Development and validation of claims-based algorithms for estimating gestational age of spontaneous abortion and termination.

To study the risk of spontaneous abortion (SAB) or termination using healthcare utilization databases, algorithms to estimate the gestational age (GA) are needed. Using Medicaid data, we developed a hierarchical algorithm to classify pregnancy outcomes. We identified the subset of potential SAB and termination cases, and abstracted the GA from linked electronic medical records (gold standard). We developed three approaches: (1) assign median GA for SAB and termination cases in the US; (2) draw a random GA from the population distributions; (3) estimate GA based on regression models. Algorithm performance was assessed based on the proportion of pregnancies with estimated GA within 1-4 weeks of the gold standard, the mean squared error (MSE) and the R-squared. Approach 1 and Approach 3 had similar performance, though approach 3 using random forest models with variables selected via the Boruta algorithm had better MSE and R-squared. For SAB, 58.0% of pregnancies were correctly classified within 2 weeks of the gold standard (MSE: 8.7, R-squared: 0.09). For termination, the proportions were 66.3% (MSE: 11.7; R-squared: 0.35). SABs and terminations can be studied in healthcare utilization data with careful implementation of validated algorithms though higher level of GA misclassification is expected compared to live births.

Rejoinder to the discussion on "LEAP: the latent exchangeability prior for borrowing information from historical data".

The discussions of our paper provide insights into the practical considerations of the latent exchangeability prior while also highlighting further extensions. In this rejoinder, we briefly summarize the discussions and provide comments.

LEAP: the latent exchangeability prior for borrowing information from historical data.

It is becoming increasingly popular to elicit informative priors on the basis of historical data. Popular existing priors, including the power prior, commensurate prior, and robust meta-analytic predictive prior, provide blanket discounting. Thus, if only a subset of participants in the historical data are exchangeable with the current data, these priors may not be appropriate. In order to combat this issue, propensity score approaches have been proposed. However, these approaches are only concerned with the covariate distribution, whereas exchangeability is typically assessed with parameters pertaining to the outcome. In this paper, we introduce the latent exchangeability prior (LEAP), where observations in the historical data are classified into exchangeable and non-exchangeable groups. The LEAP discounts the historical data by identifying the most relevant subjects from the historical data. We compare our proposed approach against alternative approaches in simulations and present a case study using our proposed prior to augment a control arm in a phase 3 clinical trial in plaque psoriasis with an unbalanced randomization scheme.

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.

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.

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.

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.

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.

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.