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Background: The concept of the population is of fundamental importance in epidemiology and statistics. In some instances, it is not possible to sample directly from the population of interest. Weighting is an established statistical approach for making inferences when the sample is not representative of this population. Methods: The effective sample size (ESS) is a descriptive statistic that can be used to accompany this type of weighted statistical analysis. The ESS is an estimate of the sample size required by an unweighted sample that achieves the same level of precision as the weighted sample. The ESS therefore reflects the amount of information retained after weighting the data and is an intuitively appealing quantity to interpret, for example by those with little or no statistical training. Results: The conventional formula for calculating ESS is derived under strong assumptions, for example that outcome data are homoscedastic. This is not always true in practice, for example for survival data. We propose three new approaches to compute the ESS, that are valid for any type of data and weighted statistical analysis, and so can be applied more generally. Conclusion: We illustrate all methods using an example and conclude that our proposals should accompany, and potentially replace, the existing approach for computing the ESS. [ABSTRACT FROM AUTHOR]

Abstract Background The concept of the population is of fundamental importance in epidemiology and statistics. In some instances, it is not possible to sample directly from the population of interest. Weighting is an established statistical approach for making inferences when the sample is not representative of this population. Methods The effective sample size (ESS) is a descriptive statistic that can be used to accompany this type of weighted statistical analysis. The ESS is an estimate of the sample size required by an unweighted sample that achieves the same level of precision as the weighted sample. The ESS therefore reflects the amount of information retained after weighting the data and is an intuitively appealing quantity to interpret, for example by those with little or no statistical training. Results The conventional formula for calculating ESS is derived under strong assumptions, for example that outcome data are homoscedastic. This is not always true in practice, for example for survival data. We propose three new approaches to compute the ESS, that are valid for any type of data and weighted statistical analysis, and so can be applied more generally. Conclusion We illustrate all methods using an example and conclude that our proposals should accompany, and potentially replace, the existing approach for computing the ESS.

Abstract Background When studying the association between treatment and a clinical outcome, a parametric multivariable model of the conditional outcome expectation is often used to adjust for covariates. The treatment coefficient of the outcome model targets a conditional treatment effect. Model-based standardization is typically applied to average the model predictions over the target covariate distribution, and generate a covariate-adjusted estimate of the marginal treatment effect. Methods The standard approach to model-based standardization involves maximum-likelihood estimation and use of the non-parametric bootstrap. We introduce a novel, general-purpose, model-based standardization method based on multiple imputation that is easily applicable when the outcome model is a generalized linear model. We term our proposed approach multiple imputation marginalization (MIM). MIM consists of two main stages: the generation of synthetic datasets and their analysis. MIM accommodates a Bayesian statistical framework, which naturally allows for the principled propagation of uncertainty, integrates the analysis into a probabilistic framework, and allows for the incorporation of prior evidence. Results We conduct a simulation study to benchmark the finite-sample performance of MIM in conjunction with a parametric outcome model. The simulations provide proof-of-principle in scenarios with binary outcomes, continuous-valued covariates, a logistic outcome model and the marginal log odds ratio as the target effect measure. When parametric modeling assumptions hold, MIM yields unbiased estimation in the target covariate distribution, valid coverage rates, and similar precision and efficiency than the standard approach to model-based standardization. Conclusion We demonstrate that multiple imputation can be used to marginalize over a target covariate distribution, providing appropriate inference with a correctly specified parametric outcome model and offering statistical performance comparable to that of the standard approach to model-based standardization.

Systematic reviews and meta-analyses play a crucial role in clinical research by providing a means of evaluating the effectiveness of interventions in situations of uncertainty. Pairwise meta-analysis, which is the most widely used method, compares active interventions to placebos or other treatments. However, this approach has limitations in its ability to assess multiple interventions simultaneously, making it less suitable for comprehensive decision-making. This is where Network Meta-analysis (NMA) comes in, which extends pairwise meta-analysis to allow for the assessment of more than two interventions within a single analysis, even when direct head-to-head comparisons are not available. NMA shares similarities with pairwise meta-analysis, including systematic literature searches, bias assessment, data extraction, and statistical pooling. Two critical assumptions underlie NMA: transitivity and consistency. NMA can be performed using frequentist or Bayesian approaches, with both fixed and random effects models. Recent developments such as population adjustment methods and Component NMA have enhanced its utility. The significant advantage of NMA is its ability to generate treatment rankings based on the probability of each treatment being the most effective. Web-based applications such as MetaInsight and NMA Studio simplify the NMA process, making it more accessible without coding skills. NMA is essential in evidence-based decision-making, providing comprehensive comparisons of multiple interventions, overcoming the limitations of pairwise meta-analysis. While challenges persist, transparency is maintained, and decision-making bodies recognize NMA's value. NMA is a powerful tool that defines the future of healthcare decision-making.

