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Stepped wedge trials (SWTs) are a type of cluster randomized trial that involve repeated measures on clusters and design-induced confounding between time and treatment. Although mixed models are commonly used to analyze SWTs, they are susceptible to misspecification particularly for cluster-longitudinal designs such as SWTs. Mixed model estimation leverages both "horizontal" or within-cluster information and "vertical" or between-cluster information. To use horizontal information in a mixed model, both the mean model and correlation structure must be correctly specified or accounted for, since time is confounded with treatment and measurements are likely correlated within clusters. Alternative non-parametric methods have been proposed that use only vertical information; these are more robust because between-cluster comparisons in a SWT preserve randomization, but these non-parametric methods are not very efficient. We propose a composite likelihood method that focuses on vertical information, but has the flexibility to recover efficiency by using additional horizontal information. We compare the properties and performance of various methods, using simulations based on COVID-19 data and a demonstration of application to the LIRE trial. We found that a vertical composite likelihood model that leverages baseline data is more robust than traditional methods, and more efficient than methods that use only vertical information. We hope that these results demonstrate the potential value of model-based vertical methods for SWTs with a large number of clusters, and that these new tools are useful to researchers who are concerned about misspecification of traditional models., (© 2024 John Wiley & Sons Ltd.)

Importance: Spanish-speaking participants are underrepresented in clinical trials, limiting study generalizability and contributing to ongoing health inequity. The Comparison of Outcomes of Antibiotic Drugs and Appendectomy (CODA) trial intentionally included Spanish-speaking participants., Objective: To describe trial participation and compare clinical and patient-reported outcomes among Spanish-speaking and English-speaking participants with acute appendicitis randomized to antibiotics., Design, Setting, and Participants: This study is a secondary analysis of the CODA trial, a pragmatic randomized trial comparing antibiotic therapy with appendectomy in adult patients with imaging-confirmed appendicitis enrolled at 25 centers across the US from May 1, 2016, to February 28, 2020. The trial was conducted in English and Spanish. All 776 participants randomized to antibiotics are included in this analysis. The data were analyzed from November 15, 2021, through August 24, 2022., Intervention: Randomization to a 10-day course of antibiotics or appendectomy., Main Outcomes and Measures: Trial participation, European Quality of Life-5 Dimensions (EQ-5D) questionnaire scores (higher scores indicating a better health status), rate of appendectomy, treatment satisfaction, decisional regret, and days of work missed. Outcomes are also reported for a subset of participants that were recruited from the 5 sites with a large proportion of Spanish-speaking participants., Results: Among eligible patients 476 of 1050 Spanish speakers (45%) and 1076 of 3982 of English speakers (27%) consented, comprising the 1552 participants who underwent 1:1 randomization (mean age, 38.0 years; 976 male [63%]). Of the 776 participants randomized to antibiotics, 238 were Spanish speaking (31%). Among Spanish speakers randomized to antibiotics, the rate of appendectomy was 22% (95% CI, 17%-28%) at 30 days and 45% (95% CI, 38%-52%) at 1 year, while in English speakers, these rates were 20% (95% CI, 16%-23%) at 30 days and 42% (95% CI 38%-47%) at 1 year. Mean EQ-5D scores were 0.93 (95% CI, 0.92-0.95) among Spanish speakers and 0.92 (95% CI, 0.91-0.93) among English speakers. Symptom resolution at 30 days was reported by 68% (95% CI, 61%-74%) of Spanish speakers and 69% (95% CI, 64%-73%) of English speakers. Spanish speakers missed 6.69 (95% CI, 5.51-7.87) days of work on average, while English speakers missed 3.76 (95% CI, 3.20-4.32) days. Presentation to the emergency department or urgent care, hospitalization, treatment dissatisfaction, and decisional regret were low for both groups., Conclusions and Relevance: A high proportion of Spanish speakers participated in the CODA trial. Clinical and most patient-reported outcomes were similar for English- and Spanish-speaking participants treated with antibiotics. Spanish speakers reported more days of missed work., Trial Registration: ClinicalTrials.gov Identifier: NCT02800785.

