Bayesian sequential designs in studies with multilevel data

In many studies in the social and behavioral sciences, the data have a multilevel structure, with subjects nested within clusters. In the design phase of such a study, the number of clusters to achieve a desired power level has to be calculated. This requires a priori estimates of the effect size and intraclass correlation coefficient. If these estimates are incorrect, the study may be under- or overpowered. This may be overcome by using a group-sequential design, where interim tests are done at various points in time of the study. Based on interim test results, a decision is made to either include additional clusters or to reject the null hypothesis and conclude the study. This contribution introduces Bayesian sequential designs as an alternative to group-sequential designs. This approach compares various hypotheses based on the support in the data for each of them. If neither hypothesis receives a sufficient degree of support, additional clusters are included in the study and the Bayes factor is recalculated. This procedure continues until one of the hypotheses receives sufficient support. This paper explains how the Bayes factor is used as a measure of support for a hypothesis and how a Bayesian sequential design is conducted. A simulation study in the setting of a two-group comparison was conducted to study the effects of the minimum and maximum number of clusters per group and the desired degree of support. It is concluded that Bayesian sequential designs are a flexible alternative to the group sequential design.

The effectiveness, efficiency, and acceptability of EMDR vs. EMDR 2.0 vs. the Flash technique in the treatment of patients with PTSD: study protocol for the ENHANCE randomized controlled trial

Background

Several widely studied therapies have proven to be effective in the treatment of post-traumatic stress disorder (PTSD). However, there is still room for improvement because not all patients benefit from trauma-focused treatments. Improvements in the treatment of PTSD can be achieved by investigating ways to enhance existing therapies, such as eye movement desensitization and reprocessing (EMDR) therapy, as well as exploring novel treatments. The purpose of the current study is to determine the differential effectiveness, efficiency, and acceptability of EMDR therapy, an adaptation of EMDR therapy, referred to as EMDR 2.0, and a novel intervention for PTSD, the so-called Flash technique. The second aim is to identify the moderators of effectiveness for these interventions. This study will be conducted among individuals diagnosed with PTSD using a randomized controlled trial design.

Methods

A total of 130 patients diagnosed with (complex) PTSD will be randomly allocated to either six sessions of EMDR therapy, EMDR 2.0, or the Flash technique. The primary outcomes used to determine treatment effectiveness include the presence of a PTSD diagnosis and the severity of PTSD symptoms. The secondary outcomes of effectiveness include symptoms of depression, symptoms of dissociation, general psychiatric symptoms, and experiential avoidance. All patients will be assessed at baseline, at 4-week post-treatment, and at 12-week follow-up. Questionnaires indexing symptoms of PTSD, depression, general psychopathology, and experiential avoidance will also be assessed weekly during treatment and bi-weekly after treatment, until the 12-week follow-up. Efficiency will be assessed by investigating the time it takes both to lose the diagnostic status of PTSD, and to achieve reliable change in PTSD symptoms. Treatment acceptability will be assessed after the first treatment session and after treatment termination.

Discussion

This study is the first to investigate EMDR 2.0 therapy and the Flash technique in a sample of participants officially diagnosed with PTSD using a randomized controlled trial design. This study is expected to improve the available treatment options for PTSD and provide therapists with alternative ways to choose a therapy beyond its effectiveness by considering moderators, efficiency, and acceptability.

Trial registration

The trial was retrospectively registered in the ISRCTN registry at 10th November 2022 under registration number ISRCTN13100019.

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

OBJECTIVE

Therapist 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.

METHOD

The 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.

RESULTS

High 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.

CONCLUSIONS

The 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.

Optimal allocation of clusters in stepped wedge designs with a decaying correlation structure

The cluster randomized stepped wedge design is a multi-period uni-directional switch design in which all clusters start in the control condition and at the beginning of each new period a random sample of clusters crosses over to the intervention condition. Such designs often use uniform allocation, with an equal number of clusters at each treatment switch. However, the uniform allocation is not necessarily the most efficient. This study derives the optimal allocation of clusters to treatment sequences in the cluster randomized stepped wedge design, for both cohort and cross-sectional designs. The correlation structure is exponential decay, meaning the correlation decreases with the time lag between two measurements. The optimal allocation is shown to depend on the intraclass correlation coefficient, the number of subjects per cluster-period and the cluster and (in the case of a cohort design) individual autocorrelation coefficients. For small to medium values of these autocorrelations those sequences that have their treatment switch earlier or later in the study are allocated a larger proportion of clusters than those clusters that have their treatment switch halfway the study. When the autocorrelation coefficients increase, the clusters become more equally distributed across the treatment sequences. For the cohort design, the optimal allocation is almost equal to the uniform allocation when both autocorrelations approach the value 1. For almost all scenarios that were studied, the efficiency of the uniform allocation is 0.8 or higher. R code to derive the optimal allocation is available online.

A review of applications of the Bayes factor in psychological research

The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian evidence synthesis, Bayesian variable selection and model averaging, and Bayesian evaluation of cognitive models. We elaborate what each application entails, give illustrative examples, and provide an overview of key references and software with links to other applications. The article is concluded with a discussion of the opportunities and pitfalls of Bayes factor applications and a sketch of corresponding future research lines. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Optimal allocation to treatment sequences in individually randomized stepped-wedge designs with attrition

BACKGROUND/AIMS

The stepped-wedge design has been extensively studied in the setting of the cluster randomized trial, but less so for the individually randomized trial. This article derives the optimal allocation of individuals to treatment sequences. The focus is on designs where all individuals start in the control condition and at the beginning of each time period some of them cross over to the intervention, so that at the end of the trial all of them receive the intervention.

