Generalized additive models for cancer mapping with incomplete covariates

Biostatistics

Volumn 5, Issue 2, 2004, Pages 177-191

  French, Jonathan L ^a   Wand, Matthew P ^b  

^a PFIZER INC   (United States)

^b HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Binary response; Expectation Maximization; Generalized linear model; Laplace approximation; Logistic regression; Method of weights; Missing data

Indexed keywords

ALGORITHM; ARTICLE; EPIDEMIOLOGY; GEOGRAPHIC INFORMATION SYSTEM; HUMAN; INCIDENCE; MALE; PROSTATE TUMOR; STATISTICAL ANALYSIS; STATISTICAL MODEL; UNITED STATES;

ALGORITHMS; DATA INTERPRETATION, STATISTICAL; EPIDEMIOLOGIC METHODS; GEOGRAPHIC INFORMATION SYSTEMS; HUMANS; INCIDENCE; MALE; MASSACHUSETTS; MODELS, STATISTICAL; PROSTATIC NEOPLASMS;

EID: 6944234049     PISSN: 14654644     EISSN: None     Source Type: Journal    
DOI: 10.1093/biostatistics/5.2.177     Document Type: Article

References (44)

1. BECK, N. AND JACKMAN, S. (1998). Beyond linearity by default: generalized additive models. American Journal of Political Science 42, 595-627.
2. BEST, N. AND WAKEFIELD, J. (1999). Accounting for inaccuracies in population counts and case registration in cancer mapping. Journal of the Royal Statistical Society, Series A 162, 363-382.
3. BOOTH, J. G. AND HOBERT, J. P. (1999). Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. Journal of the Royal Statistical Society, Series B 61, 265-285.
4. BRESLOW, N. E. AND CLAYTON, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9-25.
5. BRESLOW, N. E. AND DAY, N. E. (1987). Statistical Methods in Cancer Research. Lyon: International Agency for Research on Cancer.
6. BRUMBACK, B. A. AND RICE, J. A. (1998). Smoothing spline models for the analysis of nested and crossed samples of curves. Journal of the American Statistical Association 93, 961-1006.
7. BRUMBACK, B. A., RUPPERT, D. AND WAND, M. P. (1999). Comment on Shively, Kohn, and Wood. Journal of the American Statistical Association 94, 794-797.
8. CRAINICEANU, C., RUPPERT, D., CLAESKENS, G. AND WAND, M. P. (2004). Likelihood ratio tests of polynomial regression against a general alternative. Biometrika, to appear.
9. CRESSIE, N. (1993). Statistics for Spatial Data. New York: Wiley.
10. DAVIS, J. M. AND SPECKMAN, P. (1999). A model for predicting maximum and 8 h average ozone in Houston. Atmospheric Environment 33, 2487-2500.
11. DEMPSTER, A. P., LAIRD, N. M. AND RUBIN, D. B. (1977). Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B 39, 1-38.
12. DIGGLE, P. J., TAWN, J. A. AND MOYEED, R. A. (1998). Model-based geostatistics (Disc: p326-350). Applied Statistics 47, 299-326.
13. ENGELS, E. A., ROSENBERG, P. S. AND BIGGAR, R. J. (1999). Zoster incidence in human immunodeficiency virus-infected hemophiliacs and homosexual men, 1984-1997. Journal of Infectious Diseases 180, 1784-1789.
14. FRENCH, J. L. (2000). Analysis of environmental health data with missing values, Unpublished Sc.D. Thesis.
15. HASTIE, T. J. AND TIBSHIRANI, R. J. (1990). Generalized Additive Models. London: Chapman & Hall.
16. IBRAHIM, J. G. (1990). Incomplete data in generalized linear models. Journal of the American Statistical Association 85, 765-769.
17. IBRAHIM, J. G., CHEN, M.-H. AND LIPSITZ, S. R. (1999a). Monte Carlo EM for missing covariates in parametric regression models. Biometrics 55, 591-596.
18. IBRAHIM, J. G., CHEN, M.-H. AND LIPSITZ, S. R. (2001). Missing responses in generalized linear mixed models when the missing data mechanism is nonignorable. Biometrika 88, 551-564.
19. IBRAHIM, J. G., LIPSITZ, S. R. AND CHEN, M.-H. (1999b). Missing covariates in generalized linear models when the missing data mechanism is nonignorable. Journal of the Royal Statistical Society, Series B 61, 173-190.
