Reflection on modern methods: Calculating a sample size for a repeatability sub-study to correct for measurement error in a single continuous exposure

Using a continuous exposure variable that is measured with random error in a univariable linear regression model leads to regression dilution bias: the observed association between the exposure and outcome is smaller than it would be if the true value of the exposure could be used. A repeatability sub-study, where a sample of study participants have their data measured again, can be used to correct for this bias. It is important to perform a sample size calculation for such a sub-study, to ensure that correction factors can be estimated with sufficient precision. We describe how a previously published method can be used to calculate the sample size from the anticipated size of the correction factor and its desired precision, and demonstrate this approach using the example of the cross-sectional studies conducted as part of the International Project on Cardiovascular Disease in Russia study. We also provide correction factors calculated from repeat data from the UK Biobank study, which can be used to help plan future repeatability studies

Increasing the Availability of Psychological Treatments: A Multinational Study of a Scalable Method for Training Therapists.

BACKGROUND: One of the major barriers to the dissemination and implementation of psychological treatments is the scarcity of suitably trained therapists. A highly scalable form of Web-centered therapist training, undertaken without external support, has recently been shown to have promise in promoting therapist competence. OBJECTIVE: The aim of this study was to conduct an evaluation of the acceptability and effectiveness of a scalable independent form of Web-centered training in a multinational sample of therapists and investigate the characteristics of those most likely to benefit. METHODS: A cohort of eligible therapists was recruited internationally and offered access to Web-centered training in enhanced cognitive behavioral therapy, a multicomponent, evidence-based, psychological treatment for any form of eating disorder. No external support was provided during training. Therapist competence was assessed using a validated competence measure before training and after 20 weeks. RESULTS: A total of 806 therapists from 33 different countries expressed interest in the study, and 765 (94.9%) completed a pretraining assessment. The median number of training modules completed was 15 out of a possible 18 (interquartile range, IQR: 4-18), and 87.9% (531/604) reported that they treated at least one patient during training as recommended. Median pretraining competence score was 7 (IQR: 5-10, range: 0-19; N=765), and following training, it was 12 (IQR: 9-15, range: 0-20; N=577). The expected change in competence scores from pretraining to posttraining was 3.5 (95% CI 3.1-3.8; P<.001). After training, 52% (300/574) of therapists with complete competence data met or exceeded the competence threshold, and 45% (95% CI 41-50) of those who had not met this threshold before training did so after training. Compliance with training predicted both an increase in competence scores and meeting or exceeding the competence threshold. Expected change in competence score increased for each extra training module completed (0.19, 95% CI 0.13-0.25), and those who treated a suitable patient during training had an expected change in competence score 1.2 (95% CI 0.4-2.1) points higher than those who did not. Similarly, there was an association between meeting the competence threshold after training and the number of modules completed (odds ratio, OR=1.11, 95% CI 1.07-1.15), and treating at least one patient during training was associated with competence after training (OR=2.2, 95% CI 1.2-4.1). CONCLUSIONS: Independent Web-centered training can successfully train large numbers of therapists dispersed across a wide geographical area. This finding is of importance because the availability of a highly scalable method of training potentially increases the number of people who might receive effective psychological treatments

Applying the estimands framework to non-inferiority trials: guidance on choice of hypothetical estimands for non-adherence and comparison of estimation methods

A common concern in non-inferiority (NI) trials is that non adherence due, for example, to poor study conduct can make treatment arms artificially similar. Because intention to treat analyses can be anti-conservative in this situation, per protocol analyses are sometimes recommended. However, such advice does not consider the estimands framework, nor the risk of bias from per protocol analyses. We therefore sought to update the above guidance using the estimands framework, and compare estimators to improve on the performance of per protocol analyses. We argue the main threat to validity of NI trials is the occurrence of trial specific intercurrent events (IEs), that is, IEs which occur in a trial setting, but would not occur in practice. To guard against erroneous conclusions of non inferiority, we suggest an estimand using a hypothetical strategy for trial specific IEs should be employed, with handling of other non trial specific IEs chosen based on clinical considerations. We provide an overview of estimators that could be used to estimate a hypothetical estimand, including inverse probability weighting (IPW), and two instrumental variable approaches (one using an informative Bayesian prior on the effect of standard treatment, and one using a treatment by covariate interaction as an instrument). We compare them, using simulation in the setting of all or nothing compliance in two active treatment arms, and conclude both IPW and the instrumental variable method using a Bayesian prior are potentially useful approaches, with the choice between them depending on which assumptions are most plausible for a given trial

Power and sample-size calculations for trials that compare slopes over time: Introducing the slopepower command.