METHODS

The statistical model that takes into account the nesting of repeated measurements within subjects is presented. It is also shown how possible attrition is taken into account. The effect of the intervention is assumed to be sustained so that it does not change after the treatment switch. An exponential decay correlation structure is assumed, implying that the correlation between any two time point decreases with the time lag. Matrix algebra is used to derive the relation between the allocation of units to treatment sequences and the variance of the treatment effect estimator. The optimal allocation is the one that results in smallest variance.

RESULTS

Results are presented for three to six treatment sequences. It is shown that the optimal allocation highly depends on the correlation parameter ρ and attrition rate r between any two adjacent time points. The uniform allocation, where each treatment sequence has the same number of individuals, is often not the most efficient. For 0 . 1 ≤ ρ ≤ 0 . 9 and r = 0 , 0 . 05 , 0 . 2 , its efficiency relative to the optimal allocation is at least 0.8. It is furthermore shown how a constrained optimal allocation can be derived in case the optimal allocation is not feasible from a practical point of view.

CONCLUSION

This article provides the methodology for designing individually randomized stepped-wedge designs, taking into account the possibility of attrition. As such it helps researchers to plan their trial in an efficient way. To use the methodology, prior estimates of the degree of attrition and intraclass correlation coefficient are needed. It is advocated that researchers clearly report the estimates of these quantities to help facilitate planning future trials.

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.

Optimal placebo-treatment comparisons in trials with an incomplete within-subject design and heterogeneous costs and variances

The aim of a clinical trial is to compare placebo to one or more treatments. The within-subject design is known to be more efficient than the between-subject design. However, in some trials that implement a within-subject design it is not possible to evaluate the placebo and all treatments within each subject. The design then becomes an incomplete within-subject design. An important question is how many subjects should be allocated to each combination of placebo and treatments. This paper studies optimal allocations of subjects in trials with a placebo and two treatments under heterogenous costs and variances. Two optimality criteria that consider the placebo-treatment contrasts simultaneously are considered, and the design is derived under a budgetary constraint. More subjects are allocated to those combinations with higher variances and lower costs. The optimal allocation is compared to the uniform allocation, which allocates equal number of subjects to each placebo and treatment combination, and to the complete within-subject design, where placebo and all treatments are available in each subject. The methodology is illustrated on the basis of an example on consultation time in primary care. A Shiny app is available to facilitate use of the methodology.

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.

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.

Cannabidiol enhancement of exposure therapy in treatment refractory patients with social anxiety disorder and panic disorder with agoraphobia: A randomised controlled trial

Preclinical research suggests that enhancing CB1 receptor agonism may improve fear extinction. In order to translate this knowledge into a clinical application we examined whether cannabidiol (CBD), a hydrolysis inhibitor of the endogenous CB1 receptor agonist anandamide (AEA), would enhance the effects of exposure therapy in treatment refractory patients with anxiety disorders. Patients with panic disorder with agoraphobia or social anxiety disorder were recruited for a double-blind parallel randomised controlled trial at three mental health care centres in the Netherlands. Eight therapist-assisted exposure in vivo sessions (weekly, outpatient) were augmented with 300 mg oral CBD (n = 39) or placebo (n = 41). The Fear Questionnaire (FQ) was assessed at baseline, mid- and post-treatment, and at 3 and 6 months follow-up. Primary analyses were on an intent-to-treat basis. No differences were found in treatment outcome over time between CBD and placebo on FQ scores, neither across (β = 0.32, 95% CI [-0.60; 1.25]) nor within diagnosis groups (β = -0.11, 95% CI [-1.62; 1.40]). In contrast to our hypotheses, CBD augmentation did not enhance early treatment response, within-session fear extinction or extinction learning. Incidence of adverse effects was equal in the CBD (n = 4, 10.3%) and placebo condition (n = 6, 15.4%). In this first clinical trial examining CBD as an adjunctive therapy in anxiety disorders, CBD did not improve treatment outcome. Future clinical trials may investigate different dosage regimens.

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. Systematic reviews have shown that co-primary endpoints are not uncommon in pragmatic trials but are seldom recognized in sample size or power calculations. While methods for power analysis based on K (K≥ 2) binary co-primary endpoints are available for cluster randomized trials (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 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. This article is protected by copyright. All rights reserved.

Psychopathology and resilience in older adults with posttraumatic stress disorder: a randomized controlled trial comparing narrative exposure therapy and present-centered therapy

OBJECTIVE

Using data from a randomized controlled trial on psychotherapy for posttraumatic stress disorder (PTSD) in older adults (aged >55), this study aimed at analysing the efficacy of two psychological interventions in terms of self-reported symptoms, comorbid psychopathology and resilience outcomes.

METHOD

Thirty-three outpatients (age 55-81) with PTSD were randomly assigned to eleven sessions of narrative exposure therapy or present-centered therapy. Self-reported symptom severity of PTSD, depression and general psychopathology, along with measures of resilience (self-efficacy, quality of life and posttraumatic growth cognitions), were target outcomes. Harvard Trauma Questionnaire, Beck Depression Inventory, Brief Symptom Inventory, General Efficacy Scale, World Health Organization Quality of Life Assessment and Meaning of War Scale (personal growth) were assessed pre-treatment, post-treatment and at four months follow-up. Because of variable inter-assessment intervals, a piecewise mixed effects growth model was used to investigate treatment effects.

RESULTS

Neither post-treatment, nor at mean follow-up, between-group effects were found. At follow-up, significant medium to large within-group effect sizes were found in the NET-group for psychopathology (self-reported PTSD: Cohen's d = 0.54, p < .01; depression: Cohen's d = 0.51, p = .03; general psychopathology: Cohen's d = 0.74, p = .001), but not so in the PCT-group. Resilience (self-efficacy, quality of life and personal growth cognitions) did not significantly change in either group.