20. JAMSHIDIAN, M. AND JENNRICH, R. I. (2000). Standard errors for EM estimation. Journal of the Royal Statistical Society, Series B 62, 257-270.
21. JOHNSON, M. E., MOORE, L. M. AND YLVISAKER, D. (1990). Minimax and maximin distance designs. Journal of Statistical Planning and Inference 26, 131-148.
22. JONES, M. P. (1996). Indicator and stratification methods for missing explanatory variables in multiple linear regression. Journal of the American Statistical Association 91, 222-230.
23. KAMMANN, E. E. AND WAND, M. P. (2003). Geoadditive models. Applied Statistics 52, 1-18.
24. KELSALL, J. E. AND DIGGLE, P. J. (1998). Spatial variation in risk of disease: a nonparametric binary regression approach. Applied Statistics 47, 559-573.
25. LIN, X. AND ZHANG, D. (1999). Inference in generalized additive mixed models by using smoothing splines. Journal of the Royal Statistical Society, Series B 61, 381-400.
26. LINTON, O. B. AND HÄRDLE, W. (1996). Estimation of additive regression models with known links. Biometrika 83, 529-540.
27. LIPSITZ, S. R. AND IBRAHIM, J. G. (1996). A conditional model for incomplete covariates in parametric regression models. Biometrika 83, 916-922.
28. LITTLE, R. J. A AND RUBIN, D. B. (1987). Statistical Analysis with Missing Data. New York: Wiley.
29. LOUIS, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B 44, 226-233.
30. MASSACHUSETTS DEPARTMENT OF PUBLIC HEALTH (1997). Cancer Incidence in Massachusetts 1987-1994: City/Town Supplement. Boston, MA: MDPH.
31. McCULLOCH, C. E. (1997). Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association 92, 162-170.
32. MENG, X. L. AND RUBIN, D. B. (1991). Using the EM algorithm to obtain asymptotic variance-covariance matrices: the SEM algorithm. Journal of the American Statistical Association 86, 899-909.
33. NYCHKA, D. AND SALTZMAN, N. (1998). Design of air quality monitoring networks. In D., Nychka, Cox, L. and Piegorschs, W. (eds), Case Studies in Environmental Statistics, New York: Springer.
34. NYCHKA, D., HAALAND, P., O'CONNELL, M. AND ELLNER, S. (1998). FUNFITS, data analysis and statistical tools for estimating functions. In Nychka, D., Piegorsch, W. W. and Cox, L. H. (eds), Case Studies in Environmental Statistics, New York: Springer.
35. ROLAND, J., KEYGHOBADI, N. AND FOWNES, S. (2000). Alpine Pamassius butterfly dispersal: effects of landscape and population size. Ecology 81, 1642-1653.
36. SCHWARTZ, J. (1997). Air pollution and hospital admissions for cardiovascular disease in Tuscon. Epidemiology 8, 371-377.
37. STEELE, B. M. (1996). A modified EM algorithm for estimation in generalized mixed models. Biometrics 52, 1295-1310.
38. STEIN, M. L. (1999). Statistical Interpolation of Spatial Data: Some Theory for Kriging. New York: Springer.
39. TIERNEY, L., KASS, R. E. AND KADANE, J. B. (1989). Fully exponential Laplace approximations to expectations and variances of nonpositive functions. Journal of the American Statistical Association 84, 710-716.
40. VERBYLA, A., CULLIS, B. R., KENWARD, M. G. AND WELHAM, S. J. (1999). The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion). Applied Statistics 48, 269-300.
41. WAHBA, G. (1990). Spline Models for Observational Data. Philadelphia, PA: SIAM.
42. WALKER, S. (1996). An EM algorithm for nonlinear random effects models. Biometrics 52, 934-944.
43. WANG, Y. (1998). Smoothing spline models with correlated random errors. Journal of the American Statistical Association 93, 341-348.
44. WEI, G. C. G. AND TANNER, M. A. (1990). A Monte Carlo implementation of the EM algorithm and the poor man's data augmentation algorithms. Journal of the American Statistical Association 85, 699-704.