Objective: To compare secondary patient reported outcomes of perceptions of treatment success and function for patients treated for appendicitis with appendectomy vs. antibiotics at 30 days., Summary Background Data: The Comparison of Outcomes of antibiotic Drugs and Appendectomy trial found antibiotics noninferior to appendectomy based on 30-day health status. To address questions about outcomes among participants with lower socioeconomic status, we explored the relationship of sociodemographic and clinical factors and outcomes., Methods: We focused on 4 patient reported outcomes at 30 days: high decisional regret, dissatisfaction with treatment, problems performing usual activities, and missing >10 days of work. The randomized (RCT) and observational cohorts were pooled for exploration of baseline factors. The RCT cohort alone was used for comparison of treatments. Logistic regression was used to assess associations., Results: The pooled cohort contained 2062 participants; 1552 from the RCT. Overall, regret and dissatisfaction were low whereas problems with usual activities and prolonged missed work occurred more frequently. In the RCT, those assigned to antibiotics had more regret (Odd ratios (OR) 2.97, 95% Confidence intervals (CI) 2.05-4.31) and dissatisfaction (OR 1.98, 95%CI 1.25-3.12), and reported less missed work (OR 0.39, 95%CI 0.27-0.56). Factors associated with function outcomes included sociodemographic and clinical variables for both treatment arms. Fewer factors were associated with dissatisfaction and regret., Conclusions: Overall, participants reported high satisfaction, low regret, and were frequently able to resume usual activities and return to work. When comparing treatments for appendicitis, no single measure defines success or failure for all people. The reported data may inform discussions regarding the most appropriate treatment for individuals., Trial Registration: Clinicaltrials.gov Identifier: NCT02800785., Competing Interests: The authors report information from Price and Faine should read the remaining authors report no conflicts of interest., (Copyright © 2022 The Author(s). Published by Wolters Kluwer Health, Inc.)

Importance: A patient's belief in the likely success of a treatment may influence outcomes, but this has been understudied in surgical trials., Objective: To examine the association between patients' baseline beliefs about the likelihood of treatment success with outcomes of antibiotics for appendicitis in the Comparison of Outcomes of Antibiotic Drugs and Appendectomy (CODA) trial., Design, Setting, and Participants: This was a secondary analysis of the CODA randomized clinical trial. Participants from 25 US medical centers were enrolled between May 3, 2016, and February 5, 2020. Included in the analysis were participants with appendicitis who were randomly assigned to receive antibiotics in the CODA trial. After informed consent but before randomization, participants who were assigned to receive antibiotics responded to a baseline survey including a question about how successful they believed antibiotics could be in treating their appendicitis., Interventions: Participants were categorized based on baseline survey responses into 1 of 3 belief groups: unsuccessful/unsure, intermediate, and completely successful., Main Outcomes and Measures: Three outcomes were assigned at 30 days: (1) appendectomy, (2) high decisional regret or dissatisfaction with treatment, and (3) persistent signs and symptoms (abdominal pain, tenderness, fever, or chills). Outcomes were compared across groups using adjusted risk differences (aRDs), with propensity score adjustment for sociodemographic and clinical factors., Results: Of the 776 study participants who were assigned antibiotic treatment in CODA, a total of 425 (mean [SD] age, 38.5 [13.6] years; 277 male [65%]) completed the baseline belief survey before knowing their treatment assignment. Baseline beliefs were as follows: 22% of participants (92 of 415) had an unsuccessful/unsure response, 51% (212 of 415) had an intermediate response, and 27% (111 of 415) had a completely successful response. Compared with the unsuccessful/unsure group, those who believed antibiotics could be completely successful had a 13-percentage point lower risk of appendectomy (aRD, -13.49; 95% CI, -24.57 to -2.40). The aRD between those with intermediate vs unsuccessful/unsure beliefs was -5.68 (95% CI, -16.57 to 5.20). Compared with the unsuccessful/unsure group, those with intermediate beliefs had a lower risk of persistent signs and symptoms (aRD, -15.72; 95% CI, -29.71 to -1.72), with directionally similar results for the completely successful group (aRD, -15.14; 95% CI, -30.56 to 0.28)., Conclusions and Relevance: Positive patient beliefs about the likely success of antibiotics for appendicitis were associated with a lower risk of appendectomy and with resolution of signs and symptoms by 30 days. Pathways relating beliefs to outcomes and the potential modifiability of beliefs to improve outcomes merit further investigation., Trial Registration: ClinicalTrials.gov Identifier: NCT02800785.