CONCLUSIONS

In older adults with PTSD, the efficacy of NET extended beyond PTSD, reducing not only self-reported symptoms of PTSD but also comorbid depression and general psychopathology.

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.

Relative Effectiveness of CBT-Components and Sequencing in Indicated Depression Prevention for Adolescents: A Cluster-Randomized Microtrial

OBJECTIVE

Cognitive Behavioral Therapy (CBT) was dismantled into four modules of three sessions each: cognitive restructuring (Think), behavioral activation (Act), problem solving (Solve) and relaxation (Relax). We investigated the modules' relative effectiveness in indicated depression prevention for adolescents and examined variations in sequencing of these modules.

METHOD

We performed a pragmatic cluster-randomized microtrial with four parallel conditions: (1) Think-Act-Relax-Solve (n = 14 clusters, n = 81 participants); (2) Act-Think-Relax-Solve (n = 13, n = 69); (3) Solve-Act-Think-Relax (n = 13, n = 77); and (4) Relax-Solve-Act-Think (n = 12, n = 55). The sample consisted of 282 Dutch adolescents with elevated depressive symptoms (M_age = 13.8; 55.7% girls, 92.9% Dutch). In total 52 treatment groups were randomized as a cluster. Assessments were conducted at baseline, after each module and at 6-month follow-up with depressive symptoms as primary outcome.

RESULTS

None of the modules (Think, Act, Solve, Relax) was associated with a significant decrease in depressive symptoms after three sessions and no significant differences in effectiveness were found between the modules. All sequences of modules were associated with a significant decrease in depressive symptoms at post-intervention, except the sequence Relax-Solve-Act-Think. At 6-month follow-up, all sequences showed a significant decrease in depressive symptoms. No significant differences in effectiveness were found between the sequences at post-intervention and 6-month follow-up.

CONCLUSIONS

Regardless of the CBT technique provided, one module of three sessions may not be sufficient to reduce depressive symptoms. The sequence in which the CBT components cognitive restructuring, behavioral activation, problem solving and relaxation are offered, does not appear to significantly influence outcomes at post- intervention or 6-month follow-up.

ABBREVIATIONS

CDI-2:F: Children's Depression Inventory-2 Full-length version; CDI-2:S: Children's Depression Inventory-2 Short version; STARr: Solve, Think, Act, Relax and repeat.

Optimal allocation to treatments in a sequential multiple assignment randomized trial

One of the main questions in the design of a trial is how many subjects should be assigned to each treatment condition. Previous research has shown that equal randomization is not necessarily the best choice. We study the optimal allocation for a novel trial design, the sequential multiple assignment randomized trial, where subjects receive a sequence of treatments across various stages. A subject's randomization probabilities to treatments in the next stage depend on whether he or she responded to treatment in the current stage. We consider a prototypical sequential multiple assignment randomized trial design with two stages. Within such a design, many pairwise comparisons of treatment sequences can be made, and a multiple-objective optimal design strategy is proposed to consider all such comparisons simultaneously. The optimal design is sought under either a fixed total sample size or a fixed budget. A Shiny App is made available to find the optimal allocations and to evaluate the efficiency of competing designs. As the optimal design depends on the response rates to first-stage treatments, maximin optimal design methodology is used to find robust optimal designs. The proposed methodology is illustrated using a sequential multiple assignment randomized trial example on weight loss management.

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.

Bayesian updating: increasing sample size during the course of a study

Background

A priori sample size calculation requires an a priori estimate of the size of the effect. An incorrect estimate may result in a sample size that is too low to detect effects or that is unnecessarily high. An alternative to a priori sample size calculation is Bayesian updating, a procedure that allows increasing sample size during the course of a study until sufficient support for a hypothesis is achieved. This procedure does not require and a priori estimate of the effect size. This paper introduces Bayesian updating to researchers in the biomedical field and presents a simulation study that gives insight in sample sizes that may be expected for two-group comparisons.

Methods

Bayesian updating uses the Bayes factor, which quantifies the degree of support for a hypothesis versus another one given the data. It can be re-calculated each time new subjects are added, without the need to correct for multiple interim analyses. A simulation study was conducted to study what sample size may be expected and how large the error rate is, that is, how often the Bayes factor shows most support for the hypothesis that was not used to generate the data.

Results

The results of the simulation study are presented in a Shiny app and summarized in this paper. Lower sample size is expected when the effect size is larger and the required degree of support is lower. However, larger error rates may be observed when a low degree of support is required and/or when the sample size at the start of the study is small. Furthermore, it may occur sufficient support for neither hypothesis is achieved when the sample size is bounded by a maximum.

Conclusions

Bayesian updating is a useful alternative to a priori sample size calculation, especially so in studies where additional subjects can be recruited easily and data become available in a limited amount of time. The results of the simulation study show how large a sample size can be expected and how large the error rate is.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-021-01334-6.

Contamination: How much can an individually randomized trial tolerate?

Cluster randomization results in an increase in sample size compared to individual randomization, referred to as an efficiency loss. This efficiency loss is typically presented under an assumption of no contamination in the individually randomized trial. An alternative comparator is the sample size needed under individual randomization to detect the attenuated treatment effect due to contamination. A general framework is provided for determining the extent of contamination that can be tolerated in an individually randomized trial before a cluster randomized design yields a larger sample size. Results are presented for a variety of cluster trial designs including parallel arm, stepped-wedge and cluster crossover trials. Results reinforce what is expected: individually randomized trials can tolerate a surprisingly large amount of contamination before they become less efficient than cluster designs. We determine the point at which the contamination means an individual randomized design to detect an attenuated effect requires a larger sample size than cluster randomization under a nonattenuated effect. This critical rate is a simple function of the design effect for clustering and the design effect for multiple periods as well as design effects for stratification or repeated measures under individual randomization. These findings are important for pragmatic comparisons between a novel treatment and usual care as any bias due to contamination will only attenuate the true treatment effect. This is a bias that operates in a predictable direction. Yet, cluster randomized designs with post-randomization recruitment without blinding, are at high risk of bias due to the differential recruitment across treatment arms. This sort of bias operates in an unpredictable direction. Thus, with knowledge that cluster randomized trials are generally at a greater risk of biases that can operate in a nonpredictable direction, results presented here suggest that even in situations where there is a risk of contamination, individual randomization might still be the design of choice.