We present an empirical comparison of relative-efficacy estimate(s) from matching-adjusted indirect comparisons (MAICs) with estimates from corresponding standard anchored indirect treatment comparisons. A total of 80 comparisons were identified from 17 publications through a systematic rapid review. A standardized metric that used reported relative treatment efficacy estimates and their associated uncertainty was used to compare the methods across different treatment indications and outcome measures. On aggregate, MAICs presented for connected networks tended to report a more favorable relative-efficacy estimate for the treatment for which individual-level patient data were available relative to the reported indirect treatment comparison estimate. Although we recognize the importance of MAIC and other population adjustment methods in certain situations, we recommend that results from these analyses are interpreted with caution. Researchers and analysts should carefully consider if MAICs are appropriate where presented and whether MAICs would have added value where omitted. • Matching-adjusted indirect comparisons (MAIC) is a method that is increasing in popularity in evidence synthesis. A number of simulation studies have been carried out to assess its suitability as a method. However, simulation studies alone cannot assess bias for MAIC given the subjective nature of how or if at all MAIC is performed. • We analyze real-world MAICs to ascertain if they tend to favor the treatment for which individual patient data are available relative to the results of the standard anchored indirect treatment comparisons. • This work provides an insight into how effect estimates compare when MAIC results are reported or not reported. This can be useful for analysts to consider when appraising results arising from MAIC, or when evaluating the absence of a reported MAIC. [ABSTRACT FROM AUTHOR]

Heavily treatment-experienced (HTE) people with human immunodeficiency virus (HIV) (PWH) may not achieve virologic suppression (VS) with combination antiretroviral therapy due to multidrug resistance (MDR), intolerance, and safety concerns. These PWH often receive highly individualized treatment regimens, but these regimens may not enable PWH to achieve VS, thereby halting disease progression. Novel medications are required for treating individuals with MDR HIV. Lenacapavir (LEN), a first-in-class HIV capsid inhibitor, is under investigation for the treatment of HTE individuals with MDR HIV in the phase 2/3 CAPELLA study. This study aimed to compare LEN plus optimized background regimen (OBR) with fostemsavir (FTR) + OBR, ibalizumab (IBA) + OBR, and OBR alone in terms of VS, CD4 cell count change from baseline, immunologic recovery, and discontinuation due to adverse events, using indirect treatment comparisons. A systematic review identified clinical evidence on HIV-1 treatments in HTE PWH. A feasibility assessment evaluated the identified studies for indirect treatment comparison analyses based on population characteristics, interventions, comparators, and outcomes of interest. Unanchored simulated treatment comparisons of LEN + OBR versus comparators were conducted. LEN + OBR had 6.57 times higher odds of VS at weeks 24 to 28 than FTR + OBR (95% confidence interval [CI] 1.34-32.28), 8.93 times higher odds of VS than IBA + OBR (95% CI 2.07-38.46), and 12.74 times higher odds of VS than OBR alone (95% CI 1.70-95.37). Change from baseline in CD4 cell count was similar across LEN + OBR, FTR + OBR, and IBA + OBR. LEN + OBR has statistically significantly greater odds of VS at weeks 24 to 28 than its comparators and represents a novel treatment for people with MDR HIV. • Available evidence on the efficacy and effectiveness of different therapies in heavily treatment-experienced people with human immunodeficiency virus (HIV) is sparse. • This is the first analysis that provides comparative treatment estimates that can be used alongside other outcomes to support decisions regarding the care of people with multidrug-resistant HIV. • We have shown that lenacapavir + optimized background regimen is favored over key comparators in terms of achieving virologic suppression and therefore has potential to reduce the burden associated with virologic failure in people with multidrug-resistant HIV. [ABSTRACT FROM AUTHOR]

Aim: Indirect treatment comparisons (ITCs) are anchored on a placebo comparator, and the placebo response may vary according to drug administration route. Migraine preventive treatment studies were used to evaluate ITCs and determine whether mode of administration influences placebo response and the overall study findings. Materials & methods: Change from baseline in monthlymigraine days produced by monoclonal antibody treatments (subcutaneous, intravenous) was compared using fixed-effects Bayesian network meta-analysis (NMA), network meta-regression (NMR), and unanchored simulated treatment comparison (STC). Results: NMA and NMR provide mixed, rarely differentiated results between treatments, whereas unanchored STC strongly favors eptinezumab over other preventive treatments. Conclusion: Further investigations are needed to determine which ITC best reflects the impact of mode of administration on placebo.

