When studies use different scales to measure continuous outcomes, standardised mean differences (SMD) are required to meta-analyse the data. However, outcomes are often reported as endpoint or change from baseline scores. Combining corresponding SMDs can be problematic and available guidance advises against this practice. We aimed to examine the impact of combining the two types of SMD in meta-analyses of depression severity. We used individual participant data on pharmacological interventions (89 studies, 27,409 participants) and internet-delivered cognitive behavioural therapy (iCBT; 61 studies, 13,687 participants) for depression to compare endpoint and change from baseline SMDs at the study level. Next, we performed pairwise (PWMA) and network meta-analyses (NMA) using endpoint SMDs, change from baseline SMDs, or a mixture of the two. Study-specific SMDs calculated from endpoint and change from baseline data were largely similar, although for iCBT interventions 25% of the studies at 3 months were associated with important differences between study-specific SMDs (median 0.01, IQR -0.10, 0.13) especially in smaller trials with baseline imbalances. However, when pooled, the differences between endpoint and change SMDs were negligible. Pooling only the more favourable of the two SMDs did not materially affect meta-analyses, resulting in differences of pooled SMDs up to 0.05 and 0.13 in the pharmacological and iCBT datasets, respectively. Our findings have implications for meta-analyses in depression, where we showed that the choice between endpoint and change scores for estimating SMDs had immaterial impact on summary meta-analytic estimates. Future studies should replicate and extend our analyses to fields other than depression.

UNASSIGNED: Heterogeneous outcome correlations across treatment arms and clusters have been increasingly acknowledged in cluster randomized trials with binary endpoints, where analytical methods have been developed to study such heterogeneity. However, cluster-specific outcome variances and correlations have yet to be studied for cluster randomized trials with continuous outcomes.
UNASSIGNED: This article proposes models fitted in the Bayesian setting with hierarchical variance structure to quantify heterogeneous variances across clusters and explain it with cluster-level covariates when the outcome is continuous. The models can also be extended to analyzing heterogeneous variances in individually randomized group treatment trials, with arm-specific cluster-level covariates, or in partially nested designs. Simulation studies are carried out to validate the performance of the newly introduced models across different settings.
UNASSIGNED: Simulations showed that overall the newly introduced models have good performance, reporting low bias and approximately 95% coverage for the intraclass correlation coefficients and regression parameters in the variance model. When variances are heterogeneous, our proposed models had improved model fit over models with homogeneous variances. When used to analyze data from the Kerala Diabetes Prevention Program study, our models identified heterogeneous variances and intraclass correlation coefficients across clusters and examined cluster-level characteristics associated with such heterogeneity.
UNASSIGNED: We proposed new hierarchical Bayesian variance models to accommodate cluster-specific variances in cluster randomized trials. The newly developed methods inform the understanding of how an intervention strategy is implemented and disseminated differently across clusters and can help improve future trial design.

Since the era of evidence-based medicine, it has become a matter of course to use statistics to create objective evidence in clinical research. As an extension of this, it has become essential in clinical research to calculate the correct sample size to demonstrate a clinically significant difference before starting the study. Also, because sample size calculation methods vary from study design to study design, there is no formula for sample size calculation that applies to all designs. It is very important for us to understand this. In this review, each sample size calculation method suitable for various study designs was introduced using the R program (R Foundation for Statistical Computing). In order for clinical researchers to directly utilize it according to future research, we presented practice codes, output results, and interpretation of results for each situation.

OBJECTIVE: The standardized mean difference (SMD) can be calculated from different mean differences (MDs) and standard deviations (SDs). This study aims to investigate how clinical trials calculated, reported and interpreted the SMD, and to examine the variation between different SMDs.
METHODS: We searched the PubMed for randomized controlled trials of general medicine and psychiatry that estimated SMDs. We explored how the SMD was computed and interpreted. We calculated SMDs based on different MDs and SDs, and the variation in these SMD estimates for each study.
RESULTS: We included 161 articles. Various MDs and SDs were used to calculate SMDs, yet 69.0% studies failed to provide sufficient details. Variations in SMD estimates using different MDs and SDs in one study could be substantial (median of the absolute differences was 0.3, interquartile range IQR 0.17 to 0.53). However, 68.3% studies interpreted the SMD based on the same reference, Cohen\'s rule of thumb. The largest variations were observed in studies with small sample sizes and large reported effects.
CONCLUSIONS: SMDs using different MDs and SDs could vary considerably, but the report was often insufficient and the interpretation was oversimplified. To avoid selective reporting bias and misinterpretation, prespecifying and reporting the method and interpreting the result from multiple perspectives are desirable.