Serial Order Effect in Divergent Thinking in Five- to Six-Year-Olds: Individual Differences as Related to Executive Functions

This study examined the unfolding in real time of original ideas during divergent thinking (DT) in five- to six-year-olds and related individual differences in DT to executive functions (EFs). The Alternative Uses Task was administered with verbal prompts that encouraged children to report on their thinking processes while generating uses for daily objects. In addition to coding the originality of each use, the domain-specific DT processes memory retrieval and mental operations were coded from children’s explanations. Six EF tasks were administered and combined into composites to measure working memory, shifting, inhibition, and selective attention. The results replicated findings of a previous study with the same children but at age four years: (1) there was a serial order effect of the originality of uses; and (2) the process mental operations predicted the originality of uses. Next, the results revealed that both domain-general EFs and domain-specific executive processes played a role in the real-time unfolding of original ideas during DT. Particularly, the DT process mental operations was positively related to the early generation of original ideas, while selective attention was negatively related to the later generation of original ideas. These findings deepen our understanding of how controlled executive processes operate during DT.

The cluster randomized crossover trial: The effects of attrition in the AB/BA design and how to account for it in sample size calculations

Background/Aims:

This article studies the effect of attrition in the cluster randomized crossover trial. The focus is on the two-treatment two-period AB/BA design where attrition occurs during the washout period. Attrition may occur at either the subject level or the cluster level. In the latter case, clusters drop out entirely and provide no measurements in the second period. Subject attrition can only occur in the cohort design, where each subject receives both treatments. Cluster attrition can also occur in the cross-sectional design, where different subjects are measured in the two time periods. Furthermore, this article explores two different strategies to account for potential levels of attrition: increasing sample size and replacing those subjects who drop out by others.

Methods:

The statistical model that takes into account the nesting of subjects within clusters, and the nesting of repeated measurements within subjects is presented. The effect of attrition is evaluated on the basis of the efficiency of the treatment effect estimator. Matrix algebra is used to derive the relation between efficiency, the degree of attrition, cluster size and the intraclass correlations: the within-cluster within-period correlation, the within-cluster between-period correlation and (in the case of a cohort design) the within-subject correlation. The methodology is implemented in two Shiny Apps.

Results:

Attrition in a cluster randomized crossover trial implies a loss of efficiency. Efficiency decreases with an increase of the attrition rate. The loss of efficiency due to attrition of subjects in a cohort design is largest for small number of subjects per cluster-period, but it may be repaired to a large degree by increasing the number of subjects per cluster-period or by replacing those subjects who drop out by others. Attrition of clusters results in a larger loss of efficiency, but this loss does not depend on the number of subjects per cluster-period. Repairing for this loss requires a large increase in the number of subjects per cluster-period. The methodology of this article is illustrated by an example on the effect of lavender scent on dental patients’ anxiety.

Conclusion:

This article provides the methodology of exploring the effect of attrition in cluster randomized crossover trials, and to repair for attrition. As such, it helps researchers plan their trial in an appropriate way and avoid underpowered trials. To use the methodology, prior estimates of the degree of attrition and intraclass correlation coefficients are needed. It is advocated that researchers clearly report the estimates of these quantities to help facilitate planning future trials.

Optimal designs for group randomized trials and group administered treatments with outcomes at the subject and group level

With group randomized trials complete groups of subject are randomized to treatment conditions. Such grouping also occurs in individually randomized trials where treatment is administered in groups. Outcomes may be measured at the level of the subject, but also at the level of the group. The optimal design determines the number of groups and the number of subjects per group in the intervention and control conditions. It is found by taking a budgetary constraint into account, where costs are associated with implementing the intervention and control, and with taking measurements on subject and groups. The optimal design is found such that the effect of treatment is estimated with highest efficiency, and the total costs do not exceed the budget that is available. The design that is optimal for the outcome at the subject level is not necessarily optimal for the outcome at the group level. Multiple-objective optimal designs consider both outcomes simultaneously. Their aim is to find a design that has high efficiencies for both outcome measures. An Internet application for finding the multiple-objective optimal design is demonstrated on the basis of an example from smoking prevention in primary education, and another example on consultation time in primary care.

Effectiveness of the Boston University Approach to Psychiatric Rehabilitation in Improving Social Participation in People With Severe Mental Illnesses: A Randomized Controlled Trial

BACKGROUND

People with severe mental illnesses (SMIs) have difficulty participating in society through work or other daily activities.

AIMS

To establish the effectiveness with which the Boston University Approach to Psychiatric Rehabilitation (BPR) improves the level of social participation in people with SMIs, in the Netherlands.

METHOD

In a randomized controlled trial involving 188 people with SMIs, we compared BPR (n = 98) with an Active Control Condition (ACC, n = 90) (Trial registration ISRCTN88987322). Multilevel modeling was used to study intervention effects over two six-month periods. The primary outcome measure was level of social participation, expressed as having participated in paid or unpaid employment over the past six months, as the total hours spent in paid or unpaid employment, and as the current level of social participation. Secondary outcome measures were clients' views on rehabilitation goal attainment, Quality of Life (QOL), personal recovery, self-efficacy, and psychosocial functioning.

RESULTS

During the study, social participation, QOL, and psychosocial functioning improved in patients in both groups. However, BPR was not more effective than ACC on any of the outcomes. Better social participation was predicted by previous work experience and a lower intensity of psychiatric symptoms.

