Although the lymphatic system is clearly linked to the metastasis of most human carcinomas, the mechanisms by which lymphangiogenesis occurs in response to the presence of carcinoma remain unclear. Hierarchical models are presented to investigate the properties of lymphatic vessel production in 2997 fields taken from 20 individuals with invasive carcinoma, 21 individuals with cervical intraepithelial neoplasia and 21 controls. Such data demonstrate a high degree of correlation within tumour samples from the same individual. Joint hierarchical models utilising shared random effects are discussed and fitted in a Bayesian framework to allow for the correlation between two key outcome measures: a random cluster size (the number of lymphatic vessels in a tissue sample) and a continuous outcome (vessel size). Results show that invasive carcinoma samples are associated with increased production of smaller and more irregularly-shaped lymphatic vessels and suggest a mechanistic link between carcinoma of the cervix and lymphangiogenesis.
References
Carter, B. (2010). Cluster size variability and imbalance in cluster randomized controlled trials. Stat. Med. 29 2984–2993. MR2758393 10.1002/sim.4050Carter, B. (2010). Cluster size variability and imbalance in cluster randomized controlled trials. Stat. Med. 29 2984–2993. MR2758393 10.1002/sim.4050
Catalano, P. J. and Ryan, L. M. (1992). Bivariate latent variable models for clustered discrete and continuous outcomes. J. Amer. Statist. Assoc. 87 651–658.Catalano, P. J. and Ryan, L. M. (1992). Bivariate latent variable models for clustered discrete and continuous outcomes. J. Amer. Statist. Assoc. 87 651–658.
Chapman, C. M., Fanshawe, T. R. and Crick, T. (2013). An investigation into the changes of lymphatic vessel density due to invasive carcinoma and cervical intraepithelial lesions of the uterine cervix. Morecambe Bay Medical Journal 6 355–359.Chapman, C. M., Fanshawe, T. R. and Crick, T. (2013). An investigation into the changes of lymphatic vessel density due to invasive carcinoma and cervical intraepithelial lesions of the uterine cervix. Morecambe Bay Medical Journal 6 355–359.
Cong, X. J., Yin, G. and Shen, Y. (2007). Marginal analysis of correlated failure time data with informative cluster sizes. Biometrics 63 663–672. MR2395702 10.1111/j.1541-0420.2006.00730.xCong, X. J., Yin, G. and Shen, Y. (2007). Marginal analysis of correlated failure time data with informative cluster sizes. Biometrics 63 663–672. MR2395702 10.1111/j.1541-0420.2006.00730.x
Dunson, D. B., Chen, Z. and Harry, J. (2003). A Bayesian approach for joint modeling of cluster size and subunit-specific outcomes. Biometrics 59 521–530. MR2004257 10.1111/1541-0420.00062Dunson, D. B., Chen, Z. and Harry, J. (2003). A Bayesian approach for joint modeling of cluster size and subunit-specific outcomes. Biometrics 59 521–530. MR2004257 10.1111/1541-0420.00062
Ferlay, J., Shin, H. R., Bray, F., Forman, D., Mathers, C. and Parkin, D. M. (2008). GLOBOCAN 2008 v2.0, Cancer incidence and mortality worldwide: IARC CancerBase no. 10 [Internet] (accessed 4th March 2013).Ferlay, J., Shin, H. R., Bray, F., Forman, D., Mathers, C. and Parkin, D. M. (2008). GLOBOCAN 2008 v2.0, Cancer incidence and mortality worldwide: IARC CancerBase no. 10 [Internet] (accessed 4th March 2013).
Fitzmaurice, G. M. and Laird, N. M. (1995). Regression models for a bivariate discrete and continuous outcome with clustering. J. Amer. Statist. Assoc. 90 845–852. MR1354003 10.1080/01621459.1995.10476583Fitzmaurice, G. M. and Laird, N. M. (1995). Regression models for a bivariate discrete and continuous outcome with clustering. J. Amer. Statist. Assoc. 90 845–852. MR1354003 10.1080/01621459.1995.10476583
Gao, P., Zhou, G. Y., Yin, G., Liu, Y., Liu, Z. Y., Zhang, J. and Hao, C. Y. (2006). Lymphatic vessel density as a prognostic indicator for patients with stage I cervical carcinoma. Human Pathology 37 719–725.Gao, P., Zhou, G. Y., Yin, G., Liu, Y., Liu, Z. Y., Zhang, J. and Hao, C. Y. (2006). Lymphatic vessel density as a prognostic indicator for patients with stage I cervical carcinoma. Human Pathology 37 719–725.