Aim: This research evaluated standard Weibull mixture cure (WMC) network meta-analysis (NMA) with Bayesian hierarchical (BH)WMCNMAto inform long-term survival of therapies. Materials & methods: Four trials in previously treated metastatic non-small-cell lung cancer with PD-L1 >1% were used comparing docetaxel with nivolumab, pembrolizumab and atezolizumab. Cure parameters related to a certain treatment class were assumed to share a common distribution. Results: Standard WMC NMA predicted cure rates were 0.03 (0.01; 0.07), 0.18 (0.12; 0.24), 0.07 (0.02; 0.15) and 0.03 (0.00; 0.09) for docetaxel, nivolumab, pembrolizumab and atezolizumab, respectively,with corresponding incremental life years (LY) of 3.11 (1.65; 4.66), 1.06 (0.41; 2.37) and 0.42 (-0.57; 1.68). The Bayesian hierarchical-WMC-NMA rates were 0.06 (0.03; 0.10), 0.17 (0.11; 0.23), 0.12 (0.05; 0.20) and 0.12 (0.03; 0.23), respectively, with incremental LY of 2.35 (1.04; 3.93), 1.67 (0.68; 2.96) and 1.36 (-0.05; 3.64). Conclusion: BH-WMC-NMA impacts incremental mean LYs and cost–effectiveness ratios, potentially affecting reimbursement decisions.

John R Hurst,1 Kevin Gruffydd-Jones,2 Mousumi Biswas,3 Deniz Guranlioglu,4 Martin Jenkins,4 Neda Stjepanovic,5 Arushi Bamrara6 1UCL Respiratory, University College London, London, UK; 2GP, Box Surgery, Box, Wiltshire, UK; 3AstraZeneca, Gaithersburg, MD, USA; 4AstraZeneca, Cambridge, UK; 5AstraZeneca Gothenburg, Mölndal, Sweden; 6Parexel International, Punjab, IndiaCorrespondence: John R Hurst Email j.hurst@ucl.ac.ukBackground: This literature review assessed comparative efficacy and safety of long-acting muscarinic antagonist/long-acting β2-agonist (LAMA/LABA) fixed-dose combinations (FDCs) in patients with COPD and moderate-to-very severe airflow limitation, using evidence from direct (head-to-head) and indirect treatment comparisons.Methods: Two systematic literature reviews were conducted to identify direct comparisons (head-to-head randomized controlled trials [RCTs]) and indirect comparisons (network meta-analyses [NMAs]; indirect treatment comparisons; meta-analyses) in patients with COPD with moderate-to-very severe airflow limitation. Study/Analysis characteristics, eligibility criteria, patient characteristics, and overall conclusions were extracted from relevant publications. The review of indirect comparisons focused on NMAs reporting efficacy outcomes at 12 and 24 weeks of treatment (established durations of symptomatic studies in COPD recommended by regulators).Results: Direct comparisons: Four RCTs that provided head-to-head comparisons of LAMA/LABA FDCs were identified, and these varied in their study design, included patient population and reported endpoints. While some differences in lung function outcomes were noted, where assessed, LAMA/LABA FDCs had comparable efficacy in improving symptoms, health status, exacerbations, and comparable safety profiles. However, the differences in study methodology and patient characteristics between these studies made it difficult to draw generalizable conclusions regarding the comparative effectiveness of LAMA/LABA FDCs from the direct comparisons alone. Indirect comparisons: Six NMAs were identified that reported indirect comparisons between LAMA/LABA FDCs; five of these were within the pre-defined scope of this review. Although the scope of each NMA varied, all five concluded that LAMA/LABA FDCs were generally comparable in terms of lung function improvements, patient-reported outcomes, and safety (where assessed).Conclusion: Although there were some inconsistencies between the outcomes of RCTs and NMAs for lung function, the totality of lung function, symptoms, exacerbations, and safety data suggests that currently available LAMA/LABA FDCs have comparable efficacy and safety in patients with COPD and moderate-to-very severe airflow limitation.Keywords: chronic obstructive pulmonary disease, direct evidence, indirect treatment comparisons, LAMA/LABA, efficacy, safety

Competing Interests: Dr Langley has received honoraria as a principal investigator, scientific advisor, or speaker for AbbVie, Amgen, Boehringer Ingelheim, Bristol-Myers-Squibb, Dermavant, Dermira, Eli Lilly, GlaxoSmithKline, Janssen, Leo Pharma, Novartis, Ortho Dermatologics, Pfizer, Sanofi -Genzyme, Sun Pharma, and UCB Pharma. Drs Sanyal, Disher, and Patel and Author Situ are employees of EVERSANA, which received funding from Janssen Research and Development for this study. Authors Alulis, Hassan, Peterson, and Lee and Dr Teneralli are employees of Janssen Research and Development.