CONCLUSIONS

While ACC was as effective as BPR in improving the social participation of individuals with SMIs, much higher percentages of participants in our sample found (paid) work or other meaningful activities than in observational studies without specific support for social participation. This suggests that focused rehabilitation efforts are beneficial, irrespective of the specific methodology used.

What are the statistical implications of treatment non-compliance in cluster randomized trials: A simulation study

Subjects in randomized controlled trials do not always comply to the treatment condition they have been assigned to. This may cause the estimated effect of the intervention to be biased and also affect efficiency, coverage of confidence intervals, and statistical power. In cluster randomized trials non‐compliance may occur at the subject level but also at the cluster level. In the latter case, all subjects within the same cluster have the same compliance status. The purpose of this study is to investigate the statistical implications of non‐compliance in cluster randomized trials. A simulation study was conducted with varying degrees of non‐compliance at either the cluster level or subject level. The probability of non‐compliance depends on a covariate at the cluster or subject level. Various realistic values of the intraclass correlation coefficient and cluster size are used. The data are analyzed by intention to treat, as treated, per protocol and the instrumental variable approach. The results show non‐compliance may result in downward biased estimates of the intervention effect and an under‐ or overestimate of its standard deviation. The coverage of the confidence intervals may be too small, and in most cases, empirical power is too small. The results are more severe when the probability of non‐compliance increases and the covariate that affects compliance is unobserved. It is advocated to avoid non‐compliance. If this is not possible, compliance status and covariates that affect compliance should be measured and included in the statistical model.

Changes in heart rate and skin conductance in the 30 min preceding aggressive behavior

Aggressive behavior of inpatients threatens the safety and well-being of both mental health staff members and fellow patients. It was investigated whether heart rate and electrodermal activity can be used to signal imminent aggression. A naturalistic study was conducted in which 100 inpatients wore sensor wristbands during 5 days to monitor their heart rate and electrodermal activity while staff members recorded patients' aggressive incidents on the ward. Of the 100 patients, 36 displayed at least one aggressive incident. Longitudinal multilevel models indicated that heart rate, skin conductance level, and the number of nonspecific skin conductance responses per minute rose significantly in the 20 min preceding aggressive incidents. Although psychopathy was modestly correlated with displaying aggression, it was not a significant predictor of heart rate and skin conductance preceding aggression. The current findings may provide opportunities for the development of individual prediction models to aid acute risk assessment and to predict aggressive incidents in an earlier stage. The current results on the physiological indicators of aggression are promising for reducing aggression and improving both staff as well as patient safety in psychiatric mental health institutions.

Randomised controlled trial comparing narrative exposure therapy with present-centred therapy for older patients with post-traumatic stress disorder

BACKGROUND

Evidence-based treatment and age-specific services are required to address the needs of trauma-affected older populations. Narrative exposure therapy (NET) may present an appropriate treatment approach for this population since it provides prolonged exposure in a lifespan perspective. As yet, however, no trial on this intervention has been conducted with older adults from Western Europe.AimsExamining the efficacy of NET in a sample of older adults.

METHOD

Out-patients with post-traumatic stress disorder (PTSD), aged 55 years and over, were randomly assigned to either 11 sessions of NET (n = 18) or 11 sessions of present-centred therapy (PCT) (n = 15) and assessed on the Clinician-Administered PTSD Scale (CAPS) pre-treatment, post-treatment and at follow-up. Total scores as well as symptom scores (re-experience, avoidance and hyperarousal) were evaluated.

RESULTS

Using a piecewise mixed-effects growth model, at post-treatment a medium between-treatment effect size for CAPS total score (Cohen's d = 0.44) was found, favouring PCT. At follow-up, however, the between-treatment differences were non-significant. Drop-out rates were low (NET 6.7%, PCT 14.3%) and no participant dropped out of the study because of increased distress.

CONCLUSIONS

Both NET and PCT appear to be safe and efficacious treatments with older adults: PCT is non-intrusive and NET allows for imaginal exposure in a lifespan perspective. By selectively providing these approaches in clinical practice, patient matching can be optimised.Declaration of interestNone.

Systematic client feedback to brief therapy in basic mental healthcare: study protocol for a four-centre clinical trial

INTRODUCTION

The Partners for Change Outcome Management System (PCOMS) is a client feedback-system built on two brief visual analogue self-report scales. Prior studies of PCOMS have found effects varying from significant positive to negative. Aims of present study are; to test the predicted beneficial impact of PCOMS, while accounting for methodological flaws in prior studies and to clarify under which circumstances the addition of PCOMS to therapy has a beneficial effect.

METHODS AND ANALYSIS

This study focuses on patients applying for brief, time-limited treatments. Four centres will be randomised to either treatment as usual (TAU) or TAU with PCOMS. All participating patients will be assessed four times. The full staff in the experimental condition will be trained in PCOMS. In the second part of this study, all therapists in the PCOMS condition will fill in a questionnaire concerning the influence of regulatory focus, self-efficacy, external or internal feedback orientation and perceived feedback validity of PCOMS. Finally, patients in the PCOMS condition will be asked to give feedback through a structured interview.The primary outcome measure is the Outcome Questionnaire over the period from beginning to end of therapy. The Mental Health Continuum-Short Form and Consumer Quality Index are also completed. In the primary analysis, outcomes of the two treatment conditions on treatment outcome, patient satisfaction, costs, drop-out and duration will be examined with a three-level (within patient, between patients and between therapists) multilevel analysis. The DSM-classification, sex, education level, age of each patient and therapist factors will be included as covariates.

ETHICS AND DISSEMINATION

The Medical Ethics Committee of the University of Twente approved this study (K15-11, METC Twente). Data will be included from 1 January 2016 to 1 July 2019. Study results will be disseminated through peer-reviewed journals and conferences.

