Mixed-Poisson point process with partially observed covariates: Ecological momentary assessment of smoking

Journal of Applied Statistics

Volumn 39, Issue 4, 2012, Pages 883-899

  Neustifter, Benjamin ^a   Rathbun, Stephen L ^a   Shiffman, Saul ^b  

^a UNIVERSITY OF GEORGIA   (United States)

^b UNIVERSITY OF PITTSBURGH SCHOOL OF MEDICINE   (United States)

Author keywords

behavioral data; estimating equations; hierarchical likelihood; increasing domain asymptotics; point processes; probability sampling

Indexed keywords

EID: 84859208136     PISSN: 02664763     EISSN: 13600532     Source Type: Journal    
DOI: 10.1080/02664763.2011.626848     Document Type: Article

References (53)

1. Andersen, P. K., Klein, J. P., Knudsen, K. and Palacios, R. T. 1997. Estimation of variance in Cox's regression model with shared gamma frailties. Biometrics, 53: 1475-1484.
2. Billingsley, P. 1986. "Probability and Measure". New York: Wiley.
3. Brillinger, D. R. 1975. Statistical inference for stationary point processes. Stochastic Process. Relat. Top, 1: 55-99.
4. Chung, K. L. 1974. A Course in Probability Theory, 2, New York: Academic Press.
5. Cook, R. J. and Lawless, J. F. 2007. "The Statistical Analysis of Recurrent Events". New York: Springer.
6. Cordy, C. B. 1993. An extension of the Horvitz-Thompson theorem to point sampling from a continuous universe. Statist. Probab. Lett, 18: 353-362.
7. Cox, D. R. 1955. Some statistical methods connected with series of events. J. R. Stat. Soc. B, 17: 129-164.
8. Cox, D. R. 1972. "The statistical analysis of dependencies in point processes". In Stochastic Point Processes, Edited by: Lewis, P. A.W. 55-66. New York: Wiley.
9. Cressie, N. 1991. "Statistics for Spatial Data". New York: Wiley.
10. Ferguson, S. G., Shiffman, S. and Gwaltney, C. J. 2006. Does reducing withdrawal severity mediate nicotine patch efficacy? A randomized clinical trial. J. Consult. Clin. Psychol, 74: 1153-1161.
11. Godambe, V. P. and Thompson, M. E. 1974. Estimating equations in the presence of a nuisance parameter. Ann. Statist, 2: 568-571.
12. Guan, Y. and Loh, J. M. 2007. A thinned block bootstrap variance estimation procedure for inhomogenous spatial point patterns. J. Amer. Statist. Assoc, 102: 1377-1386.
13. Ha, I. D. and Lee, Y. 2003. Estimating frailty models via Poisson hierarchical generalized linear models. J. Comput. Graph. Statist, 12: 663-681.
14. Hendersen, R. and Oman, P. 1999. Effect of frailty on marginal regression estimates in survival analysis. J. R. Stat. Soc. B, 61: 367-379.
15. Hougaard, P. 1984. Life table methods for heterogeneous populations: Distributions describing the heterogeneity. Biometrika, 71: 75-83.
16. Kassel, J. D., Stroud, L. R. and Paronis, C. A. 2003. Smoking, stress, and negative affect: Correlation, causation, and context across stages of smoking. Psychol. Bull, 129: 270-304.
17. Krickeberg, K. 1982. "Processus ponctuels en statistique". In Ecole d'Eté de Probabilités de Sainte-Flour X, Edited by: Hennequin, P. L. New York: Springer.
18. Kutoyants, Y. A. 1984. "Parameter Estimation for Stochastic Processes". Berlin: Heldermann Verlag.
19. Lawless, J. F. 1987. Regression methods for Poisson process data. J. Amer. Statist. Assoc, 82: 808-815.
20. Lawless, J. F. 1987. Negative binomial and mixed Poisson regression. Canad. J. Statist, 15: 209-225.
21. Lawless, J. F. and Zhan, M. 1998. Analysis of interval-grouped recurrent-event data using piecewise constant rate functions. Canad. J. Statist, 26: 549-565.
22. Lee, Y. and Nelder, J. A. 1996. Hierarchical generalized linear models. J. R. Stat. Soc. B, 58: 619-678.
23. Lee, Y. and Nelder, J. A. 2001. Hierarchical generalized linear models: A synthesis of generalized linear models, random-effect models and structured dispersions. Biometrika, 88: 987-1006.
24. Liu, L. and Huang, X. L. 2009. Joint analysis of correlated repeated measures and recurrent events processes in the presence of death with application to a study on acquired immune deficiency syndrome. J. R. Stat. Soc. C, 58: 65-81.
25. McCullagh, P. and Nelder, J. A. 1989. Generalized Linear Models, 2, New York: Chapman and Hall.
26. McDermut, W. and Haaga, D. A.F. 1998. Effect of stage of change on cue relativity in continuing smokers. Exp. Clin. Psychopharmacol, 6: 316-324.
27. Rathbun, S. L. and Cressie, N. 1994. Asymptotic properties of estimators for the parameters of spatial inhomogeneous Poisson point processes. Adv. Appl. Probab, 26: 122-154.
