Linear regression with a randomly censored covariate: application to an Alzheimer's study

The association between maternal age of onset of dementia and amyloid deposition (measured by in vivo positron emission tomography (PET) imaging) in cognitively normal older offspring is of interest. In a regression model for amyloid, special methods are required due to the random right censoring of the covariate of maternal age of onset of dementia. Prior literature has proposed methods to address the problem of censoring due to assay limit of detection, but not random censoring. We propose imputation methods and a survival regression method that do not require parametric assumptions about the distribution of the censored covariate. Existing imputation methods address missing covariates, but not right censored covariates. In simulation studies, we compare these methods to the simple, but inefficient complete case analysis, and to thresholding approaches. We apply the methods to the Alzheimer's study.

[1]  J. Morris.  The Clinical Dementia Rating (CDR) , 1993, Neurology.

[2]  J. Schafer.  Multiple imputation: a primer , 1999, Statistical methods in medical research.

[3]  C. Eisdorfer,et al.  A comparison of familial and sporadic Alzheimer's disease , 1993, Neurology.

[4]  Haitao Chu,et al.  Linear Regression With an Independent Variable Subject to a Detection Limit , 2010, Epidemiology.

[5]  D. Marin,et al.  Variability of familial risk of Alzheimer disease across the late life span. , 2005, Archives of general psychiatry.

[6]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[7]  S. Santi,et al.  Structural brain changes in normal individuals with a maternal history of Alzheimer's , 2011, Neurobiology of Aging.

[8]  Cathi B. Propper,et al.  Familial patterns of risk in very late-onset Alzheimer disease. , 2003, Archives of general psychiatry.

[9]  Gina D'Angelo,et al.  An index approach for the Cox model with left censored covariates , 2008, Statistics in medicine.

[10]  Robert Gray,et al.  A Proportional Hazards Model for the Subdistribution of a Competing Risk , 1999 .

[11]  Roderick J. A. Little.  Regression with Missing X's: A Review , 1992 .

[12]  Enrique F Schisterman,et al.  The limitations due to exposure detection limits for regression models. , 2006, American journal of epidemiology.

[13]  Peter C Austin,et al.  Estimating linear regression models in the presence of a censored independent variable , 2004, Statistics in medicine.

[14]  Keith A. Johnson,et al.  Multiple imputation of a randomly censored covariate improves logistic regression analysis , 2016, Journal of applied statistics.

[15]  P. Zandi,et al.  Incidence of AD may decline in the early 90s for men, later for women , 2002, Neurology.

[16]  Michael G Kenward,et al.  Multiple imputation: current perspectives , 2007, Statistical methods in medical research.

[17]  James M. Robins,et al.  Estimation in Partially Linear Models With Missing Covariates , 2004 .

[18]  James M. Robins,et al.  Large-sample theory for parametric multiple imputation procedures , 1998 .

[19]  H. Lynn,et al.  Maximum likelihood inference for left-censored HIV RNA data. , 2001, Statistics in medicine.

[20]  Somnath Datta,et al.  Estimating the mean life time using right censored data , 2005 .

[21]  Roger A. Sugden,et al.  Multiple Imputation for Nonresponse in Surveys , 1988 .

[22]  L H Moulton,et al.  A mixture model with detection limits for regression analyses of antibody response to vaccine. , 1995, Biometrics.

[23]  K. Davis,et al.  Genetic epidemiological study of maternal and paternal transmission of Alzheimer's disease. , 1999, American journal of medical genetics.

[24]  Z. Ying,et al.  Checking the Cox model with cumulative sums of martingale-based residuals , 1993 .

[25]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[26]  Bin Nan,et al.  Semiparametric approach to regression with a covariate subject to a detection limit , 2016 .

[27]  R. Honea,et al.  Reduced gray matter volume in normal adults with a maternal family history of Alzheimer disease , 2010, Neurology.

[28]  Reisa A. Sperling,et al.  Maternal dementia age at onset in relation to amyloid burden in non-demented elderly offspring , 2016, Neurobiology of Aging.

[29]  S. Folstein,et al.  "Mini-mental state". A practical method for grading the cognitive state of patients for the clinician. , 1975, Journal of psychiatric research.

[30]  H. Toutenburg,et al.  Parametric and Nonparametric Regression with Missing X’s—A Review , 2002 .

[31]  D. Geschwind,et al.  Middle-Aged Children of Alzheimer Parents, A Pilot Study: Stable Neurocognitive Performance at 20-Year Follow-up , 2005, Journal of geriatric psychiatry and neurology.

[32]  Rachel L. Mistur,et al.  Maternal family history of Alzheimer's disease predisposes to reduced brain glucose metabolism , 2007, Proceedings of the National Academy of Sciences.

[33]  H. Chu,et al.  Maximum likelihood estimation in generalized linear models with multiple covariates subject to detection limits , 2011, Statistics in medicine.

[34]  V. Leirer,et al.  Development and validation of a geriatric depression screening scale: a preliminary report. , 1982, Journal of psychiatric research.

[35]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[36]  Peter C. Austin,et al.  Type I Error Inflation in the Presence of a Ceiling Effect , 2003 .

[37]  C. Kawas.  Clinical practice. Early Alzheimer's disease. , 2003, The New England journal of medicine.

[38]  N. Graff-Radford,et al.  Maternal Transmission of Alzheimer Disease , 2012, Alzheimer disease and associated disorders.

[39]  John X. Morris,et al.  Increased risk of dementia in mothers of Alzheimer's disease cases , 1996, Neurology.

[40]  Joseph J. Ryan,et al.  A screening procedure for estimating premorbid intelligence in the elderly , 1992 .

[41]  A. Ciampi,et al.  Effects of exposure measurement error when an exposure variable is constrained by a lower limit. , 2003, American journal of epidemiology.

[42]  Xingdong Feng,et al.  Multiple Imputation for M-Regression With Censored Covariates , 2012 .

[43]  J. Morris,et al.  Children of Persons With Alzheimer Disease: What Does the Future Hold? , 2008, Alzheimer disease and associated disorders.

[44]  David A. Schoenfeld,et al.  Partial residuals for the proportional hazards regression model , 1982 .

[45]  Thomas M. Stoker,et al.  Bias From Censored Regressors , 2009 .

[46]  Thomas M. Stoker,et al.  Estimation with Censored Regressors: Basic Issues , 2007 .

[47]  S. de Santi,et al.  Increased fibrillar amyloid-β burden in normal individuals with a family history of late-onset Alzheimer’s , 2010, Proceedings of the National Academy of Sciences.