TRIAL REGISTRATION NUMBER

NTR5466; Pre-results.

Cost-efficient designs for three-arm trials with treatment delivered by health professionals: Sample sizes for a combination of nested and crossed designs

Background This article studies the design of trials that compare three treatment conditions that are delivered by two types of health professionals. The one type of health professional delivers one treatment, and the other type delivers two treatments, hence, this design is a combination of a nested and crossed design. As each health professional treats multiple patients, the data have a nested structure. This nested structure has thus far been ignored in the design of such trials, which may result in an underestimate of the required sample size. In the design stage, the sample sizes should be determined such that a desired power is achieved for each of the three pairwise comparisons, while keeping costs or sample size at a minimum. Methods The statistical model that relates outcome to treatment condition and explicitly takes the nested data structure into account is presented. Mathematical expressions that relate sample size to power are derived for each of the three pairwise comparisons on the basis of this model. The cost-efficient design achieves sufficient power for each pairwise comparison at lowest costs. Alternatively, one may minimize the total number of patients. The sample sizes are found numerically and an Internet application is available for this purpose. The design is also compared to a nested design in which each health professional delivers just one treatment. Results Mathematical expressions show that this design is more efficient than the nested design. For each pairwise comparison, power increases with the number of health professionals and the number of patients per health professional. The methodology of finding a cost-efficient design is illustrated using a trial that compares treatments for social phobia. The optimal sample sizes reflect the costs for training and supervising psychologists and psychiatrists, and the patient-level costs in the three treatment conditions. Conclusion This article provides the methodology for designing trials that compare three treatment conditions while taking the nesting of patients within health professionals into account. As such, it helps to avoid underpowered trials. To use the methodology, a priori estimates of the total outcome variances and intraclass correlation coefficients must be obtained from experts' opinions or findings in the literature.

The Consequences of Varying Measurement Occasions in Discrete-Time Survival Analysis

Abstract. In a discrete-time survival model the occurrence of some event is measured by the end of each time interval. In practice it is not always possible to measure all subjects at the same point in time. In this study the consequences of varying measurement occasions are investigated by means of a simulation study and the analysis of data from an empirical study. The results of the simulation study suggest that the effects of varying measurement occasions are negligible, at least for the scenarios that were covered in the simulation. The empirical example shows varying measurement occasions have minor effects on parameter estimates, standard errors, and significance levels.

Community-based counseling reaches and helps bereaved people living in low-income households

OBJECTIVE

Poverty is related to increased grief-related mental health problems, leading some to suggest bereavement counseling should be tailored to income. However, information about accessibility and effectiveness of such counseling programs serving low-income households is scarce. This longitudinal study therefore investigated the association between poverty and complicated grief (CG), and the effectiveness of a community-based bereavement counseling program in serving low-income households.

METHODS

Two hundred eighty-eight participants (75% female) were enrolled. Loss-related and demographic variables were assessed at baseline. Regression analyses were used to investigate household income as a predictor of CG, and examine bereavement counseling effectiveness by comparing CG symptom change across three household income categories across three time-points: baseline (T1), T1 + 12 months (T2), and T1 + 18 months (T3).

RESULTS

Of all participants, 35.8% reported below poverty-threshold income, twice the general population's rate. Multiple regression analysis indicated poverty-threshold income was a predictor of CG symptoms over and above demographic and loss-related characteristics. Three-way interaction analysis detected a significant treatment effect for study condition across time, but no differences in treatment effects across income.

CONCLUSION

Lower household income was associated with higher CG symptoms. Since income did not predict differential treatment response, community-based bereavement counseling appeared no less efficacious for members of low-income households. Clinical or methodological significance of this article: While previous research has indicated low income may be a risk factor for mental health problems after bereavement, and it has therefore been suggested bereavement counseling should be tailored to income, no study to date has investigated the need for such tailoring. This controlled, longitudinal treatment study fills this gap in knowledge. Main findings are that low income is a key predictor of complicated grief symptoms. The study also shows that the effectiveness of one-to-one bereavement counseling does not appear to differ according to income level.

Effectiveness of bereavement counselling through a community-based organization: A naturalistic, controlled trial

This controlled, longitudinal investigation tested the effectiveness of a bereavement counselling model for adults on reducing complicated grief (CG) symptoms. Participants (N = 344; 79% female; mean age: 49.3 years) were adult residents of Scotland who were bereaved of a close relation or partner, experiencing elevated levels of CG, and/or risks of developing CG. It was hypothesized that participants who received intervention would experience a greater decline in CG levels immediately following the intervention compared to the control participants, but the difference would diminish at follow‐up (due to relapse). Data were collected via postal questionnaire at 3 time points: baseline (T), post‐intervention (T + 12 months), and follow‐up (T + 18 months). CG, post‐traumatic stress, and general psychological distress were assessed at all time points. Multilevel analyses controlling for relevant covariates were conducted to examine group differences in symptom levels over time. A stepwise, serial gatekeeping procedure was used to correct for multiple hypothesis testing. A main finding was that, contrary to expectations, counselling intervention and control group participants experienced a similar reduction in CG symptoms at postmeasure. However, intervention participants demonstrated a greater reduction in symptom levels at follow‐up (M = 53.64; d = .33) compared to the control group (M = 62.00). Results suggest community‐based bereavement counselling may have long‐term beneficial effects. Further longitudinal treatment effect investigations with extensive study intervals are needed.

How large are the consequences of covariate imbalance in cluster randomized trials: a simulation study with a continuous outcome and a binary covariate at the cluster level

BACKGROUND

The number of clusters in a cluster randomized trial is often low. It is therefore likely random assignment of clusters to treatment conditions results in covariate imbalance. There are no studies that quantify the consequences of covariate imbalance in cluster randomized trials on parameter and standard error bias and on power to detect treatment effects.

