Standardized Martingale Residuals Applied to Grouped Left Truncated Observations of Dementia Cases
- 87 Downloads
The use of martingale residuals have been proposed for modelchecking and also to get a non-parametric estimate of the effectof an explanatory variable. We apply this approach to an epidemiologicalproblem which presents two characteristics: the data are lefttruncated due to delayed entry in the cohort; the data are groupedinto geographical units (parishes). This grouping suggests anatural way of smoothing the graph of residuals which is to computethe sum of the residuals for each parish. It is also naturalto present a graph with standardized residuals. We derive thevariances of the estimated residuals for left truncated datawhich allows computing the standardized residuals. This methodis applied to the study of dementia in a cohort of old people,and to the possible effect of the concentration of aluminum andsilica in drinking water on the risk of developing dementia.
Unable to display preview. Download preview PDF.
- A. C. Alfrey, G. R. Legendre, W. D. Kaehny, “The dialysis encephalopathy syndrome: possible aluminum intoxication,” N Engl J Med vol. 294 pp. 184-188, 1976.Google Scholar
- P. K. Andersen, Ø. Borgan, R. D. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer-Verlag: New York, 1993.Google Scholar
- W. E. Barlow, R. L. Prentice, “Residuals for relative risk regression,” Biometrika vol. 75 pp. 65-74, 1988.Google Scholar
- J. D. Birchall, J. S. Chappell, “Aluminum, water chemistry and Alzheimer's disease,” Lancet 1989; i pp. 953, 1989.Google Scholar
- D. Commenges, L. Letenneur, P. Joly, A. Alioum and J. F. Dartigues, “Modelling age-specific risk: application to dementia,” Stat Med vol. 17 pp. 1973-1988, 1998.Google Scholar
- D. Commenges and H. Jacqmin-Gadda, “Generalized score test of homogeneity based on correlated random effects model,” J Roy Stat Soc B vol. 59 pp. 157-171, 1997.Google Scholar
- T. R. Fleming and D. P. Harrington, Counting Processes and Survival Analysis, Wiley: New-York, 1991.Google Scholar
- H. Jacqmin-Gadda, D. Commenges, L. Letenneur, J. F. Dartigues, “Silica and aluminum in drinking water and cognitive impairment in the elderly,” Epidemiology vol. 7 pp. 281-285, 1996.Google Scholar
- C. N. Martyn, D. J. Barker, C. Osmond, E. C. Harris, J. A. Edwardson, R. F. Lacey, “Geographical relation between Alzheimer's disease and aluminum in drinking water,” Lancet vol. 1; i pp. 59-62, 1989.Google Scholar
- C. N. Martyn, D. N. Coggon, H. Inskip, R. F. Lacey, W. F. Young, “Aluminum concentrations in drinking water and risk of Alzheimer's disease,” Epidemiology vol. 8 pp. 281-6, 1997.Google Scholar