Marginal mean models for zero-inflated count data.

Zero-inflated regression models have emerged as a popular tool within the parametric framework to characterize count data with excess zeros. Despite their increasing popularity, much of the literature on real applications of these models has centered around the latent class formulation where the mean response of the so-called at-risk or susceptible population and the susceptibility probability are both related to covariates. While this formulation in some instances provides an interesting representation of the data, it often fails to produce easily interpretable covariate effects on the overall mean response. In this article, we propose two approaches that circumvent this limitation. The first approach consists of estimating the effect of covariates on the overall mean from the assumed latent class models, while the second approach formulates a model that directly relates the overall mean to covariates. Our results are illustrated by extensive numerical simulations and an application to an oral health study on low income African-American children, where the overall mean model is used to evaluate the effect of sugar consumption on caries indices.

Estimating model-based nonnegative population marginal means in application to medical expenditures covered by different health care policies - A study on Medical Expenditure Panel Survey.

The medical care expenditure is historically an important public health issue, which greatly impacts the government's health policies as well as patients' financial and medical decisions. In population health research, we commonly discretize a numeric attribute to a few ordinal groups to examine population characteristics. Oftentimes, the population marginal mean estimation by the ANOVA approach is inflexible since it uses pre-defined grouping of the covariate. In this paper, we propose a method to estimate the population marginal mean using the B-spline-based regression in a manner of a generalized additive model as an alternative for the ANOVA. Since the medical expenditure is always nonnegative, a Bayesian approach is also implemented for the nonnegative constraint on the marginal mean estimates. The proposed method is flexible to estimate marginal means for user-specified grouping after model fitting in a post-hoc manner, a clear advantage over the ANOVA approach. We show that this method is inferentially superior to the ANOVA through theoretical investigations and an extensive Monte Carlo study. The real data analysis using Medical Expenditure Panel Survey data assisted by some visualization tools demonstrates an applicability of the proposed approach and leads us some interesting observations that may be relevant to public health discussions.

Two-part models with stochastic processes for modelling longitudinal semicontinuous data: Computationally efficient inference and modelling the overall marginal mean.

Several researchers have described two-part models with patient-specific stochastic processes for analysing longitudinal semicontinuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice, the high dimensional integrations involved in the marginal likelihood (i.e. integrated over the stochastic processes) significantly complicates model fitting. Thus, non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this paper, we describe an efficient method of implementation by demonstrating how the high dimensional integrations involved in the marginal likelihood can be computed efficiently. Specifically, by using a property of the multivariate normal distribution and the standard marginal cumulative distribution function identity, we transform the marginal likelihood so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can then be efficiently evaluated. Hence, maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterisation and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.

A comparison of approaches for stratifying on the propensity score to reduce bias.

RATIONALE, AIMS, AND OBJECTIVES: Stratification is a popular propensity score (PS) adjustment technique. It has been shown that stratifying the PS into 5 quantiles can remove over 90% of the bias due to the covariates used to generate the PS. Because of this finding, many investigators partition their data into 5 quantiles of the PS without examining whether a more robust solution (one that increases covariate balance while potentially reducing bias in the outcome analysis) can be found for their data. Two approaches (referred to herein as PSCORE and PSTRATA) obtain the optimal stratification solution by repeatedly dividing the data into strata until balance is achieved between treatment and control groups on the PS. These algorithms differ in how they partition the data, and it is not known which is better, or if either is better than a 5-quantile default approach, for reducing bias in treatment effect estimates. METHOD: Monte Carlo simulations and empirical data are used to assess whether PS strata defined by PSCORE, PSTRATA, or 5 quantiles is best at reducing bias in treatment effect estimates, when used within a marginal mean weighting framework (MMWS). These estimates are further compared to results derived using inverse probability of treatment weights (IPTW). RESULTS: PSTRATA was slightly better than PSCORE in balancing covariates and reducing bias, while both approaches outperformed the 5-quantile approach. Overall MMWS using any stratification method outperformed IPTW. CONCLUSIONS: Investigators should routinely use stratification approaches that obtain the optimal stratification solution, rather than simply partitioning the data into 5 quantiles of the PS. Moreover, MMWS (in conjunction with an optimal stratification approach) should be considered as an alternative to IPTW in studies that use PS weights.

Finite-sample corrected generalized estimating equation of population average treatment effects in stepped wedge cluster randomized trials.

