Biomaterial Database

Non-ignorable missing covariates in generalized linear models. 1999

S R Lipsitz, and J G Ibrahim, and M H Chen, and H Peterson

Department of Biostatistics, Harvard School of Public Health, Boston, MA 02115, USA.

We propose a likelihood method for estimating parameters in generalized linear models with missing covariates and a non-ignorable missing data mechanism. In this paper, we focus on one missing covariate. We use a logistic model for the probability that the covariate is missing, and allow this probability to depend on the incomplete covariate. We allow the covariates, including the incomplete covariate, to be either categorical or continuous. We propose an EM algorithm in this case. For a missing categorical covariate, we derive a closed form expression for the E- and M-steps of the EM algorithm for obtaining the maximum likelihood estimates (MLEs). For a missing continuous covariate, we use a Monte Carlo version of the EM algorithm to obtain the MLEs via the Gibbs sampler. The methodology is illustrated using an example from a breast cancer clinical trial in which time to disease progression is the outcome, and the incomplete covariate is a quality of life physical well-being score taken after the start of therapy. This score may be missing because the patients are sicker, so this covariate could be non-ignorably missing.

UI	MeSH Term	Description	Entries
D009010	Monte Carlo Method	In statistics, a technique for numerically approximating the solution of a mathematical problem by studying the distribution of some random variable, often generated by a computer. The name alludes to the randomness characteristic of the games of chance played at the gambling casinos in Monte Carlo. (From Random House Unabridged Dictionary, 2d ed, 1993)	Method, Monte Carlo
D011788	Quality of Life	A generic concept reflecting concern with the modification and enhancement of life attributes, e.g., physical, political, moral, social environment as well as health and disease.	HRQOL,Health-Related Quality Of Life,Life Quality,Health Related Quality Of Life
D001943	Breast Neoplasms	Tumors or cancer of the human BREAST.	Breast Cancer,Breast Tumors,Cancer of Breast,Breast Carcinoma,Cancer of the Breast,Human Mammary Carcinoma,Malignant Neoplasm of Breast,Malignant Tumor of Breast,Mammary Cancer,Mammary Carcinoma, Human,Mammary Neoplasm, Human,Mammary Neoplasms, Human,Neoplasms, Breast,Tumors, Breast,Breast Carcinomas,Breast Malignant Neoplasm,Breast Malignant Neoplasms,Breast Malignant Tumor,Breast Malignant Tumors,Breast Neoplasm,Breast Tumor,Cancer, Breast,Cancer, Mammary,Cancers, Mammary,Carcinoma, Breast,Carcinoma, Human Mammary,Carcinomas, Breast,Carcinomas, Human Mammary,Human Mammary Carcinomas,Human Mammary Neoplasm,Human Mammary Neoplasms,Mammary Cancers,Mammary Carcinomas, Human,Neoplasm, Breast,Neoplasm, Human Mammary,Neoplasms, Human Mammary,Tumor, Breast
D002986	Clinical Trials as Topic	Works about pre-planned studies of the safety, efficacy, or optimum dosage schedule (if appropriate) of one or more diagnostic, therapeutic, or prophylactic drugs, devices, or techniques selected according to predetermined criteria of eligibility and observed for predefined evidence of favorable and unfavorable effects. This concept includes clinical trials conducted both in the U.S. and in other countries.	Clinical Trial as Topic
D003627	Data Interpretation, Statistical	Application of statistical procedures to analyze specific observed or assumed facts from a particular study.	Data Analysis, Statistical,Data Interpretations, Statistical,Interpretation, Statistical Data,Statistical Data Analysis,Statistical Data Interpretation,Analyses, Statistical Data,Analysis, Statistical Data,Data Analyses, Statistical,Interpretations, Statistical Data,Statistical Data Analyses,Statistical Data Interpretations
D004358	Drug Therapy	The use of DRUGS to treat a DISEASE or its symptoms. One example is the use of ANTINEOPLASTIC AGENTS to treat CANCER.	Chemotherapy,Pharmacotherapy,Therapy, Drug,Chemotherapies,Drug Therapies,Pharmacotherapies,Therapies, Drug
D005260	Female		Females
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D000465	Algorithms	A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.	Algorithm
D016013	Likelihood Functions	Functions constructed from a statistical model and a set of observed data which give the probability of that data for various values of the unknown model parameters. Those parameter values that maximize the probability are the maximum likelihood estimates of the parameters.	Likelihood Ratio Test,Maximum Likelihood Estimates,Estimate, Maximum Likelihood,Estimates, Maximum Likelihood,Function, Likelihood,Functions, Likelihood,Likelihood Function,Maximum Likelihood Estimate,Test, Likelihood Ratio