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Functional Linear Regression Models for Nonignorable Missing Scalar Responses.

ABSTRACT: As an important part of modern health care, medical imaging data, which can be regarded as densely sampled functional data, have been widely used for diagnosis, screening, treatment, and prognosis, such as finding breast cancer through mammograms. The aim of this paper is to propose a functional linear regression model for using functional (or imaging) predictors to predict clinical outcomes (e.g., disease status), while addressing missing clinical outcomes. We introduce an exponential tilting semiparametric model to account for the nonignorable missing data mechanism. We develop a set of estimating equations and its associated computational methods for both parameter estimation and the selection of the tuning parameters. We also propose a bootstrap resampling procedure for carrying out statistical inference. Under some regularity conditions, we systematically establish the asymptotic properties (e.g., consistency and convergence rate) of the estimates calculated from the proposed estimating equations. Simulation studies and a real data analysis are used to illustrate the finite sample performance of the proposed methods.

SUBMITTER: Li T

PROVIDER: S-EPMC6191855 | biostudies-literature | 2018 Oct

REPOSITORIES: biostudies-literature

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Functional Linear Regression Models for Nonignorable Missing Scalar Responses.

Li Tengfei T Xie Fengchang F Feng Xiangnan X Ibrahim Joseph G JG Zhu Hongtu H

Statistica Sinica 20181001 4

As an important part of modern health care, medical imaging data, which can be regarded as densely sampled functional data, have been widely used for diagnosis, screening, treatment, and prognosis, such as finding breast cancer through mammograms. The aim of this paper is to propose a functional linear regression model for using functional (or imaging) predictors to predict clinical outcomes (e.g., disease status), while addressing missing clinical outcomes. We introduce an exponential tilting s ...[more]

PMID: 30344426

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Project description:The reference evapotranspiration (ETo) is considered one of the primary variables for water resource management, irrigation practices, agricultural and hydro-meteorological studies, and modeling different hydrological processes. Therefore, an accurate prediction of ETo is essential. A large number of empirical methods have been developed by numerous scientists and specialists worldwide to estimate ETo from different climatic variables. The FAO56 Penman-Monteith (PM) is the most accepted and accurate model to estimate ETo in various environments and climatic conditions. However, the FAO56-PM method requires radiation, air temperature, air humidity, and wind speed data. In this study in Adana Plain, which has a Mediterranean climate for the summer growing season, using 22-year daily climatic data, the performance of the FAO56-PM method was evaluated with different combinations of climatic variables when climatic data were missing. Additionally, the performances of Hargreaves-Samani (HS) and HS (A&G) equations were assessed, and multiple linear regression models (MLR) were developed using different combinations of climatic variables. The FAO56-PM method could accurately estimate daily ETo when wind speed (U) and relative humidity (RH) data were unavailable, using the procedures suggested by FAO56 Paper (RMSEs were smaller than 0.4 mm d-1, and percent relative errors (REs) were smaller than 9%). Hargreaves-Samani (A&G) and HS equations could not estimate daily ETo accurately according to the statistical indices (RMSEs = 0.772-0.957 mm d-1; REs (%) = 18.2-22.6; R2 = 0.604-0.686, respectively). On the other hand, MLR models' performance varied according to a combination of different climatic variables. According to t-stat and p values of independent variables for MLR models, solar radiation (Rs) and sunshine hours (n) variables had more effect on estimating ETo than other variables. Therefore, the models that used Rs and n data estimated daily ETo more accurately than the others. RMSE values of the models that used Rs were between 0.288 to 0.529 mm d-1; RE(%) values were between 6.2%-11.5% in the validation process. RMSE values of the models that used n were between 0.457 to 0.750 mm d-1; RE(%) values were between 9.9%-16.3% in the validation process. The models based only on air temperature had the worst performance (RMSE = 1.117 mm d-1; RE(%) = 24.2; R2 = 0.423).

Dataset Information

Functional Linear Regression Models for Nonignorable Missing Scalar Responses.

Publications

Functional Linear Regression Models for Nonignorable Missing Scalar Responses.

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