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 trueδ^$$ \hat{\delta} $$ 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 trueδ^$$ \hat{\delta} $$ 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.
IMPORTANCEIn 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
Writing Group for the CODA Collaborative 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. OBJECTIVETo assess patient factors associated with undergoing appendectomy within 30 days of initiating antibiotics for appendicitis. DESIGN, SETTING, AND PARTICIPANTSIn 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. RESULTSOf 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.
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