Stepped wedge cluster randomized controlled trials are typically analyzed using models that assume the full effect of the treatment is achieved instantaneously. We provide an analytical framework for scenarios in which the treatment effect varies as a function of exposure time (time since the start of treatment) and define the "effect curve" as the magnitude of the treatment effect on the linear predictor scale as a function of exposure time. The "time-averaged treatment effect" (TATE) and "long-term treatment effect" (LTE) are summaries of this curve. We analytically derive the expectation of the estimator δ ^ $$ \hat{\delta} $$ resulting from a model that assumes an immediate treatment effect and show that it can be expressed as a weighted sum of the time-specific treatment effects corresponding to the observed exposure times. Surprisingly, although the weights sum to one, some of the weights can be negative. This implies that δ ^ $$ \hat{\delta} $$ may be severely misleading and can even converge to a value of the opposite sign of the true TATE or LTE. We describe several models, some of which make assumptions about the shape of the effect curve, that can be used to simultaneously estimate the entire effect curve, the TATE, and the LTE. We evaluate these models in a simulation study to examine the operating characteristics of the resulting estimators and apply them to two real datasets., (© 2022 John Wiley & Sons Ltd.)

Stepped wedge cluster randomized trials are often analysed using linear mixed effects models that may include random effects for cluster, time and/or treatment. We investigate the impact of misspecification of the random effects structure of the model. Specifically, we considered two cases of misspecification of the random effects in a cross-sectional stepped wedge cluster randomized trials model - fit a linear mixed effects model with random time effects but the true model includes random treatment effects (case 1) or fit a linear mixed effects model with random treatment effect but the true model includes random time effects (case 2) - and derived the variance of the estimated treatment effect under misspecification. We defined two measures of the effect of misspecification: validity and efficiency. Validity is the ratio of the model-based variance of the treatment effect from the mis-specified model divided by the true variance of the treatment effect from the mis-specified model (based on a sandwich estimate of the variance). Efficiency is the ratio of the model-based variance of the treatment effect from the correctly specified model divided by the true variance of the treatment effect from the mis-specified model. We found that validity is less than 1.0 (anti-conservative) in almost all situations investigated with the exception of case 1 with two sequences, when validity could be greater than 1.0. Efficiency is less than 1 in all cases and depends on the intracluster correlation coefficient, the relative magnitude of the variance of the misclassified variance component, and the number of sequences. In general, there is no universal recommendation as to the most robust approach except for the case of a classic stepped wedge cluster randomized trial with only 2 sequences, where fitting a random time model is less likely to lead to anti-conservative inference compared with fitting a random intervention model.