28. Rathbun, S. L., Shiffman, S. and Gwaltney, C. J. 2007. Modelling the effects of partially observed covariates on Poisson process intensity. Biometrika, 94: 153-165.
29. Rathbun, S. L., Song, X., Neustifter, B. and Shiffman, S. Probability sampling framework for modeling the impact of time-varying covariates on lifetimes to events. Appl. Statist., in review,
30. Royden, H. L. 2006. "Real Analysis". New York: McMillan Publishing Co.
31. Sayette, M. and Hufford, M. 1994. Effects of cue exposure and deprivation on cognitive resources in smokers. J. Abnorm. Psychol, 103: 812-818.
32. Schoenberg, F. P. 2005. Consistent parametric estimation of the intensity of a spatio-temporal point process. J. Statist. Plann. Inference, 128: 79-93.
33. Shiffman, S. and Waters, A. J. 2004. Negative affect and smoking lapses: A prospective analysis. J. Consult. Clin. Psychol, 72: 192-201.
34. Shiffman, S. and Stone, A. A. 1998. "Ecological momentary assessment: A new tool for behavioral medicine research". In Technology and Methods in Behavioral Medicine, Edited by: Krantz, D. S. and Baum, A. 117-131. Philadelphia: Lawrence Erlbaum Associates.
35. Shiffman, S., Paty, J. A., Gnys, M., Kassel, J. D. and Hickcox, M. 2002. Immediate antecedents of cigarette smoking: An analysis from ecological momentary assessment. J. Abnorm. Psychol, 111: 531-545.
36. Shiffman, S., Scharf, D. M., Shadel, W. G., Gwaltney, C. J., Dang, Q. and Paton, S. M. 2006. Analyzing milestones in smoking cessation: Illustration in a nicotine patch trial in adult smokers. J. Consult. Clin. Psychol, 74: 276-285.
37. Smyth, J., Wonderlich, S., Miltenberger, R., Mitchell, J. and Rorty, M. 2001. The use of ecological momentary assessment approaches in eating disorder research. Int. J. Eat. Disord, 30: 83-95.
38. Stone, A. A. and Shiffman, S. 2002. Capturing momentary, self-report data: A proposal for reporting guidelines. Ann. Behav. Med, 24: 236-243.
39. Stone, A. A., Broderick, J. B., Porter, L. and Kaell, A. T. 1997. The experience of rheumatoid arthritis pain and fatigue: Examining momentary reports and correlates over one week. Arthritis Care Res, 10: 185-193.
40. Stone, A. A., Schwartz, J. E., Neale, J. M., Shiffman, S., Marco, C. A., Hickcox, M., Paty, J., Porter, L. S. and Cruise, L. J. 1998. A comparison of coping assessed by ecological momentary assessment and retrospective recall. J. Pers. Soc. Psychol, 74: 1670-1680.
41. Stone, A. A., Broderick, J. B., Shiffman, S. and Schwartz, J. E. 2004. Understanding recall of weekly pain from a momentary assessment perspective: Absolute agreement, between- and within-person consistency, and judged change in weekly pain. Pain, 107: 61-69.
42. Thall, P. F. 1988. Mixed Poisson likelihood regression models for longitudinal interval count data. Biometrics, 44: 197-209.
43. Tsiatis, A. A. and Davidian, M. 2004. Joint modeling of longitudinal and time-to-event data: An overview. Statist. Sinica, 14: 809-834.
44. Vaupel, J. W., Manton, K. G. and Stallard, E. 1979. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16: 439-454.
45. Waagepetersen, R. 2008. Estimating functions for inhomogenous spatial point processes with incomplete covariate data. Biometrika, 95: 351-363.
46. Warren, C. A. and McDonough, B. E. 1999. Event-related brain potentials as indicators of smoking cue-reactivity. Clin. Neurophysiol, 110: 1570-1584.
47. Wulfsohn, M. S. and Tsiatis, A. A. 1997. A joint model of survival and longitudinal data measured with error. Biometrics, 53: 330-339.
48. Yuan, K.-H. 1997. A theorem on uniform convergence of stochastic functions with applications. J. Multivariate Anal, 62: 100-109.
49. Yuan, K.-H. and Jennrich, R. I. 1998. Asymptotics of estimating equations under natural conditions. J. Multivariate Anal, 65: 245-260.
50. Zeng, D. and Lin, D. Y. 2007. Maximum likelihood estimation in semiparametric regression models with censored data. J. Royal Stat. Soc. B, 69: 507-564.
51. Zeng, D. and Lin, D. Y. 2007. Semiparametric transformation models with random effects for recurrent events. J. Amer. Statist. Assoc, 102: 167-180.
52. Zeng, D. and Lin, D. Y. 2009. Semiparametric transformation models with random effects for joint analysis of recurrent and terminal events. Biometrics, 65: 746-752.
53. Zhang, H. P., Ye, Y. Q., Diggle, P. and Shi, J. 2008. Joint modeling of time series measures and recurrent events and analysis of the effects of air quality on respiratory systems. J. Amer. Statist. Assoc, 103: 48-60.