METHODS

The consequences of covariance imbalance in unadjusted and adjusted linear mixed models are investigated by means of a simulation study. The factors in this study are the degree of imbalance, the covariate effect size, the cluster size and the intraclass correlation coefficient. The covariate is binary and measured at the cluster level; the outcome is continuous and measured at the individual level.

RESULTS

The results show covariate imbalance results in negligible parameter bias and small standard error bias in adjusted linear mixed models. Ignoring the possibility of covariate imbalance while calculating the sample size at the cluster level may result in a loss in power of at most 25 % in the adjusted linear mixed model. The results are more severe for the unadjusted linear mixed model: parameter biases up to 100 % and standard error biases up to 200 % may be observed. Power levels based on the unadjusted linear mixed model are often too low. The consequences are most severe for large clusters and/or small intraclass correlation coefficients since then the required number of clusters to achieve a desired power level is smallest.

CONCLUSIONS

The possibility of covariate imbalance should be taken into account while calculating the sample size of a cluster randomized trial. Otherwise more sophisticated methods to randomize clusters to treatments should be used, such as stratification or balance algorithms. All relevant covariates should be carefully identified, be actually measured and included in the statistical model to avoid severe levels of parameter and standard error bias and insufficient power levels.

PTSD after childbirth: A predictive ethological model for symptom development

BACKGROUND

Childbirth can be a traumatic experience occasionally leading to posttraumatic stress disorder (PTSD). This study aimed to assess childbirth-related PTSD risk-factors using an etiological model inspired by the transactional model of stress and coping.

METHODS

348 out of 505 (70%) Dutch women completed questionnaires during pregnancy, one week postpartum, and three months postpartum. A further 284 (56%) also completed questionnaires ten months postpartum. The model was tested using path analysis.

RESULTS

Antenatal depressive symptoms (β=.15, p<.05), state anxiety (β=.17, p<.01), and perinatal psychoform (β=.17, p<.01) and somatoform (β=.17, p<.01) dissociation were identified as PTSD symptom risk factors three months postpartum. Antenatal depressive symptoms (β=.31, p<.001) and perinatal somatoform dissociation (β=.14, p<.05) predicted symptoms ten months postpartum.

LIMITATIONS

Almost a third of our sample was lost at three months postpartum, and 44% at ten months. The sample size was relatively small. The present study did not control for prior PTSD. The PTSD A criterion was not considered an exclusion criteria for model testing, and the fit index of the ten months model was just below suggested cut-off values.

CONCLUSIONS

Screening for high risk pregnant women should focus on antenatal depression, anxiety and dissociative tendencies. Hospital staff and midwives are advised to be vigilant for perinatal dissociation after intense negative emotions. To help regulate perinatal negative emotional responses, hospital staff and midwifes are recommended to provide information about birth procedures and be attentive to women's birth-related needs.

Optimal designs in longitudinal trials with varying treatment effects and discrete-time survival endpoints

It is plausible to assume that the treatment effect in a longitudinal study will vary over time. It can become either stronger or weaker as time goes on. Here, we extend previous work on optimal designs for discrete-time survival analysis to trials with the treatment effect varying over time. In discrete-time survival analysis, subjects are measured in discrete time intervals, while they may experience the event at any point in time. We focus on studies where the width of time intervals is fixed beforehand, meaning that subjects are measured more often when the study duration increases. The optimal design is defined as the optimal combination of the number of subjects, the number of measurements for each subject, and the optimal proportion of subjects assigned to the experimental condition. We study optimal designs for different optimality criteria and linear cost functions. We illustrate the methodology of finding optimal designs using a clinical trial that studies the effect of an outpatient mental health program on reducing substance abuse among patients with severe mental illness. We observe that optimal designs depend to some extent on the rate at which group differences vary across time intervals and the direction of these changes over time. We conclude that an optimal design based on the assumption of a constant treatment effect is not likely to be efficient if the treatment effect varies across time.

Optimal treatment allocation for placebo-treatment comparisons in trials with discrete-time survival endpoints

In many randomized controlled trials, treatment groups are of equal size, but this is not necessarily the best choice. This paper provides a methodology to calculate optimal treatment allocations for longitudinal trials when we wish to compare multiple treatment groups with a placebo group, and the comparisons may have unequal importance. The focus is on trials with a survival endpoint measured in discrete time. We assume the underlying survival process is Weibull and show that values for the parameters in the Weibull distribution have an impact on the optimal treatment allocation scheme in an interesting way. Additionally, we incorporate different cost considerations at the subject and measurement levels and determine the optimal number of time periods. We also show that when many events occur at the beginning of the trial, fewer time periods are more efficient. As an application, we revisit a risperidone maintenance treatment trial in schizophrenia and use our proposed methodology to redesign it and compare merits of our optimal design.

The Effect of Discretizing Survival Times in Randomized Controlled Trials

The aim of survival analysis is to study if and when some event occurs. With continuous-time analysis subjects are followed until the time they experience the event or drop out. In practice, subjects cannot always be followed continuously and event occurrence is measured in time periods. This type of survival analysis is known as discrete-time survival analysis and measuring subjects discretely rather than continuously results in a loss of information. The aim of this paper is to study the effects of discretizing survival times for randomized controlled trials by means of a simulation study. It is shown that parameter and standard error biases of both approaches are small and those of the discrete-time approach are only slightly larger than those of the continuous-time approach. The number of time periods has a negligible effect on bias. Power levels hardly differ across the two approaches, so following subjects continuously is not necessary, except when a detailed estimate of the underlying baseline hazard function is needed.

