Search

Propensity score methods are commonly used in statistical analyses of observational data to reduce the impact of confounding bias in estimations of average treatment effect. While the propensity score is defined as the conditional probability of a subject being in the treatment group given that subject's covariates, the most precise estimation of average treatment effect results from specifying the propensity score as a function of true confounders and predictors only. This property has been demonstrated via simulation in multiple prior research articles. However, we have seen no theoretical explanation as to why this should be so. This paper provides that theoretical proof. Furthermore, this paper presents a method for performing the necessary variable selection by means of elastic net regression, and then estimating the propensity scores so as to obtain optimal estimates of average treatment effect. The proposed method is compared against two other recently introduced methods, outcome-adaptive lasso and covariate balancing propensity score. Extensive simulation analyses are employed to determine the circumstances under which each method appears most effective. We applied the proposed methods to examine the effect of pre-cardiac surgery coagulation indicator on mortality based on a linked dataset from a retrospective review of 1390 patient medical records at Jewish Hospital (Louisville, KY) with the Society of Thoracic Surgeons database. [ABSTRACT FROM AUTHOR]

There is a dearth of robust methods to estimate the causal effects of multiple treatments when the outcome is binary. This paper uses two unique sets of simulations to propose and evaluate the use of Bayesian additive regression trees in such settings. First, we compare Bayesian additive regression trees to several approaches that have been proposed for continuous outcomes, including inverse probability of treatment weighting, targeted maximum likelihood estimator, vector matching, and regression adjustment. Results suggest that under conditions of non-linearity and non-additivity of both the treatment assignment and outcome generating mechanisms, Bayesian additive regression trees, targeted maximum likelihood estimator, and inverse probability of treatment weighting using generalized boosted models provide better bias reduction and smaller root mean squared error. Bayesian additive regression trees and targeted maximum likelihood estimator provide more consistent 95% confidence interval coverage and better large-sample convergence property. Second, we supply Bayesian additive regression trees with a strategy to identify a common support region for retaining inferential units and for avoiding extrapolating over areas of the covariate space where common support does not exist. Bayesian additive regression trees retain more inferential units than the generalized propensity score-based strategy, and shows lower bias, compared to targeted maximum likelihood estimator or generalized boosted model, in a variety of scenarios differing by the degree of covariate overlap. A case study examining the effects of three surgical approaches for non-small cell lung cancer demonstrates the methods. [ABSTRACT FROM AUTHOR]

Constructing causal inference methods to handle longitudinal data in observational studies is of high interest. In an observational setting, treatment assignment at each clinical visit follows a decision strategy where the treating clinician selects treatment based on current and past clinical measurements as well as treatment histories. These time-dependent structures, coupled with inherent correlations between and within each visit, add on to the data complexity. Despite recent interest in Bayesian causal methods, only a limited literature has explored approaches to handle longitudinal data and no method handles repeatedly measured outcomes. In this paper, we extended two Bayesian approaches: Bayesian estimation of marginal structural models and two-stage Bayesian propensity score analysis to handle a repeatedly measured outcome. Our proposed methods permit causal estimation of treatment effects at each visit. Time-dependent inverse probability of treatment weights are obtained from the Markov chain Monte Carlo samples of the posterior treatment assignment model for each follow-up visit. We use a simulation study to validate and compare the proposed methods and illustrate our approaches through a study of intravenous immunoglobulin therapy in treating newly diagnosed juvenile dermatomyositis. [ABSTRACT FROM AUTHOR]

When establishing an effective treatment with binary data in a two-stage design, one-sided tests for a proportion p are employed. Researchers use the parameter configuration at the boundary of the null hypothesis space to determine a rejection region and an optimal design. However, it is unclear whether the (maximum) Type I error rate is achieved at the boundary especially when the sample size in stage 2 varies. In this paper, we first prove that this is true for a large family of tests in adaptive two-stage designs by showing that any test in the family has a nondecreasing power in p and then derive optimal designs. Second, similar results are established for m-stage designs with m > 2. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The problem of how to best select variables for confounding adjustment forms one of the key challenges in the evaluation of exposure or treatment effects in observational studies. Routine practice is often based on stepwise selection procedures that use hypothesis testing, change-in-estimate assessments or the lasso, which have all been criticised for - amongst other things - not giving sufficient priority to the selection of confounders. This has prompted vigorous recent activity in developing procedures that prioritise the selection of confounders, while preventing the selection of so-called instrumental variables that are associated with exposure, but not outcome (after adjustment for the exposure). A major drawback of all these procedures is that there is no finite sample size at which they are guaranteed to deliver treatment effect estimators and associated confidence intervals with adequate performance. This is the result of the estimator jumping back and forth between different selected models, and standard confidence intervals ignoring the resulting model selection uncertainty. In this paper, we will develop insight into this by evaluating the finite-sample distribution of the exposure effect estimator in linear regression, under a number of the aforementioned confounder selection procedures. We will show that by making clever use of propensity scores, a simple and generic solution is obtained in the context of generalized linear models, which overcomes this concern (under weaker conditions than competing proposals). Specifically, we propose to use separate regularized regressions for the outcome and propensity score models in order to construct a doubly robust 'g-estimator'; when these models are sufficiently sparse and correctly specified, standard confidence intervals for the g-estimator implicitly incorporate the uncertainty induced by the variable selection procedure. [ABSTRACT FROM AUTHOR]

