Management System (PCOMS). Primary outcome measure was the Outcome Questionnaire (OQ-45). Effects of the two treatment conditions on treatment outcome, patient satisfaction, dropout rate, costs, and treatment duration were assessed using a three-level multilevel analysis. DSM-classification, sex, and age of each patient were included as covariates. Results: In both analyses, SCF significantly improved treatment outcome, particularly in the first three months. No significant effects were found on the other outcome variables. Conclusions: Addition of systematic client feedback to treatment as usual, is likely to have a beneficial impact in outpatient psychological treatment. Implementation requires a careful plan of action. Clinical or methodological significance of this article: This study, with large sample size and several independent outcome measures, provides strong evidence that addition of systematic client feedback to outpatient psychological treatment can have a beneficial effect on treatment outcome (symptoms and wellbeing), particularly in the first three months. However, implementation requires a careful plan of action

Data Collection Expert Prior Elicitation in Survey Design: Two Case Studies

Data collection staff involved in sampling designs, monitoring and analysis of surveys often have a good sense of the response rate that can be expected in a survey, even when this survey is new or done at a relatively low frequency. They make expectations of response rates, and, subsequently, costs on an almost continuous basis. Rarely, however, are these expectations formally structured. Furthermore, the expectations usually are point estimates without any assessment of precision or uncertainty. In recent years, the interest in adaptive survey designs has increased. These designs lean heavily on accurate estimates of response rates and costs. In order to account for inaccurate estimates, a Bayesian analysis of survey design parameters is very sensible. The combination of strong intrinsic knowledge of data collection staff and a Bayesian analysis is a natural next step. In this article, prior elicitation is developed for design parameters with the help of data collection staff. The elicitation is applied to two case studies in which surveys underwent a major redesign and direct historic survey data was unavailable

The effect of therapist characteristics on the use and outcome of systematic client feedback in outpatient mental healthcare

ObjectiveTherapist characteristics are known to affect treatment outcome in general and could also influence the use of systematic client feedback (SCF). The current study explores the effect of feedback orientation, regulatory focus, self-efficacy, attitude towards feedback resources and perceived feedback validity on the use and outcome of SCF in outpatient mental healthcare.MethodThe data of therapists (n = 12) and patients (n = 504) of two outpatient centres offering brief psychological treatment were analysed when SCF, based on the Partners for Change Outcome Management System (PCOMS), was added to treatment as usual. The data of therapists were obtained through a therapist questionnaire composed of relevant characteristics from feedback studies in social and organizational psychology. The effect on the use of SCF was analysed using logistic regression; whereas, the effect on outcome was assessed using a two-level multilevel analysis. Regular use of SCF and the Outcome Questionnaire (OQ-45) were used as outcome variables. DSM-classification, sex and age of each patient were included as covariates.ResultsHigh perceived feedback validity significantly increased the use of SCF. No significant therapist characteristics effects were found on outcome, but high promotion focus was associated with treating more complex patients.ConclusionsThe perceived feedback validity of SCF is likely to have an influence on its use and is probably affected by the changes in the organizational climate

A multilevel structural equation model for assessing a drug effect on a patient reported outcome measure in on-demand medication data.

We analyze data from a clinical trial investigating the effect of an on-demand drug for women with low sexual desire. These data consist of a varying number of measurements/events across patients of when the drug was taken, including data on a patient-reported outcome consisting of five items measuring an unobserved construct (latent variable). Traditionally, these data are aggregated prior to analysis by composing one sum score per event and averaging this sum score over all observed events. In this paper, we explain the drawbacks of this aggregating approach. One drawback is that these averages have different standard errors because the variance of the underlying events differs between patients and because the number of events per patient differs. Another drawback is the implicit assumption that all items have equal weight in relation to the latent variable being measured. We propose a multilevel structural equation model, treating the events (level 1) as nested observations within patients (level 2), as alternative analysis method to overcome these drawbacks. The model we apply includes a factor model measuring a latent variable at the level of the event and at the level of the patient. Then, in the same model, the latent variables are regressed on covariates to assess the drug effect. We discuss the inferences obtained about the efficacy of the on-demand drug using our proposed model. We further illustrate how to test for measurement invariance across grouping covariates and levels using the same model

The relation between creativity and students’ performance on different types of geometrical problems in elementary education

Aim: In the current study we aimed to investigate the relation between creativity and mathematical problem solving in the upper grades of elementary school. Methods: To examine how student’s levels of general creativity were related to their performance on different types of geometrical problems, a geometry test with diverse problems was administered to a sample of 1665 Dutch students from third to sixth grade, as well as a creativity test. The geometry test consisted of four closed-ended routine problems, six closed-ended non-routine problems (related to a visual artwork) and four open-ended non-routine problems (multiple solutions problems). The Test of Creative Thinking—Drawing Production was used to measure students’ creativity. Multivariate multilevel analyses were conducted to take the nested structure of the data into account. Results: The results showed that creativity was a significant predictor of students’ performance on all types of geometrical problems, but most strongly associated with performance on open-ended non-routine problems, suggesting that students with higher levels of creativity perform better in solving geometry problems in general, but especially in geometry problems asking for multiple solutions