Browsing by Subject "Subgroup analysis"

This dissertation is devoted to modeling complex data from the

Bayesian perspective via constructing priors with latent structures.

There are three major contexts in which this is done -- strategies for

the analysis of dynamic longitudinal data, estimating

shape-constrained functions, and identifying subgroups. The

methodology is illustrated in three different

interdisciplinary contexts: (1) adaptive measurement testing in

education; (2) emulation of computer models for vehicle crashworthiness; and (3) subgroup analyses based on biomarkers.

Chapter 1 presents an overview of the utilized latent structured

priors and an overview of the remainder of the thesis. Chapter 2 is

motivated by the problem of analyzing dichotomous longitudinal data

observed at variable and irregular time points for adaptive

measurement testing in education. One of its main contributions lies

in developing a new class of Dynamic Item Response (DIR) models via

specifying a novel dynamic structure on the prior of the latent

trait. The Bayesian inference for DIR models is undertaken, which

permits borrowing strength from different individuals, allows the

retrospective analysis of an individual's changing ability, and

allows for online prediction of one's ability changes. Proof of

posterior propriety is presented, ensuring that the objective

Bayesian analysis is rigorous.

Chapter 3 deals with nonparametric function estimation under

shape constraints, such as monotonicity, convexity or concavity. A

motivating illustration is to generate an emulator to approximate a computer

model for vehicle crashworthiness. Although Gaussian processes are

very flexible and widely used in function estimation, they are not

naturally amenable to incorporation of such constraints. Gaussian

processes with the squared exponential correlation function have the

interesting property that their derivative processes are also

Gaussian processes and are jointly Gaussian processes with the

original Gaussian process. This allows one to impose shape constraints

through the derivative process. Two alternative ways of incorporating derivative

information into Gaussian processes priors are proposed, with one

focusing on scenarios (important in emulation of computer

models) in which the function may have flat regions.

Chapter 4 introduces a Bayesian method to control for multiplicity

in subgroup analyses through tree-based models that limit the

subgroups under consideration to those that are a priori plausible.

Once the prior modeling of the tree is accomplished, each tree will

yield a statistical model; Bayesian model selection analyses then

complete the statistical computation for any quantity of interest,

resulting in multiplicity-controlled inferences. This research is

motivated by a problem of biomarker and subgroup identification to

develop tailored therapeutics. Chapter 5 presents conclusions and

some directions for future research.

Subgroup analyses are frequently conducted in comparative effectiveness research and randomized clinical trials to assess evidence of heterogeneous treatment effect across patient subpopulations. Though widely used in medical research, causal inference methods for conducting statistical analyses on a range of pre-specified subpopulations remain underdeveloped, particularly in observational studies. This dissertation develops and extends propensity score methods for causal subgroup analysis.

In Chapter 2, we develop a suite of analytical methods and visualization tools for causal subgroup analysis. First, we introduce the estimand of subgroup weighted average treatment effect and provide the corresponding propensity score weighting estimator. We show that balancing covariates within a subgroup bounds the bias of the estimator of subgroup causal effects. Second, we propose to use the overlap weighting method to achieve exact balance within subgroups. We further propose a method that combines overlap weighting and LASSO, to balance the bias-variance tradeoff in subgroup analysis. Finally, we design a new diagnostic plot---the Connect-S plot---for visualizing the subgroup covariate balance. Extensive simulation studies are presented to compare the proposed method with several existing methods. We apply the proposed methods to the observational COMPARE-UF study to evaluate the causal effects of Myomectomy versus Hysterectomy on the relief of symptoms and quality of life (a continuous outcome) in a number of pre-specified subgroups of patients with uterine fibroids.

In Chapter 3, we investigate the propensity score weighting method for causal subgroup analysis with time-to-event outcomes. We introduce two causal estimands, the subgroup marginal hazard ratio and subgroup restricted average causal effect, and provide corresponding propensity score weighting estimators. We analytically established that the bias of subgroup restricted average causal effect is determined by subgroup covariate balance. Using extensive simulations, we compare the performance of various combination of propensity score models (logistic regression, random forests, LASSO, and generalized boosted models) and weighting schemes (inverse probability weighting, and overlap weighting) for estimating the survival causal estimands. We find that the logistic model with subgroup-covariate interactions selected by LASSO consistently outperforms other propensity score models. Also, overlap weighting generally outperforms inverse probability weighting in terms of balance, bias and variance, and the advantage is particularly pronounced in small subgroups and/or in the presence of poor overlap. Again, we apply the methods to the COMPARE-UF study with a time-to-event outcome, the time to disease recurrence after receiving a procedure.

In Chapter 4, we extend propensity score weighting methodology for covariate adjustment to improve the precision and power of subgroup analyses in RCTs. We fit a logistic regression propensity model with pre-specified covariate-subgroup interactions. We show that by construction, overlap weighting exactly balances the covariates with interaction terms in each subgroup. Extensive simulations are performed to compare the operating characteristics of unadjusted estimator, different propensity score weighting estimators and the analysis of covariance estimator. We apply these methods to the HF-ACTION trial to evaluate the effect of exercise training on 6-minute walk test in several pre-specified subgroups.