Statistical Methods in Medical Research最新文献

Clustered current status data frequently occur in many fields of survival studies. Some potential factors related to the hazards of interest cannot be directly observed but are characterized through multiple correlated observable surrogates. In this article, we propose a joint modeling method for regression analysis of clustered current status data with latent variables and potentially informative cluster sizes. The proposed models consist of a factor analysis model to characterize latent variables through their multiple surrogates and an additive hazards frailty model to investigate covariate effects on the failure time and incorporate intra-cluster correlations. We develop an estimation procedure that combines the expectation-maximization algorithm and the weighted estimating equations. The consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the proposed method is assessed via a series of simulation studies. This procedure is applied to analyze clustered current status data from the National Toxicology Program on a tumorigenicity study given by the United States Department of Health and Human Services.

Restricted cubic splines (RCS) allow analysts to model nonlinear relations between continuous covariates and the outcome in a regression model. When using RCS with the Cox proportional hazards model, there is no longer a single hazard ratio for the continuous variable. Instead, the hazard ratio depends on the values of the covariate for the two individuals being compared. Thus, using age as an example, when one assumes a linear relation between age and the log-hazard of the outcome there is a single hazard ratio comparing any two individuals whose age differs by 1 year. However, when allowing for a nonlinear relation between age and the log-hazard of the outcome, the hazard ratio comparing the hazard of the outcome between a 31- and a 30-year-old may differ from the hazard ratio comparing the hazard of the outcome between an 81- and an 80-year-old. We describe four methods to describe graphically the relation between a continuous variable and the outcome when using RCS with a Cox model. These graphical methods are based on plots of relative hazard ratios, cumulative incidence, hazards, and cumulative hazards against the continuous variable. Using a case study of patients presenting to hospital with heart failure and a series of mathematical derivations, we illustrate that the four methods will produce qualitatively similar conclusions about the nature of the relation between a continuous variable and the outcome. Use of these methods will allow for an intuitive communication of the nature of the relation between the variable and the outcome.

Predicting patient survival probabilities based on observed covariates is an important assessment in clinical practice. These patient-specific covariates are often measured over multiple follow-up appointments. It is then of interest to predict survival based on the history of these longitudinal measurements, and to update predictions as more observations become available. The standard approaches to these so-called 'dynamic prediction' assessments are joint models and landmark analysis. Joint models involve high-dimensional parameterizations, and their computational complexity often prohibits including multiple longitudinal covariates. Landmark analysis is simpler, but discards a proportion of the available data at each 'landmark time'. In this work, we propose a 'delayed kernel' approach to dynamic prediction that sits somewhere in between the two standard methods in terms of complexity. By conditioning hazard rates directly on the covariate measurements over the observation time frame, we define a model that takes into account the full history of covariate measurements but is more practical and parsimonious than joint modelling. Time-dependent association kernels describe the impact of covariate changes at earlier times on the patient's hazard rate at later times. Under the constraints that our model (a) reduces to the standard Cox model for time-independent covariates, and (b) contains the instantaneous Cox model as a special case, we derive two natural kernel parameterizations. Upon application to three clinical data sets, we find that the predictive accuracy of the delayed kernel approach is comparable to that of the two existing standard methods.

We describe a novel approach for recovering the underlying parameters of the SIR dynamic epidemic model from observed data on case incidence. We formulate a discrete-time approximation of the original continuous-time model and search for the parameter vector that minimizes the standard least squares criterion function. We show that the gradient vector and matrix of second-order derivatives of the criterion function with respect to the parameters adhere to their own systems of difference equations and thus can be exactly calculated iteratively. Applying our new approach, we estimated a four-parameter SIR model from daily reported cases of COVID-19 during the SARS-CoV-2 Omicron/BA.1 surge of December 2021-March 2022 in New York City. The estimated SIR model showed a tight fit to the observed data, but less so when we excluded residual cases attributable to the Delta variant during the initial upswing of the wave in December. Our analyses of both the real-world COVID-19 data and simulated case incidence data revealed an important problem of weak parameter identification. While our methods permitted for the separate estimation of the infection transmission parameter and the infection persistence parameter, only a linear combination of these two key parameters could be estimated with precision. The SIR model appears to be an adequate reduced-form description of the Omicron surge, but it is not necessarily the correct structural model. Prior information above and beyond case incidence data may be required to sharply identify the parameters and thus distinguish between alternative epidemic models.

In this article, we present a joint modeling approach for zero-inflated longitudinal count measurements and time-to-event outcomes. For the longitudinal sub-model, a mixed effects Hurdle model is utilized, incorporating various distributional assumptions such as zero-inflated Poisson, zero-inflated negative binomial, or zero-inflated generalized Poisson. For the time-to-event sub-model, a Cox proportional hazard model is applied. For the functional form linking the longitudinal outcome history to the hazard of the event, a linear combination is used. This combination is derived from the current values of the linear predictors of Hurdle mixed effects. Some other forms are also considered, including a linear combination of the current slopes of the linear predictors of Hurdle mixed effects as well as the shared random effects. A Markov chain Monte Carlo method is implemented for Bayesian parameter estimation. Dynamic prediction using joint modeling is highly valuable in personalized medicine, as discussed here for joint modeling of zero-inflated longitudinal count measurements and time-to-event outcomes. We assess and demonstrate the effectiveness of the proposed joint models through extensive simulation studies, with a specific emphasis on parameter estimation and dynamic predictions for both over-dispersed and under-dispersed data. We finally apply the joint model to longitudinal microbiome pregnancy and HIV data sets.

