Bayesian design of clinical trials using the scale transformed power prior.

There are many Bayesian design methods allowing for the incorporation of historical data for sample size determination (SSD) in situations where the outcome in the historical data is the same as the outcome of a new study. However, there is a dearth of methods supporting the incorporation of data from a previously completed clinical trial that investigated the same or similar treatment as the new trial but had a primary outcome that is different. We propose a simulation-based Bayesian SSD framework using the partial-borrowing scale transformed power prior (straPP). The partial-borrowing straPP is developed by applying a novel scale transformation to a traditional power prior on the parameters from the historical data model to make the information better align with the new data model. The scale transformation is based on the assumption that the standardized parameters (i.e., parameters multiplied by the square roots of their respective Fisher information matrices) are equal. To illustrate the method, we present results from simulation studies that use real data from a previously completed clinical trial to design a new clinical trial with a primary time-to-event endpoint.

Safety signal detection with control of latent factors.

Postmarket drug safety database like vaccine adverse event reporting system (VAERS) collect thousands of spontaneous reports annually, with each report recording occurrences of any adverse events (AEs) and use of vaccines. We hope to identify signal vaccine-AE pairs, for which certain vaccines are statistically associated with certain adverse events (AE), using such data. Thus, the outcomes of interest are multiple AEs, which are binary outcomes and could be correlated because they might share certain latent factors; and the primary covariates are vaccines. Appropriately accounting for the complex correlation among AEs could improve the sensitivity and specificity of identifying signal vaccine-AE pairs. We propose a two-step approach in which we first estimate the shared latent factors among AEs using a working multivariate logistic regression model, and then use univariate logistic regression model to examine the vaccine-AE associations after controlling for the latent factors. Our simulation studies show that this approach outperforms current approaches in terms of sensitivity and specificity. We apply our approach in analyzing VAERS data and report our findings.

Predicting Treatment Effects of a New-to-Market Drug in Clinical Practice Based on Phase III Randomized Trial Results.

Trial results may not be generalizable to target populations treated in clinical practice with different distributions of baseline characteristics that modify the treatment effect. We used outcome models developed with trial data to predict treatment effects in Medicare populations. We used data from the Randomized Evaluation of Long-Term Anticoagulation Therapy trial (RE-LY), which investigated the effect of dabigatran vs. warfarin on stroke or systemic embolism (stroke/SE) among patients with atrial fibrillation. We developed outcome models by fitting proportional hazards models in trial data. Target populations were trial-eligible Medicare beneficiaries who initiated dabigatran or warfarin in 2010-2011 ("early") and 2010-2017 ("extended"). We predicted 2-year risk ratios (RRs) and risk differences (RDs) for stroke/SE, major bleeding, and all-cause death in the Medicare populations using the observed baseline characteristics. The trial and early target populations had similar mean (SD) CHADS2 scores (2.15 (SD 1.13) vs. 2.15 (SD 0.91)) but different mean ages (71 vs. 79 years). Compared with RE-LY, the early Medicare population had similar predicted benefit of dabigatran vs. warfarin for stroke/SE (trial RR = 0.63, 95% confidence interval (CI) = 0.50 to 0.76 and RD = -1.37%, -1.96% to -0.77%, Medicare RR = 0.73, 0.65 to 0.82 and RD = -0.92%, -1.26% to -0.59%) and risks for major bleeding and all-cause death. The time-extended target population showed similar results. Outcome model-based prediction facilitates estimating the average treatment effects of a drug in different target populations when treatment and outcome data are unreliable or unavailable. The predicted effects may inform payers' coverage decisions for patients, especially shortly after a drug's launch when observational data are scarce.

Risk of Severe Hypoglycemia With Newer Second-line Glucose-lowering Medications in Older Adults With Type 2 Diabetes Stratified by Known Indicators of Hypoglycemia Risk.

