Local Box–Cox transformation on time-varying parametric models for smoothing estimation of conditional CDF with longitudinal data

ABSTRACT

Nonparametric estimation and inferences of conditional distribution functions with longitudinal data have important applications in biomedical studies, such as epidemiological studies and longitudinal clinical trials. Estimation approaches without any structural assumptions may lead to inadequate and numerically unstable estimators in practice. We propose in this paper a nonparametric approach based on time-varying parametric models for estimating the conditional distribution functions with a longitudinal sample. Our model assumes that the conditional distribution of the outcome variable at each given time point can be approximated by a parametric model after local Box–Cox transformation. Our estimation is based on a two-step smoothing method, in which we first obtain the raw estimators of the conditional distribution functions at a set of disjoint time points, and then compute the final estimators at any time by smoothing the raw estimators. Applications of our two-step estimation method have been demonstrated through a large epidemiological study of childhood growth and blood pressure. Finite sample properties of our procedures are investigated through a simulation study. Application and simulation results show that smoothing estimation from time-variant parametric models outperforms the existing kernel smoothing estimator by producing narrower pointwise bootstrap confidence band and smaller root mean squared error.

KEYWORDS:

• Conditional distributions
• local polynomials
• longitudinal data
• time-dependent parameters
• time-varying parametric models
• two-step smoothing

2010 AMS SUBJECT CLASSIFICATION:

• 62G08

Acknowledgements

We would like to thank the National Hearth, Lung and Blood Institute (NHLBI) for providing us the NGHS (National Growth and Health Study) data.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The NGHS was supported by contract #NO1-HC-55023-26 and grant #U01-HL48941-44 from the NHLBI.