Importance: In the Comparison of Outcomes of Antibiotic Drugs and Appendectomy (CODA) trial, which found antibiotics to be noninferior, approximately half of participants randomized to receive antibiotics had outpatient management with hospital discharge within 24 hours. If outpatient management is safe, it could increase convenience and decrease health care use and costs., Objective: To assess the use and safety of outpatient management of acute appendicitis., Design, Setting, and Participants: This cohort study, which is a secondary analysis of the CODA trial, included 776 adults with imaging-confirmed appendicitis who received antibiotics at 25 US hospitals from May 1, 2016, to February 28, 2020., Exposures: Participants randomized to antibiotics (intravenous then oral) could be discharged from the emergency department based on clinician judgment and prespecified criteria (hemodynamically stable, afebrile, oral intake tolerated, pain controlled, and follow-up confirmed). Outpatient management and hospitalization were defined as discharge within or after 24 hours, respectively., Main Outcomes and Measures: Outcomes compared among patients receiving outpatient vs inpatient care included serious adverse events (SAEs), appendectomies, health care encounters, satisfaction, missed workdays at 7 days, and EuroQol 5-dimension (EQ-5D) score at 30 days. In addition, appendectomy incidence among outpatients and inpatients, unadjusted and adjusted for illness severity, was compared., Results: Among 776 antibiotic-randomized participants, 42 (5.4%) underwent appendectomy within 24 hours and 8 (1.0%) did not receive their first antibiotic dose within 24 hours, leaving 726 (93.6%) comprising the study population (median age, 36 years; range, 18-86 years; 462 [63.6%] male; 437 [60.2%] White). Of these participants, 335 (46.1%; site range, 0-89.2%) were discharged within 24 hours, and 391 (53.9%) were discharged after 24 hours. Over 7 days, SAEs occurred in 0.9 (95% CI, 0.2-2.6) per 100 outpatients and 1.3 (95% CI, 0.4-2.9) per 100 inpatients; in the appendicolith subgroup, SAEs occurred in 2.3 (95% CI, 0.3-8.2) per 100 outpatients vs 2.8 (95% CI, 0.6-7.9) per 100 inpatients. During this period, appendectomy occurred in 9.9% (95% CI, 6.9%-13.7%) of outpatients and 14.1% (95% CI, 10.8%-18.0%) of inpatients; adjusted analysis demonstrated a similar difference in incidence (-4.0 percentage points; 95% CI, -8.7 to 0.6). At 30 days, appendectomies occurred in 12.6% (95% CI, 9.1%-16.7%) of outpatients and 19.0% (95% CI, 15.1%-23.4%) of inpatients. Outpatients missed fewer workdays (2.6 days; 95% CI, 2.3-2.9 days) than did inpatients (3.8 days; 95% CI, 3.4-4.3 days) and had similar frequency of return health care visits and high satisfaction and EQ-5D scores., Conclusions and Relevance: These findings support that outpatient antibiotic management is safe for selected adults with acute appendicitis, with no greater risk of complications or appendectomy than hospital care, and should be included in shared decision-making discussions of patient preferences for outcomes associated with nonoperative and operative care., Trial Registration: ClinicalTrials.gov Identifier: NCT02800785.

Importance: For adults with appendicitis, several randomized clinical trials have demonstrated that antibiotics are an effective alternative to appendectomy. However, it remains unknown how the characteristics of patients in such trials compare with those of patients who select their treatment and whether outcomes differ., Objective: To compare participants in the Comparison of Outcomes of Antibiotic Drugs and Appendectomy (CODA) randomized clinical trial (RCT) with a parallel cohort study of participants who declined randomization and self-selected treatment., Design, Setting, and Participants: The CODA trial was conducted in 25 US medical centers. Participants were enrolled between May 3, 2016, and February 5, 2020; all participants were eligible for at least 1 year of follow-up, with all follow-up ending in 2021. The randomized cohort included 1094 adults with appendicitis; the self-selection cohort included patients who declined participation in the randomized group, of whom 253 selected appendectomy and 257 selected antibiotics. In this secondary analysis, characteristics and outcomes in both self-selection and randomized cohorts are described with an exploratory analysis of cohort status and receipt of appendectomy., Interventions: Appendectomy vs antibiotics., Main Outcomes and Measures: Characteristics among participants randomized to either appendectomy or antibiotics were compared with those of participants who selected their own treatment., Results: Clinical characteristics were similar across the self-selection cohort (510 patients; mean age, 35.8 years [95% CI, 34.5-37.1]; 218 female [43%; 95% CI, 39%-47%]) and the randomized group (1094 patients; mean age, 38.2 years [95% CI, 37.4-39.0]; 386 female [35%; 95% CI, 33%-38%]). Compared with the randomized group, those in the self-selection cohort were less often Spanish speaking (n = 99 [19%; 95% CI, 16%-23%] vs n = 336 [31%; 95% CI, 28%-34%]), reported more formal education (some college or more, n = 355 [72%; 95% CI, 68%-76%] vs n = 674 [63%; 95% CI, 60%-65%]), and more often had commercial insurance (n = 259 [53%; 95% CI, 48%-57%] vs n = 486 [45%; 95% CI, 42%-48%]). Most outcomes were similar between the self-selection and randomized cohorts. The number of patients undergoing appendectomy by 30 days was 38 (15.3%; 95% CI, 10.7%-19.7%) among those selecting antibiotics and 155 (19.2%; 95% CI, 15.9%-22.5%) in those who were randomized to antibiotics (difference, 3.9%; 95% CI, -1.7% to 9.5%). Differences in the rate of appendectomy were primarily observed in the non-appendicolith subgroup., Conclusions and Relevance: This secondary analysis of the CODA RCT found substantially similar outcomes across the randomized and self-selection cohorts, suggesting that the randomized trial results are generalizable to the community at large., Trial Registration: ClinicalTrials.gov Identifier: NCT02800785.