BACKGROUND: Severe hypoglycemia is associated with adverse clinical outcomes. We evaluated the risk of severe hypoglycemia in older adults initiating newer glucose-lowering medications overall and across strata of known indicators of high hypoglycemia risk. METHODS: We conducted a comparative-effectiveness cohort study of older adults aged >65 years with type 2 diabetes initiating sodium-glucose cotransporter 2 inhibitors (SGLT2i) versus dipeptidyl peptidase-4 inhibitors (DPP-4i) or SGLT2i versus glucagon-like peptide-1 receptor agonists (GLP-1RA) using Medicare claims (3/2013-12/2018) and Medicare-linked-electronic health records. We identified severe hypoglycemia requiring emergency or inpatient visits using validated algorithms. After 1:1 propensity score matching, we estimated hazard ratios (HR) and rate differences (RD) per 1,000 person-years. Analyses were stratified by baseline insulin, sulfonylurea, cardiovascular disease (CVD), chronic kidney disease (CKD), and frailty. RESULTS: Over a median follow-up of 7 (interquartile range: 4-16) months, SGLT2i was associated with a reduced risk of hypoglycemia versus DPP-4i (HR 0.75 [0.68, 0.83]; RD -3.21 [-4.29, -2.12]), and versus GLP-1RA (HR 0.90 [0.82, 0.98]; RD -1.33 [-2.44, -0.23]). RD for SGLT2i versus DPP-4i was larger in patients using baseline insulin than in those not, although HRs were similar. In patients using baseline sulfonylurea, the risk of hypoglycemia was lower in SGLT2i versus DPP-4i (HR 0.57 [0.49, 0.65], RD -6.80 [-8.43, -5.16]), while the association was near-null in those without baseline sulfonylurea. Results stratified by baseline CVD, CKD and frailty were similar to the overall cohort findings. Findings for the GLP-1RA comparison were similar. CONCLUSIONS: SGLT2i was associated with a lower hypoglycemia risk versus incretin-based medications, with larger associations in patients using baseline insulin or sulfonylurea.

A Bayesian approach to study design and analysis with type I error rate control for response variables of mixed types.

There has been increased interest in the design and analysis of studies consisting of multiple response variables of mixed types. For example, in clinical trials, it is desirable to establish efficacy for a treatment effect in primary and secondary outcomes. In this article, we develop Bayesian approaches for hypothesis testing and study planning for data consisting of multiple response variables of mixed types with covariates. We assume that the responses are correlated via a Gaussian copula, and that the model for each response is, marginally, a generalized linear model (GLM). Taking a fully Bayesian approach, the proposed method enables inference based on the joint posterior distribution of the parameters. Under some mild conditions, we show that the joint distribution of the posterior probabilities under any Bayesian analysis converges to a Gaussian copula distribution as the sample size tends to infinity. Using this result, we develop an approach to control the type I error rate under multiple testing. Simulation results indicate that the method is more powerful than conducting marginal regression models and correcting for multiplicity using the Bonferroni-Holm Method. We also develop a Bayesian approach to sample size determination in the presence of response variables of mixed types, extending the concept of probability of success (POS) to multiple response variables of mixed types.

Comparing Effectiveness and Safety of SGLT2 Inhibitors vs DPP-4 Inhibitors in Patients With Type 2 Diabetes and Varying Baseline HbA1c Levels.

Importance: Sodium-glucose cotransporter 2 inhibitor (SGLT2i) therapy has been associated with cardiovascular benefits and a few adverse events; however, whether the comparative effectiveness and safety profiles vary with differences in baseline hemoglobin A1c (HbA1c) levels is unknown. Objective: To compare cardiovascular effectiveness and safety of treatment with SGLT2i vs dipeptidyl peptidase 4 inhibitor (DPP-4i) in adults with type 2 diabetes (T2D) (1) overall and (2) at varying baseline HbA1c levels. Design, Setting, and Participants: A new-user comparative effectiveness and safety research study was conducted among 144 614 commercially insured adults, initiating treatment with SGLT2i or DPP-4i and with a recorded T2D diagnosis at baseline and at least 1 HbA1c laboratory result recorded within 3 months before treatment initiation. Interventions: The intervention consisted of the initiation of treatment with SGLT2i or DPP-4i. Main Outcomes and Measures: Primary outcomes were a composite of myocardial infarction, stroke, or all-cause death (modified major adverse cardiovascular events [MACE]) and hospitalization for heart failure (HHF). Safety outcomes were hypovolemia, fractures, falls, genital infections, diabetic ketoacidosis (DKA), acute kidney injury (AKI), and lower-limb amputation. Incidence rate (IR) per 1000 person-years, hazard ratios (HR) and rate differences (RD) with their 95% CIs were estimated controlling for 128 covariates. Results: A total of 144 614 eligible adults (mean [SD] age, 62 [12.4] years; 54% male participants) with T2D initiating treatment with a SGLT2i (n = 60 523) or a DPP-4i (n = 84 091) were identified; 44 099 had an HbA1c baseline value of less than 7.5%, 52 986 between 7.5% and 9%, and 47 529 greater than 9%. Overall, 87 274 eligible patients were 1:1 propensity score-matched: 24 052 with HbA1c less than 7.5%; 32 290 with HbA1c between 7.5% and 9%; and 30 932 with HbA1c greater than 9% (to convert percentage of total hemoglobin to proportion of total hemoglobin, multiply by 0.01). The initiation of SGLT2i vs DPP-4i was associated with a reduction in the risk of modified MACE (IR per 1000 person-years 17.13 vs 20.18, respectively; HR, 0.85; 95% CI, 0.75-0.95; RD, -3.02; 95% CI, -5.23 to -0.80) and HHF (IR per 1000 person-years 3.68 vs 8.08, respectively; HR, 0.46; 95% CI, 0.35 to 0.57; RD -4.37; 95% CI, -5.62 to -3.12) over a mean follow-up of 8 months, with no evidence of treatment effect heterogeneity across the HbA1c levels. Treatment with SGLT2i showed an increased risk of genital infections and DKA and a reduced AKI risk compared with DPP-4i. Findings were consistent by HbA1c levels, except for a more pronounced risk of genital infections associated with SGLT2i for HbA1c levels of 7.5% to 9% (IR per 1000 person-years 68.5 vs 22.8, respectively; HR, 3.10; 95% CI, 2.68-3.58; RD, 46.22; 95% CI, 40.54-51.90). Conclusions and Relevance: In this comparative effectiveness and safety research study among adults with T2D, SGLT2i vs DPP-4i treatment initiators had a reduced risk of modified MACE and HHF, an increased risk of genital infections and DKA, and a lower risk of AKI, regardless of baseline HbA1c.