Trials of interventions that aim to slow disease progression may analyze a continuous outcome by comparing its change over time—its slope—between the treated and the untreated group using a linear mixed model. To perform a sample-size calculation for such a trial, one must have estimates of the parameters that govern the between- and within-subject variability in the outcome, which are often unknown. The algebra needed for the sample-size calculation can also be complex for such trial designs. We have written a new user-friendly command, slopepower, that performs sample-size or power calculations for trials that compare slope outcomes. The package is based on linear mixed-model methodology, described for this setting by Frost, Kenward, and Fox (2008, Statistics in Medicine 27: 3717–3731). In the first stage of this approach, slopepower obtains estimates of mean slopes together with variances and covariances from a linear mixed model fit to previously collected user-supplied data. In the second stage, these estimates are combined with user input about the target effectiveness of the treatment and design of the future trial to give an estimate of either a sample size or a statistical power. In this article, we present the slopepower command, briefly explain the methodology behind it, and demonstrate how it can be used to help plan a trial and compare the sample sizes needed for different trial designs

Using the Internet to Train Therapists: Randomized Comparison of Two Scalable Methods.

BACKGROUND: One of the major barriers to the dissemination and implementation of psychological treatments is the scarcity of suitably trained therapists. The currently accepted method of training is not scalable. Recently, a scalable form of training, Web-centered training, has been shown to have promise. OBJECTIVE: The goal of our research was to conduct a randomized comparison of the relative effects of independent and supported Web-centered training on therapist competence and investigate the persistence of the effects. METHODS: Eligible therapists were recruited from across the United States and Canada. They were randomly assigned to 1 of 2 forms of training in enhanced cognitive behavior therapy (CBT-E), a multicomponent evidence-based psychological treatment for any form of eating disorder. Independent training was undertaken autonomously, while supported training was accompanied by support from a nonspecialist worker. Therapist competence was assessed using a validated competence measure before training, after 20 weeks of training, and 6 months after the completion of training. RESULTS: A total of 160 therapists expressed interest in the study, and 156 (97.5%) were randomized to the 2 forms of training (81 to supported training and 75 to independent training). Mixed effects analysis showed an increase in competence scores in both groups. There was no difference between the 2 forms of training, with mean difference for the supported versus independent group being -0.06 (95% Cl -1.29 to 1.16, P=.92). A total of 58 participants (58/114, 50.9%) scored above the competence threshold; three-quarters (43/58, 74%) had not met this threshold before training. There was no difference between the 2 groups in the odds of scoring over the competence threshold (odds ratio [OR] 1.02, 95% CI 0.52 to 1.99; P=.96). At follow-up, there was no significant difference between the 2 training groups (mean difference 0.19, 95% Cl -1.27 to 1.66, P=.80). Overall, change in competence score from end of training to follow-up was not significant (mean difference -0.70, 95% CI -1.52 to 0.11, P=.09). There was also no difference at follow-up between the training groups in the odds of scoring over the competence threshold (OR 0.95, 95% Cl 0.34 to 2.62; P=.92). CONCLUSIONS: Web-centered training was equally effective whether undertaken independently or accompanied by support, and its effects were sustained. The independent form of Web-centered training is particularly attractive as it provides a means of training large numbers of geographically dispersed therapists at low cost, thereby overcoming several obstacles to the widespread dissemination of psychological treatments

Cluster randomized trials with a small number of clusters: which analyses should be used?