Mixed models are commonly used to analyze stepped wedge trials (SWTs) to account for clustering and repeated measures on clusters. One critical issue researchers face is whether to include a random time effect or a random treatment effect. When the wrong model is chosen, inference on the treatment effect may be invalid. We explore asymptotic and finite-sample convergence of variance component estimates when the model is misspecified and how misspecification affects the estimated variance of the treatment effect. For asymptotic results, we rely on analytical solutions rather than simulation studies, which allow us to succinctly describe the convergence of misspecified estimates, even though there are multiple roots for each misspecified model. We found that both direction and magnitude of the bias associated with model-based standard errors depends on the study design and magnitude of the true variance components. We identify some scenarios in which choosing the wrong random effect has a large impact on model-based inference. However, many trends depend on trial design and assumptions about the true correlation structure, so we provide tools for researchers to investigate specific scenarios of interest. We use data from an SWT on disinvesting from weekend services in hospital wards to demonstrate how these results can be applied as a sensitivity analysis, which quantifies the impact of misspecification under a variety of settings and directly compares the potential consequences of different modeling choices. Our results will provide guidance for prespecified model choices and supplement sensitivity analyses to inform confidence in the validity of results., (© 2022 John Wiley & Sons Ltd.)

Importance: Use of antibiotics for the treatment of appendicitis is safe and has been found to be noninferior to appendectomy based on self-reported health status at 30 days. Identifying patient characteristics associated with a greater likelihood of appendectomy within 30 days in those who initiate antibiotics could support more individualized decision-making., Objective: To assess patient factors associated with undergoing appendectomy within 30 days of initiating antibiotics for appendicitis., Design, Setting, and Participants: In this cohort study using data from the Comparison of Outcomes of Antibiotic Drugs and Appendectomy (CODA) randomized clinical trial, characteristics among patients who initiated antibiotics were compared between those who did and did not undergo appendectomy within 30 days. The study was conducted at 25 US medical centers; participants were enrolled between May 3, 2016, and February 5, 2020. A total of 1552 participants with acute appendicitis were randomized to antibiotics (776 participants) or appendectomy (776 participants). Data were analyzed from September 2020 to July 2021., Exposures: Appendectomy vs antibiotics., Main Outcomes and Measures: Conditional logistic regression models were fit to estimate associations between specific patient factors and the odds of undergoing appendectomy within 30 days after initiating antibiotics. A sensitivity analysis was performed excluding participants who underwent appendectomy within 30 days for nonclinical reasons., Results: Of 776 participants initiating antibiotics (mean [SD] age, 38.3 [13.4] years; 286 [37%] women and 490 [63%] men), 735 participants had 30-day outcomes, including 154 participants (21%) who underwent appendectomy within 30 days. After adjustment for other factors, female sex (odds ratio [OR], 1.53; 95% CI, 1.01-2.31), radiographic finding of wider appendiceal diameter (OR per 1-mm increase, 1.09; 95% CI, 1.00-1.18), and presence of appendicolith (OR, 1.99; 95% CI, 1.28-3.10) were associated with increased odds of undergoing appendectomy within 30 days. Characteristics that are often associated with increased risk of complications (eg, advanced age, comorbid conditions) and those clinicians often use to describe appendicitis severity (eg, fever: OR, 1.28; 95% CI, 0.82-1.98) were not associated with odds of 30-day appendectomy. The sensitivity analysis limited to appendectomies performed for clinical reasons provided similar results regarding appendicolith (adjusted OR, 2.41; 95% CI, 1.49-3.91)., Conclusions and Relevance: This cohort study found that presence of an appendicolith was associated with a nearly 2-fold increased risk of undergoing appendectomy within 30 days of initiating antibiotics. Clinical characteristics often used to describe severity of appendicitis were not associated with odds of 30-day appendectomy. This information may help guide more individualized decision-making for people with appendicitis.