The scale transformed power prior for use with historical data from a different outcome model.

We develop the scale transformed power prior for settings where historical and current data involve different data types, such as binary and continuous data. This situation arises often in clinical trials, for example, when historical data involve binary responses and the current data involve some other type of continuous or discrete outcome. The power prior, proposed by Ibrahim and Chen, does not address the issue of different data types. Herein, we develop a new type of power prior, which we call the scale transformed power prior (straPP). The straPP is constructed by transforming the power prior for the historical data by rescaling the parameter using a function of the Fisher information matrices for the historical and current data models, thereby shifting the scale of the parameter vector from that of the historical to that of the current data. Examples are presented to motivate the need for such a transformation, and simulation studies are presented to illustrate the performance advantages of the straPP over the power prior and other informative and noninformative priors. A real dataset from a clinical trial undertaken to study a novel transitional care model for stroke survivors is used to illustrate the methodology.

A hierarchical prior for generalized linear models based on predictions for the mean response.

There has been increased interest in using prior information in statistical analyses. For example, in rare diseases, it can be difficult to establish treatment efficacy based solely on data from a prospective study due to low sample sizes. To overcome this issue, an informative prior to the treatment effect may be elicited. We develop a novel extension of the conjugate prior of Chen and Ibrahim (2003) that enables practitioners to elicit a prior prediction for the mean response for generalized linear models, treating the prediction as random. We refer to the hierarchical prior as the hierarchical prediction prior (HPP). For independent and identically distributed settings and the normal linear model, we derive cases for which the hyperprior is a conjugate prior. We also develop an extension of the HPP in situations where summary statistics from a previous study are available. The HPP allows for discounting based on the quality of individual level predictions, and simulation results suggest that, compared to the conjugate prior and the power prior, the HPP efficiency gains (e.g., lower mean squared error) where predictions are incompatible with the data. An efficient Monte Carlo Markov chain algorithm is developed. Applications illustrate that inferences under the HPP are more robust to prior-data conflict compared to selected nonhierarchical priors.

Bayesian multivariate probability of success using historical data with type I error rate control.

In clinical trials, it is common to have multiple clinical outcomes (e.g., coprimary endpoints or a primary and multiple secondary endpoints). It is often desirable to establish efficacy in at least one of multiple clinical outcomes, which leads to a multiplicity problem. In the frequentist paradigm, the most popular methods to correct for multiplicity are typically conservative. Moreover, despite guidance from regulators, it is difficult to determine the sample size of a future study with multiple clinical outcomes. In this article, we introduce a Bayesian methodology for multiple testing that asymptotically guarantees type I error control. Using a seemingly unrelated regression model, correlations between outcomes are specifically modeled, which enables inference on the joint posterior distribution of the treatment effects. Simulation results suggest that the proposed Bayesian approach is more powerful than the method of Holm (1979), which is commonly utilized in practice as a more powerful alternative to the ubiquitous Bonferroni correction. We further develop multivariate probability of success, a Bayesian method to robustly determine sample size in the presence of multiple outcomes.