Non-adherence to assigned treatment is a common issue in cluster randomised trials. In these settings, the efficacy estimand may also be of interest. Many methodological contributions in recent years have advocated using instrumental variables to identify and estimate the local average treatment effect. However, the clustered nature of randomisation in cluster randomised trials adds to the complexity of such analyses. In this paper, we show that the local average treatment effect can be estimated via two-stage least squares regression using cluster-level summaries of the outcome and treatment received under certain assumptions. We propose the use of baseline variables to adjust the cluster-level summaries before performing two-stage least squares in order to improve efficiency. Implementation needs to account for the reduced sample size, as well as the possible heteroscedasticity, to obtain valid inferences. Simulations are used to assess the performance of two-stage least squares of cluster-level summaries under cluster-level or individual-level non-adherence, with and without weighting and robust standard errors. The impact of adjusting for baseline covariates and of appropriate degrees of freedom correction for inference is also explored. The methods are then illustrated by re-analysing a cluster randomised trial carried out in a specific UK primary care setting. Two-stage least squares estimation using cluster-level summaries provides estimates with small to negligible bias and coverage close to nominal level, provided the appropriate small sample degrees of freedom correction and robust standard errors are used for inference. [ABSTRACT FROM AUTHOR]

Ordinal responses are common in clinical studies. Although the proportional odds model is a popular option for analyzing ordered-categorical data, it cannot control the type I error rate when the proportional odds assumption fails to hold. The latent Weibull model was recently shown to be a superior candidate for modeling ordinal data, with remarkably better performance than the latent normal model when the data are highly skewed. In clinical trials with ordinal responses, a balanced design is common, with equal sample allocation for each treatment. However, a more ethical approach is to adopt a response-adaptive allocation scheme in which more patients receive the better treatment. In this paper, we propose the use of the doubly adaptive biased coin design to generate treatment allocations that benefit the trial participants. The proposed treatment allocation scheme not only allows more patients to receive the better treatment, it also maintains compatible test power for the comparison of treatment efficiencies. A clinical example is used to illustrate the proposed procedure. [ABSTRACT FROM AUTHOR]

All models of this paper involve R x C contingency tables in which the total frequency is fixed (full multinomial model), or in which the row totals are fixed (product multinomial model). For the most part, we assume that the column categories are ordered. For the full multinomial model the null hypothesis of interest is independence, i.e., the (ij)th cell probability is the product of the marginal probabilities of the ith row and jth column. In the product multinomial model the null hypothesis is that the R multinomial distributions have the same vector of cell probabilities. Our review includes (1) a careful listing of two-sided and one-sided alternatives, and (2) methodology to reduce the loss of efficiency of tests because of the discreteness of the model (The methodologies discussed are efficient in several senses. Tests are exact. Tests have very favorable and robust power properties. Tests make use of back-up statistics, thereby providing a finer grid of p-values. In some special cases, e.g., a 2 x C table and a one-sided alternative, conditional p-values are found, within seconds, simply by entering row frequencies into a given website. Thus, computational efficiency is exceptional.), and (3) a critique of some exact linear permutation tests (that are conditional on row and column margins) for both two-sided and some one-sided alternatives. Furthermore, recommendations as to which tests to use for specific alternatives are made. [ABSTRACT FROM AUTHOR]

Since the early work of RA Fisher, exact methods have been recognized as important tools in data analysis because they provide valid statistical inference even with small sample sizes, or with sparse or skewed data. With the recent advance of computational power and the availability of commercial software packages, exact methods have gained substantial popularity over the past two decades. However, most of these exact methods have been devoted to testing classical null hypotheses of no differences, and until recently little was known about exact methods dealing with non-inferiority or equivalence hypotheses. The presence of nuisance parameters in testing non-inferiority/equivalence hypotheses presents a special challenge for exact methods because of the intense computational requirement. In this paper, we review exact methods available for proving non-inferiority or equivalence of two treatments with a dichotomous endpoint. First, we present the general methodology for conducting exact tests for non-inferiority or equivalence; we then discuss several unconditional and conditional methods available for constructing hypothesis tests and confidence intervals based on three commonly used measures, namely, the difference, relative risk, and odds ratio of two independent proportions or rates. Finally, we illustrate with several examples the application of these exact methods in analysing and planning non-inferiority or equivalence trials. [ABSTRACT FROM AUTHOR]