The use of propensity score methods has become ubiquitous in causal inference. At the heart of these methods is the positivity assumption. Violation of the positivity assumption leads to the presence of extreme propensity score weights when estimating average causal effects, which affects statistical inference. To circumvent this issue, trimming or truncating methods have been widely used. Unfortunately, these methods require that we pre-specify a threshold. There are a number of alternative methods to deal with the lack of positivity when we estimate the average treatment effect (ATE). However, no other methods exist beyond trimming and truncation to deal with the same issue when the goal is to estimate the average treatment effect on the treated (ATT). In this article, we propose a propensity score weight-based alternative for the ATT, called overlap weighted average treatment effect on the treated. The appeal of our proposed method lies in its ability to obtain similar or even better results than trimming and truncation while relaxing the constraint to choose an a priori threshold (or related measures). The performance of the proposed method is illustrated via a series of Monte Carlo simulations and a data analysis on racial disparities in health care expenditures.

In medical studies, repeated measurements of biomarkers and time-to-event data are often collected during the follow-up period. To assess the association between these two outcomes, joint models are frequently considered. The most common approach uses a linear mixed model for the longitudinal part and a proportional hazard model for the survival part. The latter assumes a linear relationship between the survival covariates and the log hazard. In this work, we propose an extension allowing the inclusion of nonlinear covariate effects in the survival model using Bayesian penalized B-splines. Our model is valid for non-Gaussian longitudinal responses since we use a generalized linear mixed model for the longitudinal process. A simulation study shows that our method gives good statistical performance and highlights the importance of taking into account the possible nonlinear effects of certain survival covariates. Data from patients with a first progression of glioblastoma are analysed to illustrate the method.

The hazard function represents one of the main quantities of interest in the analysis of survival data. We propose a general approach for parametrically modelling the dynamics of the hazard function using systems of autonomous ordinary differential equations (ODEs). This modelling approach can be used to provide qualitative and quantitative analyses of the evolution of the hazard function over time. Our proposal capitalises on the extensive literature on ODEs which, in particular, allows for establishing basic rules or laws on the dynamics of the hazard function via the use of autonomous ODEs. We show how to implement the proposed modelling framework in cases where there is an analytic solution to the system of ODEs or where an ODE solver is required to obtain a numerical solution. We focus on the use of a Bayesian modelling approach, but the proposed methodology can also be coupled with maximum likelihood estimation. A simulation study is presented to illustrate the performance of these models and the interplay of sample size and censoring. Two case studies using real data are presented to illustrate the use of the proposed approach and to highlight the interpretability of the corresponding models. We conclude with a discussion on potential extensions of our work and strategies to include covariates into our framework. Although we focus on examples of Medical Statistics, the proposed framework is applicable in any context where the interest lies in estimating and interpreting the dynamics of the hazard function.

In a recent 12-week smoking cessation trial, varenicline tartrate failed to show significant improvements in enhancing end-of-treatment abstinence when compared with placebo among adolescents and young adults. The original analysis aimed to assess the average effect across the entire population using timeline followback methods, which typically involve overdispersed binomial counts. We instead propose to investigate treatment effect heterogeneity among latent classes of participants using a Bayesian beta-binomial piecewise linear growth mixture model specifically designed to address longitudinal overdispersed binomial responses. Within each class, we fit a piecewise linear beta-binomial mixed model with random changepoints for each study group to detect critical windows of treatment efficacy. Using this model, we can cluster subjects who share similar characteristics, estimate the class-specific mean abstinence trends for each study group, and quantify the treatment effect over time within each class. Our analysis identified two classes of subjects: one comprising high-abstinent individuals, typically young adults and light smokers, in which varenicline led to improved abstinence; and another comprising low-abstinent individuals for whom varenicline showed no discernible effect. These findings highlight the importance of tailoring varenicline to specific participant subgroups, thereby advancing precision medicine in smoking cessation studies.

Approaches to population size estimation are of importance across a wide spectrum of disciplines, especially when census and simple random sampling are impractical. The capture-recapture method and the multiplier-benchmark method are two commonly used approaches that use data that partially capture the target population and overlap in a known way. Due to similarities in required data structures, the approaches are often used interchangeably without a critical appraisal of the underlying assumptions, especially in the two-sample case. Here, we describe the similarities and differences of the sampling mechanisms and assumptions underlying both approaches. We emphasize that the capture-recapture method assumes data sources as random samples and describes two-way inclusion histories, while in multiplier-benchmark method, one source captures a fixed sub-population, and the one-way inclusion histories are modeled. We also discuss the implications of these differences through simulation and real data to guide the choice of method in practice. A careful study of the data structures, relationships, and data generation processes is crucial for assessing the appropriateness of using these methods.