Goldstein, H., Yang, M., Omar, R., Turner, R. and Thompson, S. (2000). Meta-analysis using multilevel models with an application to the study of class size effects. J. R. Stat. Soc. Ser. C. Appl. Stat. 49 399–412. MR1824548 10.1111/1467-9876.00200Goldstein, H., Yang, M., Omar, R., Turner, R. and Thompson, S. (2000). Meta-analysis using multilevel models with an application to the study of class size effects. J. R. Stat. Soc. Ser. C. Appl. Stat. 49 399–412. MR1824548 10.1111/1467-9876.00200
Gombos, Z., Xu, X., Chu, C. S., Zhang, P. J. and Acs, G. (2005). Peritumoral lymphatic vessel density and vascular endothelial growth factor C expression in early-stage squamous cell carcinoma of the uterine cervix. Clinical Cancer Research 11 8364–8371.Gombos, Z., Xu, X., Chu, C. S., Zhang, P. J. and Acs, G. (2005). Peritumoral lymphatic vessel density and vascular endothelial growth factor C expression in early-stage squamous cell carcinoma of the uterine cervix. Clinical Cancer Research 11 8364–8371.
Gueorguieva, R. V. (2005). Comments about joint modeling of cluster size and binary and continuous subunit-specific outcomes. Biometrics 61 862–867. MR2196176 10.1111/j.1541-020X.2005.00409_1.xGueorguieva, R. V. (2005). Comments about joint modeling of cluster size and binary and continuous subunit-specific outcomes. Biometrics 61 862–867. MR2196176 10.1111/j.1541-020X.2005.00409_1.x
Gueorguieva, R. V. and Agresti, A. (2001). A correlated probit model for joint modeling of clustered binary and continuous reponses. J. Amer. Statist. Assoc. 96 1102–1112. MR1947258 10.1198/016214501753208762Gueorguieva, R. V. and Agresti, A. (2001). A correlated probit model for joint modeling of clustered binary and continuous reponses. J. Amer. Statist. Assoc. 96 1102–1112. MR1947258 10.1198/016214501753208762
Hibbs, A. M., Black, D., Palermo, L., Cnaan, A., Luan, X., Truog, W. E., Walsh, M. C. and Ballard, R. A. (2010). Accounting for multiple births in neonatal and perinatal trials: Systematic review and case study. J. Pediatr. 156 202–208.Hibbs, A. M., Black, D., Palermo, L., Cnaan, A., Luan, X., Truog, W. E., Walsh, M. C. and Ballard, R. A. (2010). Accounting for multiple births in neonatal and perinatal trials: Systematic review and case study. J. Pediatr. 156 202–208.
Ibrahim, J. G., Chu, H. and Chen, L. M. (2010). Basic concepts and methods for joint models of longitudinal and survival data. J. Clin. Oncol. 28 2796–2801.Ibrahim, J. G., Chu, H. and Chen, L. M. (2010). Basic concepts and methods for joint models of longitudinal and survival data. J. Clin. Oncol. 28 2796–2801.
Longatto-Filho, A., Pinheiro, C., Pereira, S. M. M., Etlinger, D., Moreira, M. A. R., Jubé, L. F., Quieroz, G. S., Baltazar, F. and Schmitt, F. C. (2007). Lymphatic vessel density and epithelial D2-40 immunoreactivity in pre-invasive and invasive lesions of the uterine cervix. Gynecologic Oncology 107 45–51.Longatto-Filho, A., Pinheiro, C., Pereira, S. M. M., Etlinger, D., Moreira, M. A. R., Jubé, L. F., Quieroz, G. S., Baltazar, F. and Schmitt, F. C. (2007). Lymphatic vessel density and epithelial D2-40 immunoreactivity in pre-invasive and invasive lesions of the uterine cervix. Gynecologic Oncology 107 45–51.
