On semiparametric modelling, estimation and inference for survival data subject to dependent censoring

When modelling survival data, it is common to assume that the survival time $T$ is conditionally independent of the censoring time $C$ given a set of covariates. However, there are numerous situations in which this assumption is not realistic. The goal of this paper is therefore to develop a semiparametric normal transformation model which assumes that, after a proper nonparametric monotone transformation, the vector $(T, C)$ follows a linear model, and the vector of errors in this bivariate linear model follows a standard bivariate normal distribution with a possibly nondiagonal covariance matrix. We show that this semiparametric model is identifiable, and propose estimators of the nonparametric transformation, the regression coefficients and the correlation between the error terms. It is shown that the estimators of the model parameters and the transformation are consistent and asymptotically normal. We also assess the finite-sample performance of the proposed method by comparing it with an estimation method under a fully parametric model. Finally, our method is illustrated using data from the AIDS Clinical Trial Group 175 study.

A semiparametric linear transformation model to estimate causal effects for survival data

Semiparametric linear transformation models serve as useful alternatives to the Cox proportional hazard model. In this study, we use the semiparametric linear transformation model to analyze survival data with selective compliance. We estimate regression parameters and the transformation function based on pseudo-likelihood and a series of estimating equations. We show that the estimators for the regression parameters and transformation function are consistent and asymptotically normal, and both converge to their true values at the rate of n ^-1/2, the convergence rate expected for a parametric model. The practical utility of the methods is confirmed via simulations as well as an application of a clinical trial to evaluate the effectiveness of sentinel node biopsy in guiding the treatment of invasive melanoma.

How to analyze longitudinal multilevel physical activity data with many zeros?

BACKGROUND

Physical activity (PA) is a modifiable lifestyle factor for many chronic diseases with established health benefits. PA outcomes are measured and assessed in many longitudinal studies, but their analyses often pose difficulties due to the presence of many zeros, extreme skewness, and lack of independence, which render standard regression methods inappropriate.

METHODS

A two-part multilevel modeling approach is used to analyze the heterogeneous and correlated PA data. In the first part, a logistic mixed regression model is fitted to estimate the prevalence of PA and factors associated with PA participation over time. For subjects engaging in PA, a gamma mixed regression model is adopted in the second part to assess the effects of predictor variables on the repeated PA outcomes nested within clusters. Extra variations are accommodated within the modeling process by random effects assigned to each cluster and each subject in the cohort.

RESULTS

The findings in a longitudinal multilevel study of a community-based PA intervention for older adults demonstrate the effectiveness of the intervention program and enable the identification of pertinent factors affecting participation and PA levels over time.

CONCLUSIONS

The two-part mixed regression approach provides a practical and statistically valid method to analyze the skewed and correlated PA data with many zeros. The methodology can be extended to handle complex hierarchical or multilevel settings by suitable specification of the covariance structure in the random components, model fitting of which can be performed in STATA using GLLAMM with various user-specified options.