Objective: To compare the relative efficacy of infliximab, adalimumab and golimumab through adjusted indirect treatment comparisons (ITCs). Methods: An exhaustive search was performed until October 2013. Databases consulted were MEDLINE, EMBASE, the Cochrane Library, the Centre for Reviews and Dissemination and the Web of Science. Randomized control trials (RCTs) comparing the efficacy of infliximab, adalimumab or golimumab versus placebo, in terms of clinical remission, clinical response and mucosal healing, were included. In the case that more than one RCT fulfilled the inclusion criteria for the same drug, a metanalysis was undertaken using a fixed effects model. ITCs were carried out using the method proposed by Bucher et al. Results: 6 RCTs published in 5 papers were included: 2 for infliximab (ACT 1 and ACT 2), 2 for adalimumab (ULTRA 1 y ULTRA 2) and 2 for golimumab (PURSUIT-SC y PURSUIT-M).In these RTCs, each biological agent was superior in efficacy to placebo. The results of the adjusted ITC are the following. In relation to the clinical remission, in the induction and maintenance period, there are no statistically significant differences between the three anti-TNF drugs. In relation to the clinical response and mucosal healing, in the induction period, there are statistically significant differences between infliximab and adalimumab. Conclusion: In view of the results obtained, infliximab, adalimumab and golimumab appear to be similarly effective therapeutic alternatives. Therefore, other considerations such as safety, tolerance and cost-effectiveness should be taken into account in order to select the most appropriate treatment

Aim: Indirect treatment comparisons (ITCs) are anchored on a placebo comparator, and the placebo response may vary according to drug administration route. Migraine preventive treatment studies were used to evaluate ITCs and determine whether mode of administration influences placebo response and the overall study findings. Materials & methods: Change from baseline in monthly migraine days produced by monoclonal antibody treatments (subcutaneous, intravenous) was compared using fixed-effects Bayesian network meta-analysis (NMA), network meta-regression (NMR), and unanchored simulated treatment comparison (STC). Results: NMA and NMR provide mixed, rarely differentiated results between treatments, whereas unanchored STC strongly favors eptinezumab over other preventive treatments. Conclusion: Further investigations are needed to determine which ITC best reflects the impact of mode of administration on placebo.

Aim: This research evaluated standard Weibull mixture cure (WMC) network meta-analysis (NMA) with Bayesian hierarchical (BH) WMC NMA to inform long-term survival of therapies. Materials & methods: Four trials in previously treated metastatic non-small-cell lung cancer with PD-L1 >1% were used comparing docetaxel with nivolumab, pembrolizumab and atezolizumab. Cure parameters related to a certain treatment class were assumed to share a common distribution. Results: Standard WMC NMA predicted cure rates were 0.03 (0.01; 0.07), 0.18 (0.12; 0.24), 0.07 (0.02; 0.15) and 0.03 (0.00; 0.09) for docetaxel, nivolumab, pembrolizumab and atezolizumab, respectively, with corresponding incremental life years (LY) of 3.11 (1.65; 4.66), 1.06 (0.41; 2.37) and 0.42 (-0.57; 1.68). The Bayesian hierarchical-WMC-NMA rates were 0.06 (0.03; 0.10), 0.17 (0.11; 0.23), 0.12 (0.05; 0.20) and 0.12 (0.03; 0.23), respectively, with incremental LY of 2.35 (1.04; 3.93), 1.67 (0.68; 2.96) and 1.36 (-0.05; 3.64). Conclusion: BH-WMC-NMA impacts incremental mean LYs and cost-effectiveness ratios, potentially affecting reimbursement decisions.

This network meta-analysis aimed to compare the clinical efficacy and safety among 7 newer targeted agents for the treatment of metastatic renal cell carcinoma (mRCC). All randomised clinical trials (RCTs) of targeted therapeutic drugs for mRCC were included. The study selection, data extraction and quality assessment were performed independently by two reviewers. The analysis evaluated efficacy outcomes [improvement in the median progression-free survival (PFS)] and safety outcomes (number of withdrawals due to adverse events). The network analysis included direct and indirect analyses. The quality of the selected studies was assessed using the Grading of Recommendations, Assessment, Development and Evaluations (GRADE) method. We identified 7 articles eligible for inclusion in the study. The direct comparison of the targeted agents indicated better efficacy in terms of longer PFS, but worse safety (more withdrawals due to adverse events). The indirect analysis demonstrated that axitinib was significantly more effective compared to panzopanib; sunitinib was superior to sorafenib and temsirolimus regarding efficacy outcome, without any statistically significant difference in the safety outcome. The results of the quality assessment indicated moderate scores using the GRADE method. In conclusion, the result of this network analysis suggested that sunitinib and axitinib may be more clinically efficient and axitinib is associated with a lower risk of adverse events compared to sorafenib, pazopanib and temsirolimus.