BACKGROUND: Cluster randomized trials (CRTs) are increasingly used to assess the effectiveness of health interventions. Three main analysis approaches are: cluster-level analyses, mixed-models and generalized estimating equations (GEEs). Mixed models and GEEs can lead to inflated type I error rates with a small number of clusters, and numerous small-sample corrections have been proposed to circumvent this problem. However, the impact of these methods on power is still unclear. METHODS: We performed a simulation study to assess the performance of 12 analysis approaches for CRTs with a continuous outcome and 40 or fewer clusters. These included weighted and unweighted cluster-level analyses, mixed-effects models with different degree-of-freedom corrections, and GEEs with and without a small-sample correction. We assessed these approaches across different values of the intraclass correlation coefficient (ICC), numbers of clusters and variability in cluster sizes. RESULTS: Unweighted and variance-weighted cluster-level analysis, mixed models with degree-of-freedom corrections, and GEE with a small-sample correction all maintained the type I error rate at or below 5% across most scenarios, whereas uncorrected approaches lead to inflated type I error rates. However, these analyses had low power (below 50% in some scenarios) when fewer than 20 clusters were randomized, with none reaching the expected 80% power. CONCLUSIONS: Small-sample corrections or variance-weighted cluster-level analyses are recommended for the analysis of continuous outcomes in CRTs with a small number of clusters. The use of these corrections should be incorporated into the sample size calculation to prevent studies from being underpowered

The association between anthropometric measures of adiposity and the progression of carotid atherosclerosis.

BACKGROUND: Few reports are available on the contribution of general and abdominal obesity to the progression of carotid atherosclerosis in late adulthood. This study investigated the impact of four simple anthropometric measures of general and abdominal obesity on the progression of carotid atherosclerosis and the extent to which the association between adiposity and the progression of plaque burden is mediated by cardiometabolic markers. METHODS: Four thousand three hundred forty-five adults (median age 60) from the population-based Tromsø Study were followed over 7 years from the first carotid ultrasound screening to the next. The progression of carotid atherosclerosis was measured in three ways: incidence of plaques in previously plaque-free participants; change in the number of plaques; and total plaque area (TPA). We used generalised linear models to investigate the association between each adiposity measure - body mass index (BMI), waist circumference (WC), waist-to-hip ratio (WHR), and waist-to-height ratio (WHtR) - and each outcome. Models were adjusted for potential confounders (age, sex, smoking, education, physical activity). The pathways through which any associations observed might operate were investigated by further adjusting for cardiometabolic mediators (systolic blood pressure, cholesterol, and HbA1c). RESULTS: There was little evidence that adiposity was related to the formation of new plaques during follow-up. However, abdominal adiposity was associated with TPA progression. WHtR showed the largest effect size (mean change in TPA per one standard deviation (SD) increase in WHtR of 0.665 mm2, 95% confidence interval 0.198, 1.133) while BMI showed the smallest. Effect sizes were substantially reduced after the adjustment for potential mediators. CONCLUSIONS: Abdominal obesity indirectly measured with WC seems more strongly associated with the progression of TPA than general obesity. These associations appear to be largely mediated by known cardiometabolic markers

A comparison of a structured home-based rehabilitation programme with conventional supervised pulmonary rehabilitation:A randomised non-inferiority trial

Background: Standardised home-based pulmonary rehabilitation (PR) programmes offer an alternative model to centre-based supervised PR for which uptake is currently poor. We determined if a structured home-based unsupervised PR programme was non-inferior to supervised centre-based PR for participants with COPD. Methods: A total of 287 participants with COPD who were referred to PR (187 male, mean (SD) age 68 (8.86) years, FEV1% predicted 48.34 (17.92)) were recruited. They were randomised to either centre-based PR or a structured unsupervised home-based PR programme including a hospital visit with a healthcare professional trained in motivational interviewing, a self-management manual and two telephone calls. Fifty-eight (20%) withdrew from the centre-based group and 51 (18%) from the home group. The primary outcome was dyspnoea domain in the chronic respiratory disease questionnaire (Chronic Respiratory Questionnaire Self-Report; CRQ-SR) at 7 weeks. Measures were taken blinded. We undertook a modified intention-to-treat (mITT) complete case analysis, comparing groups according to original random allocation and with complete data at follow-up. The non-inferiority margin was 0.5 units. Results: There was evidence of significant gains in CRQ-dyspnoea at 7 weeks in both home and centre-based groups. There was inconclusive evidence that home-based PR was non-inferior to PR in dyspnoea (mean group difference, mITT: −0.24, 95% CI −0.61 to 0.12, p=0.18), favouring the centre group at 7 weeks. Conclusions: The standardised home-based programme provides benefits in dyspnoea. Further evidence is needed to definitively determine if the health benefits of the standardised home-based programme are non-inferior or equivalent to supervised centre-based rehabilitation