Stepped wedge designs are increasingly commonplace and advantageous for cluster randomized trials when it is both unethical to assign placebo, and it is logistically difficult to allocate an intervention simultaneously to many clusters. We study marginal mean models fit with generalized estimating equations for assessing treatment effectiveness in stepped wedge cluster randomized trials. This approach has advantages over the more commonly used mixed models that (1) the population-average parameters have an important interpretation for public health applications and (2) they avoid untestable assumptions on latent variable distributions and avoid parametric assumptions about error distributions, therefore, providing more robust evidence on treatment effects. However, cluster randomized trials typically have a small number of clusters, rendering the standard generalized estimating equation sandwich variance estimator biased and highly variable and hence yielding incorrect inferences. We study the usual asymptotic generalized estimating equation inferences (i.e., using sandwich variance estimators and asymptotic normality) and four small-sample corrections to generalized estimating equation for stepped wedge cluster randomized trials and for parallel cluster randomized trials as a comparison. We show by simulation that the small-sample corrections provide improvement, with one correction appearing to provide at least nominal coverage even with only 10 clusters per group. These results demonstrate the viability of the marginal mean approach for both stepped wedge and parallel cluster randomized trials. We also study the comparative performance of the corrected methods for stepped wedge and parallel designs, and describe how the methods can accommodate interval censoring of individual failure times and incorporate semiparametric efficient estimators.

Improving causal inference with a doubly robust estimator that combines propensity score stratification and weighting.

RATIONALE, AIMS AND OBJECTIVES: When a randomized controlled trial is not feasible, health researchers typically use observational data and rely on statistical methods to adjust for confounding when estimating treatment effects. These methods generally fall into 3 categories: (1) estimators based on a model for the outcome using conventional regression adjustment; (2) weighted estimators based on the propensity score (ie, a model for the treatment assignment); and (3) "doubly robust" (DR) estimators that model both the outcome and propensity score within the same framework. In this paper, we introduce a new DR estimator that utilizes marginal mean weighting through stratification (MMWS) as the basis for weighted adjustment. This estimator may prove more accurate than treatment effect estimators because MMWS has been shown to be more accurate than other models when the propensity score is misspecified. We therefore compare the performance of this new estimator to other commonly used treatment effects estimators. METHOD: Monte Carlo simulation is used to compare the DR-MMWS estimator to regression adjustment, 2 weighted estimators based on the propensity score and 2 other DR methods. To assess performance under varied conditions, we vary the level of misspecification of the propensity score model as well as misspecify the outcome model. RESULTS: Overall, DR estimators generally outperform methods that model one or the other components (eg, propensity score or outcome). The DR-MMWS estimator outperforms all other estimators when both the propensity score and outcome models are misspecified and performs equally as well as other DR estimators when only the propensity score is misspecified. CONCLUSIONS: Health researchers should consider using DR-MMWS as the principal evaluation strategy in observational studies, as this estimator appears to outperform other estimators in its class.

Combining machine learning and propensity score weighting to estimate causal effects in multivalued treatments.

RATIONALE, AIMS AND OBJECTIVES: Interventions with multivalued treatments are common in medical and health research; examples include comparing the efficacy of competing interventions and contrasting various doses of a drug. In recent years, there has been growing interest in the development of methods that estimate multivalued treatment effects using observational data. This paper extends a previously described analytic framework for evaluating binary treatments to studies involving multivalued treatments utilizing a machine learning algorithm called optimal discriminant analysis (ODA). METHOD: We describe the differences between regression-based treatment effect estimators and effects estimated using the ODA framework. We then present an empirical example using data from an intervention including three study groups to compare corresponding effects. RESULTS: The regression-based estimators produced statistically significant mean differences between the two intervention groups, and between one of the treatment groups and controls. In contrast, ODA was unable to discriminate between distributions of any of the three study groups. CONCLUSIONS: Optimal discriminant analysis offers an appealing alternative to conventional regression-based models for estimating effects in multivalued treatment studies because of its insensitivity to skewed data and use of accuracy measures applicable to all prognostic analyses. If these analytic approaches produce consistent treatment effect P values, this bolsters confidence in the validity of the results. If the approaches produce conflicting treatment effect P values, as they do in our empirical example, the investigator should consider the ODA-derived estimates to be most robust, given that ODA uses permutation P values that require no distributional assumptions and are thus, always valid.

Combining propensity score-based stratification and weighting to improve causal inference in the evaluation of health care interventions.

When a randomized controlled trial is not feasible, a key strategy in observational studies is to ensure that intervention and control groups are comparable on observed characteristics and assume that the remaining unmeasured characteristics will not bias the results. In the past few years, propensity score-based techniques such as matching, stratification and weighting have become increasingly popular for evaluating health care interventions. Recently, marginal mean weighting through stratification (MMWS) has been introduced as a flexible pre-processing approach that combines the salient features of propensity score stratification and weighting to remove imbalances of pre-intervention characteristics between two or more groups under study. The weight is then used within the appropriate outcome model to provide unbiased estimates of treatment effects. In this paper, the MMWS technique is introduced by illustrating its implementation in three typical experimental conditions: a binary treatment (treatment versus control), an ordinal level treatment (varying doses) and nominal treatments (multiple independent arms). These methods are demonstrated in the context of health care evaluations by examining the pre-post difference in hospitalizations following the implementation of a disease management program for patients with congestive heart failure. Because of the flexibility and wide application of MMWS, it should be considered as an alternative procedure for use with observational data to evaluate the effectiveness of health care interventions.