Reviewing of Different Methods for Handling Longitudinal Count data

In this paper, we will review the methods that used to handle longitudinal data in the case of marginal models when inferences about the population average are the primary focus [1] or when future applications of the results require the expectation of the response as a function of the current covariates [7]. We will review the generalized estimating equations method (GEE), quadratic inference functions (QIF), generalized quasi likelihood (GQL) and the generalized method of moments (GMM). These methods will be reviewed by discussing its advantages and disadvantages in more details.

Penalized Quadratic Inference Function-Based Variable Selection for Generalized Partially Linear Varying Coefficient Models with Longitudinal Data

Semiparametric generalized varying coefficient partially linear models with longitudinal data arise in contemporary biology, medicine, and life science. In this paper, we consider a variable selection procedure based on the combination of the basis function approximations and quadratic inference functions with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency, sparsity, and asymptotic normality of the resulting estimators. The finite sample performance of the proposed methods is evaluated through extensive simulation studies and a real data analysis.

Efficient parameter estimation for multivariate accelerated failure time model via the quadratic inference functions method

A popular approach, generalized estimating equations (GEE), has been applied to the multivariate accelerated failure time (AFT) model of the clustered and censored data. However, this method needs to estimate the correlation parameters and calculate the inverse of the correlation matrix. Meanwhile, the efficiency of the parameter estimators is low when the correlation structure is misspecified and/or the marginal distribution is heavy-tailed. This paper proposes using the quadratic inference functions (QIF) with a mixture correlation structure to estimate the coefficients in the multivariate AFT model, which can avoid estimating the correlation parameters and computing the inverse matrix of the correlation matrix. Moreover, the estimator derived from the QIF is consistent and asymptotically normal. Simulation studies indicate that the proposed method outperforms the method based on GEE when the marginal distribution has a heavy tail. Finally, the proposed method is used to analyze a real dataset for illustration.