Effect of crustal stress state on magmatic stalling and ascent: case study from Puyehue-Cordón Caulle, Chile

AbstractThe Southern Volcanic Zone (SVZ) in Chile is an active continental arc with a complex history of volcanism, where a range of magmatic compositions have been erupted in a variety of styles. In the Central SVZ, both monogenetic and polygenetic volcanoes exist, in close proximity to the Liquiñe-Ofqui Fault System (LOFS), but with variable local stress states. Previous studies have inferred varying crustal storage timescales, controlled by the orientation of volcanic centres relative to the N-S striking LOFS and σHMax in this region. To assess the relationship between volcanism and crustal stress states affected by large-scale tectonic structures and edifice controls, we present whole rock geochemical data, to ensure consistency in source dynamics and crustal processing, mineral-specific compositional data, thermobarometry, and Fe–Mg diffusion modelling in olivine crystals from mafic lavas, to assess ascent timescales, from the stratovolcanic edifice of Puyehue-Cordón Caulle and proximal small eruptive centres. Textural observations highlight differences in crystal maturation timescales between centres in inferred compression, transpression, and extension, yet source melting dynamics remain constant. Only samples from the stratovolcanic edifice (in regional compression) preserve extensive zonation in olivine macrocrysts; these textures are generally absent from proximal small eruptive centres in transtension or extension. The zonation in olivines from stratovolcanic lavas yields timescales on the order of a few days to a few weeks, suggesting that even in environments which inhibit ascent, timescales between unrest and eruption of mafic magmas may be short. Significantly, high-resolution compositional profiles from olivine grains in the studied samples record evidence for post-eruptive growth and diffusion, highlighting the importance of careful interpretation of diffusion timescales from zoned minerals in more slowly cooled lavas when compared with tephra samples.</jats:p

Effect of crustal stress state on magmatic stalling and ascent: case study from Puyehue-Cordón Caulle, Chile

The Southern Volcanic Zone (SVZ) in Chile is an active continental arc with a complex history of volcanism, where a range of magmatic compositions have been erupted in a variety of styles. In the Central SVZ, both monogenetic and polygenetic volcanoes exist, in close proximity to the Liquiñe-Ofqui Fault System (LOFS), but with variable local stress states. Previous studies have inferred varying crustal storage timescales, controlled by the orientation of volcanic centres relative to the N-S striking LOFS and σHMax in this region. To assess the relationship between volcanism and crustal stress states affected by large-scale tectonic structures and edifice controls, we present whole rock geochemical data, to ensure consistency in source dynamics and crustal processing, mineral-specific compositional data, thermobarometry, and Fe–Mg diffusion modelling in olivine crystals from mafic lavas, to assess ascent timescales, from the stratovolcanic edifice of Puyehue-Cordón Caulle and proximal small eruptive centres. Textural observations highlight differences in crystal maturation timescales between centres in inferred compression, transpression, and extension, yet source melting dynamics remain constant. Only samples from the stratovolcanic edifice (in regional compression) preserve extensive zonation in olivine macrocrysts; these textures are generally absent from proximal small eruptive centres in transtension or extension. The zonation in olivines from stratovolcanic lavas yields timescales on the order of a few days to a few weeks, suggesting that even in environments which inhibit ascent, timescales between unrest and eruption of mafic magmas may be short. Significantly, high-resolution compositional profiles from olivine grains in the studied samples record evidence for post-eruptive growth and diffusion, highlighting the importance of careful interpretation of diffusion timescales from zoned minerals in more slowly cooled lavas when compared with tephra samples