Lunn, D. J., Thomas, A., Best, N. and Spiegelhalter, D. (2000). WinBUGS—A Bayesian modelling framework: Concepts, structure, and extensibility. Stat. Comput. 10 325–337.Lunn, D. J., Thomas, A., Best, N. and Spiegelhalter, D. (2000). WinBUGS—A Bayesian modelling framework: Concepts, structure, and extensibility. Stat. Comput. 10 325–337.
Ma, R., Jørgensen, B. and Willms, J. D. (2009). Clustered binary data with random cluster sizes: A dual Poisson modelling approach. Stat. Model. 9 137–150. MR2750122 10.1177/1471082X0800900203Ma, R., Jørgensen, B. and Willms, J. D. (2009). Clustered binary data with random cluster sizes: A dual Poisson modelling approach. Stat. Model. 9 137–150. MR2750122 10.1177/1471082X0800900203
Neuhaus, J. M. and McCulloch, C. E. (2011). Estimation of covariate effects in generalized linear mixed models with informative cluster sizes. Biometrika 98 147–162. MR2804216 10.1093/biomet/asq066Neuhaus, J. M. and McCulloch, C. E. (2011). Estimation of covariate effects in generalized linear mixed models with informative cluster sizes. Biometrika 98 147–162. MR2804216 10.1093/biomet/asq066
Panageas, K. S., Schrag, D., Localio, A. R., Venkatraman, E. S. and Begg, C. B. (2007). Properties of analysis methods that account for clustering in volume-outcome studies when the primary predictor is cluster size. Stat. Med. 26 2017–2035. MR2364289 10.1002/sim.2657Panageas, K. S., Schrag, D., Localio, A. R., Venkatraman, E. S. and Begg, C. B. (2007). Properties of analysis methods that account for clustering in volume-outcome studies when the primary predictor is cluster size. Stat. Med. 26 2017–2035. MR2364289 10.1002/sim.2657
Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D. and the R Core team (2008). nlme: Linear and nonlinear mixed effects models. R package version 3.1-89.Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D. and the R Core team (2008). nlme: Linear and nonlinear mixed effects models. R package version 3.1-89.
R Development Core Team (2008). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.R Development Core Team (2008). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
Regan, M. M. and Catalano, P. J. (1999). Likelihood models for clustered binary and continuous outcomes: Application to developmental toxicology. Biometrics 55 760–768.Regan, M. M. and Catalano, P. J. (1999). Likelihood models for clustered binary and continuous outcomes: Application to developmental toxicology. Biometrics 55 760–768.
Ten Have, T. R. and Chinchilli, V. M. (1998). Two-stage negative binomial and overdispersed Poisson models for clustered developmental toxicity data with random cluster size. J. Agric. Biol. Environ. Stat. 3 75–98. MR1817034 10.2307/1400624Ten Have, T. R. and Chinchilli, V. M. (1998). Two-stage negative binomial and overdispersed Poisson models for clustered developmental toxicity data with random cluster size. J. Agric. Biol. Environ. Stat. 3 75–98. MR1817034 10.2307/1400624
Williamson, J. M., Datta, S. and Satten, G. A. (2003). Marginal analyses of clustered data when cluster size is informative. Biometrics 59 36–42. MR1978471 10.1111/1541-0420.00005Williamson, J. M., Datta, S. and Satten, G. A. (2003). Marginal analyses of clustered data when cluster size is informative. Biometrics 59 36–42. MR1978471 10.1111/1541-0420.00005
Zhang, S., Yu, H. and Zhang, L. (2009). Clinical implications of increased lymph vessel density in the lymphatic metastasis of early stage invasive cervical carcinoma: A clinical immunohistochemical method study. BMC Cancer 9 1–6.Zhang, S., Yu, H. and Zhang, L. (2009). Clinical implications of increased lymph vessel density in the lymphatic metastasis of early stage invasive cervical carcinoma: A clinical immunohistochemical method study. BMC Cancer 9 1–6.