Background: Stepped-wedge designs (SWD) are increasingly used to evaluate the impact of changes to the process of care within health care systems. However, to generate definitive evidence, a correct sample size calculation is crucial to ensure such studies are properly powered. The seminal work of Hussey and Hughes (Contemp Clin Trials 28(2):182-91, 2004) provides an analytical formula for power calculations with normal outcomes using a linear model and simple random effects. However, minimal development and evaluation have been done for power calculation with non-normal outcomes on their natural scale (e.g., logit, log). For example, binary endpoints are common, and logistic regression is the natural multilevel model for such clustered data., Methods: We propose a power calculation formula for SWD with either normal or non-normal outcomes in the context of generalized linear mixed models by adopting the Laplace approximation detailed in Breslow and Clayton (J Am Stat Assoc 88(421):9-25, 1993) to obtain the covariance matrix of the estimated parameters., Results: We compare the performance of our proposed method with simulation-based sample size calculation and demonstrate its use on a study of patient-delivered partner therapy for STI treatment and a study that assesses the impact of providing additional benchmark prevalence information in a radiologic imaging report. To facilitate adoption of our methods we also provide a function embedded in the R package "swCRTdesign" for sample size and power calculation for multilevel stepped-wedge designs., Conclusions: Our method requires minimal computational power. Therefore, the proposed procedure facilitates rapid dynamic updates of sample size calculations and can be used to explore a wide range of design options or assumptions., (© 2021. The Author(s).)

Background and Objective: Stepped wedge trials (SWTs) are a type of cluster-randomized trial that are commonly used to evaluate health care interventions. Most SWT-related software packages have restrictive assumptions about the study design and correlation structure of the data. The objective of this paper is to present a package and corresponding web-based graphical user interface (GUI) that provide researchers with another, more flexible option for SWT design and analysis., Methods: We developed an Rpackage swCRTdesign ('stepped wedge Cluster Randomized Trial design'), which uses a random effects model to account for correlation in the data induced by a SWT design. Possible sources of correlation include clusters, time within clusters, and treatment within clusters., Results: swCRTdesign allows a user to calculate power, simulate SWT data to streamline simulation studies (e.g. to estimate power), and create descriptive summaries and plots. Additionally, a GUI, developed using shiny, is available to calculate power and create power curves and design plots., Conclusions: The swCRTdesign package accommodates a wide variety of SWT designs, and makes it easy to account for some sources of correlation which are not found in other packages. The user-friendly web-based GUI makes some swCRTdesign features accessible to researchers not familiar with R. These two resources will make appropriately complex SWT calculations more accessible to scientists from a wide variety of backgrounds., Competing Interests: Declaration of Competing Interest The authors have declared no conflict of interest., (Copyright © 2020 Elsevier B.V. All rights reserved.)