UNASSIGNED: In non-randomized studies (NRSs) where a continuous outcome variable (e.g., depressive symptoms) is assessed at baseline and follow-up, it is common to observe imbalance of the baseline values between the treatment/exposure group and control group. This may bias the study and consequently a meta-analysis (MA) estimate. These estimates may differ across statistical methods used to deal with this issue. Analysis of individual participant data (IPD) allows standardization of methods across studies. We aimed to identify methods used in published IPD-MAs of NRSs for continuous outcomes, and to compare different methods to account for baseline values of outcome variables in IPD-MA of NRSs using two empirical examples from the Thyroid Studies Collaboration (TSC).
UNASSIGNED: For the first aim we systematically searched in MEDLINE, EMBASE, and Cochrane from inception to February 2021 to identify published IPD-MAs of NRSs that adjusted for baseline outcome measures in the analysis of continuous outcomes. For the second aim, we applied analysis of covariance (ANCOVA), change score, propensity score and the naïve approach (ignores the baseline outcome data) in IPD-MA from NRSs on the association between subclinical hyperthyroidism and depressive symptoms and renal function. We estimated the study and meta-analytic mean difference (MD) and relative standard error (SE). We used both fixed- and random-effects MA.
UNASSIGNED: Ten of 18 (56%) of the included studies used the change score method, seven (39%) studies used ANCOVA and one the propensity score (5%). The study estimates were similar across the methods in studies in which groups were balanced at baseline with regard to outcome variables but differed in studies with baseline imbalance. In our empirical examples, ANCOVA and change score showed study results on the same direction, not the propensity score. In our applications, ANCOVA provided more precise estimates, both at study and meta-analytical level, in comparison to other methods. Heterogeneity was higher when change score was used as outcome, moderate for ANCOVA and null with the propensity score.
UNASSIGNED: ANCOVA provided the most precise estimates at both study and meta-analytic level and thus seems preferable in the meta-analysis of IPD from non-randomized studies. For the studies that were well-balanced between groups, change score, and ANCOVA performed similarly.

Appropriate handling of aggregate missing outcome data is necessary to minimise bias in the conclusions of systematic reviews. The two-stage pattern-mixture model has been already proposed to address aggregate missing continuous outcome data. While this approach is more proper compared with the exclusion of missing continuous outcome data and simple imputation methods, it does not offer flexible modelling of missing continuous outcome data to investigate their implications on the conclusions thoroughly. Therefore, we propose a one-stage pattern-mixture model approach under the Bayesian framework to address missing continuous outcome data in a network of interventions and gain knowledge about the missingness process in different trials and interventions. We extend the hierarchical network meta-analysis model for one aggregate continuous outcome to incorporate a missingness parameter that measures the departure from the missing at random assumption. We consider various effect size estimates for continuous data, and two informative missingness parameters, the informative missingness difference of means and the informative missingness ratio of means. We incorporate our prior belief about the missingness parameters while allowing for several possibilities of prior structures to account for the fact that the missingness process may differ in the network. The method is exemplified in two networks from published reviews comprising a different amount of missing continuous outcome data.

Power analysis is a key component for planning prospective studies such as clinical trials. However, some journals in biomedical and psychosocial sciences ask for power analysis for data already collected and analysed before accepting manuscripts for publication. In this report, post hoc power analysis for retrospective studies is examined and the informativeness of understanding the power for detecting significant effects of the results analysed, using the same data on which the power analysis is based, is scrutinised. Monte Carlo simulation is used to investigate the performance of posthoc power analysis.

The rank-ordered logit (rologit) model was recently introduced as a robust approach for analysing continuous outcomes, with the linear exposure effect estimated by scaling the rank-based log-odds estimate. Here we extend the application of the rologit model to continuous outcomes with ties and ordinal outcomes treated as imperfectly-observed continuous outcomes. By identifying the functional relationship between survival times and continuous outcomes, we explicitly establish the equivalence between the rologit and Cox models to justify the use of the Breslow, Efron and perturbation methods in the analysis of continuous outcomes with ties. Using simulation, we found all three methods perform well with few ties. Although an increasing extent of ties increased the bias of the log-odds and linear effect estimates and resulted in reduced power, which was somewhat worse when the model was mis-specified, the perturbation method maintained a type I error around 5%, while the Efron method became conservative with heavy ties but outperformed Breslow. In general, the perturbation method had the highest power, followed by the Efron and then the Breslow method. We applied our approach to three real-life datasets, demonstrating a seamless analytical workflow that uses stratification for confounder adjustment in studies of continuous and ordinal outcomes.

In the medical literature, hundreds of prediction models are being developed to predict health outcomes in individuals. For continuous outcomes, typically a linear regression model is developed to predict an individual\'s outcome value conditional on values of multiple predictors (covariates). To improve model development and reduce the potential for overfitting, a suitable sample size is required in terms of the number of subjects (n) relative to the number of predictor parameters (p) for potential inclusion. We propose that the minimum value of n should meet the following four key criteria: (i) small optimism in predictor effect estimates as defined by a global shrinkage factor of ≥0.9; (ii) small absolute difference of ≤ 0.05 in the apparent and adjusted R2 ; (iii) precise estimation (a margin of error ≤ 10% of the true value) of the model\'s residual standard deviation; and similarly, (iv) precise estimation of the mean predicted outcome value (model intercept). The criteria require prespecification of the user\'s chosen p and the model\'s anticipated R2 as informed by previous studies. The value of n that meets all four criteria provides the minimum sample size required for model development. In an applied example, a new model to predict lung function in African-American women using 25 predictor parameters requires at least 918 subjects to meet all criteria, corresponding to at least 36.7 subjects per predictor parameter. Even larger sample sizes may be needed to additionally ensure precise estimates of key predictor effects, especially when important categorical predictors have low prevalence in certain categories.

Sample size justification is required for all clinical studies. However, to many biomedical and clinical researchers, power and sample size analysis seems like a magic trick of statisticians. In this note, we discuss power and sample size calculations and show that biomedical and clinical investigators play a significant role in making such analyses possible and meaningful. Thus, power analysis is really an interactive process and scientific researchers and statisticians are equal partners in the research enterprise.
所有的临床研究都需要对样本量进行辨证。然 而，对于众多生物医学和临床研究人员来说，把握度 和样本量看起来就像一个统计学家的魔术。在本文中， 我们讨论了把握度和样本量的计算，并说明生物医学 和临床研究人员在该分析的可行性和意义中具有重要 作用。因此，把握度分析的确是一个互动的过程，并 且科学研究人员和统计人员在研究团队中是平等合作 的伙伴。.