A simulation study of sample size demonstrated the importance of the number of events per variable to develop prediction models in clustered data

OBJECTIVES

This study aims to investigate the influence of the amount of clustering [intraclass correlation (ICC) = 0%, 5%, or 20%], the number of events per variable (EPV) or candidate predictor (EPV = 5, 10, 20, or 50), and backward variable selection on the performance of prediction models.

STUDY DESIGN AND SETTING

Researchers frequently combine data from several centers to develop clinical prediction models. In our simulation study, we developed models from clustered training data using multilevel logistic regression and validated them in external data.

RESULTS

The amount of clustering was not meaningfully associated with the models' predictive performance. The median calibration slope of models built in samples with EPV = 5 and strong clustering (ICC = 20%) was 0.71. With EPV = 5 and ICC = 0%, it was 0.72. A higher EPV related to an increased performance: the calibration slope was 0.85 at EPV = 10 and ICC = 20% and 0.96 at EPV = 50 and ICC = 20%. Variable selection sometimes led to a substantial relative bias in the estimated predictor effects (up to 118% at EPV = 5), but this had little influence on the model's performance in our simulations.

CONCLUSION

We recommend at least 10 EPV to fit prediction models in clustered data using logistic regression. Up to 50 EPV may be needed when variable selection is performed.

Analyzing indirect effects in cluster randomized trials. The effect of estimation method, number of groups and group sizes on accuracy and power

Cluster randomized trials assess the effect of an intervention that is carried out at the group or cluster level. Ajzen's theory of planned behavior is often used to model the effect of the intervention as an indirect effect mediated in turn by attitude, norms and behavioral intention. Structural equation modeling (SEM) is the technique of choice to estimate indirect effects and their significance. However, this is a large sample technique, and its application in a cluster randomized trial assumes a relatively large number of clusters. In practice, the number of clusters in these studies tends to be relatively small, e.g., much less than fifty. This study uses simulation methods to find the lowest number of clusters needed when multilevel SEM is used to estimate the indirect effect. Maximum likelihood estimation is compared to Bayesian analysis, with the central quality criteria being accuracy of the point estimate and the confidence interval. We also investigate the power of the test for the indirect effect. We conclude that Bayes estimation works well with much smaller cluster level sample sizes such as 20 cases than maximum likelihood estimation; although the bias is larger the coverage is much better. When only 5–10 clusters are available per treatment condition even with Bayesian estimation problems occur.

PODSE: a computer program for optimal design of trials with discrete-time survival endpoints

In experimental settings, one or more groups of subjects receive a treatment and they are compared to a group of subjects that receives a standard treatment or no treatment at all. These compared groups might have an equal number of subjects or some of the groups might have more participants relative to the other groups. Moreover, subjects in these groups can be followed over a short or a long period. To conduct experiments in a sufficient way, researchers should find a good design in the planning phase of the trial. The optimal design for experimental studies on event occurrence with discrete-time survival endpoints where two treatment groups are followed over time, is an optimal combination of the number of time periods, the total number of participants in the trial and the proportion of subjects in the experimental group. It is easy to find the best design for such studies using the PODSE program.

Optimal Designs for Event History Analysis

The aim of event history analysis is to study the occurrence and timing of events, such as premature psychotherapy termination or drinking onset, and to relate the probability of event occurrence to relevant covariates. In the social sciences, the timing of the event is often measured discretely by using time intervals, which implies the exact timing of event occurrence is unknown. The optimal number of subjects and time intervals need to be decided upon in the design stage of a trial with discrete-time survival endpoints. This paper shows how the optimal design depends on the underlying survival function and the costs to include a subject relative to the costs to take a measurement. Furthermore, the effects of attrition on the optimal design are studied. An example on drinking onset illustrates the proposed methodology.

Accrual by groups in trials with discrete-time survival endpoints

BACKGROUND

In many fields of science, event status is often recorded in intervals or at discrete points in time and can be investigated in experimental settings. Conducting such trials requires thorough planning before they are actually performed.

PURPOSE

To investigate accrual by groups in a trial with discrete-time survival endpoints and to describe how to choose the number of accrual groups, the size of the accrual groups, and the duration of the trial to achieve a sufficient power level.

METHODS

In trials with multiple time periods, the event status is recorded at the end of each period, but the event may occur at any time between the time points the measurements are taken. Therefore, time is recorded discretely, but the underlying process is continuous. To find the risk of event occurrence in each time interval, a continuous-time survival function is used and the generalized linear model is applied.

RESULTS

It is observed that the combination of the number of accrual groups, the size of the accrual groups, and the duration of the trial that gives a sufficient power level depends on the shape of the continuous-time survival function, the proportion of subjects who have experienced the event after a fixed number of time periods, and the size of the treatment effect.

LIMITATIONS

The results of the study are only presented graphically, because there is no simple closed-form expression for finding the variance of the treatment effect. The authors provide MATLAB software to perform the power calculations.

CONCLUSIONS

More subjects should be recruited in each accrual group or more accrual groups should be included if the effect size or the proportion of the subjects who have experienced the event after a fixed number of time periods decreases, or the probability of the event occurrence is concentrated toward the end of the study duration.

Sample Size Issues for Cluster Randomized Trials With Discrete-Time Survival Endpoints

With cluster randomized trials complete groups of subjects are randomized to treatment conditions. An important question might be whether and when the subjects experience a particular event, such as smoking initiation or recovery from disease. In the social sciences the timing of such events is often measured in discrete time by using time intervals. At the planning phase of a cluster randomized trial one should decide on the number of clusters and cluster size such that parameters are estimated accurately and sufficient power on the test on treatment effect is achieved. On basis of a simulation study it is concluded that regression coefficients are estimated more accurately than the variance of the random cluster effect. In addition, it is shown that power increases with cluster size and number of clusters, and that a sufficient power cannot always be achieved by using larger cluster sizes at a fixed number of clusters.