## Abstract

Original language | English |
---|---|

Pages (from-to) | 1166-1183 |

Number of pages | 18 |

Journal | Biometrical Journal |

Volume | 59 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2017 |

## Keywords

- Cure fraction
- Mixed models
- Repeated measures
- Spatial frailty
- Time-to-event analysis

## Access to Document

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*Biometrical Journal*,

*59*(6), 1166-1183. https://doi.org/10.1002/bimj.201600159

**Joint analysis of longitudinal and survival AIDS data with a spatial fraction of long-term survivors: A Bayesian approach**. In: Biometrical Journal. 2017 ; Vol. 59, No. 6. pp. 1166-1183.

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*Biometrical Journal*, vol. 59, no. 6, pp. 1166-1183. https://doi.org/10.1002/bimj.201600159

**Joint analysis of longitudinal and survival AIDS data with a spatial fraction of long-term survivors: A Bayesian approach.**/ Martins, R.; Silva, G.L.; Andreozzi, V.

In: Biometrical Journal, Vol. 59, No. 6, 2017, p. 1166-1183.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Joint analysis of longitudinal and survival AIDS data with a spatial fraction of long-term survivors: A Bayesian approach

AU - Martins, R.

AU - Silva, G.L.

AU - Andreozzi, V.

N1 - Export Date: 11 December 2017 Correspondence Address: Martins, R.; Centro de Investigação Interdisciplinar Egas Moniz (CiiEM), Escola Superior de Saúde Egas Moniz, Quinta da Granja, Monte de CaparicaPortugal; email: ruimartins@egasmoniz.edu.pt References: Andrinopoulou, E.-R., Rizopoulos, D., Takkenberg, J., Lesaffre, E., Combined dynamic predictions using joint models of two longitudinal outcomes and competing risk data (2015) Statistical Methods in Medical Research, , https://doi.org/10.1177/0962280215588340; Banerjee, S., Carlin, B., Gelfand, A., (2004) Hierarchical Modeling and Analysis for Spatial Data, , Chapman & Hall/CRC, Boca Raton, FL; Berkson, J., Gage, R., Survival curve for cancer patients following treatment (1952) Journal of the American Statistical Association, 47, pp. 501-515; Besag, J., York, J., Mollie, A., Bayesian image restoration with two application in spatial statistics (1991) Annals of the Institute of Statistical Mathematics, 43, pp. 1-59; Brezger, A., Lang, S., Generalized structured additive regression based on Bayesian P-splines (2006) Computational Statistics and Data Analysis, 50, pp. 967-991; Brown, E.R., Ibrahim, J.G., Bayesian approaches to joint cure-rate and longitudinal models with applications to cancer vaccine trials (2003) Biometrics, 59, pp. 686-693; Brown, E.R., Ibrahim, J.G., DeGruttola, V., A flexible B-spline model for multiple longitudinal biomarkers and survival (2005) Biometrics, 61, pp. 64-73; Chen, M., Ibrahim, J., Sinha, D., A new Bayesian model for survival data with a surviving fraction (1999) Journal of the American Statistical Association, 94, pp. 909-919; Chen, M.H., Ibrahim, J.G., Sinha, D., A new joint model for longitudinal and survival data with a cure fraction (2004) Journal of Multivariate Analysis, 91, pp. 18-34; Christensen, R., Johnson, W., Branscum, A., Hanson, T., (2011) Bayesian Ideas and Data Analysis—An Introduction for Scientists and Statisticians, , CRC Press, Boca Raton, FL; Cooner, F., Banerjee, S., Carlin, B., Sinha, D., Flexible cure rate modeling under latent activation schemes (2007) Journal of the American Statistical Association, 102, pp. 560-572; Cooner, F., Banerjee, S., McBean, A.M., Modelling geographically referenced survival data with a cure fraction (2006) Statistical Methods in Medical Research, 15, pp. 307-324; Deapen, D., Cockburn, M., Pinder, R., Lu, S., Wohl, A., Population-based linkage of AIDS and cancer registries (2007) American Journal of Preventive Medicine, 33, pp. 134-136; Eilers, P., Marx, B., Flexible smoothing with B-splines and penalties (1996) Statistical Science, 11, pp. 89-102; Eilers, P., Marx, B., (2004) Splines, knots and penalties, , Technical report, Department of Medical Statistics, Leiden University Medical Center; Ewell, M., Ibrahim, J., The large sample distribution of the weighted log rank statistic under general local alternatives (1997) Lifetime Data Analysis, 3, pp. 5-12; Farewell, V., The use of mixture models for the analysis of survival data with long-term survivors (1982) Biometrics, 38, pp. 1041-1046; Farewell, V., Mixture models in survival analysis: are they worth the risk (1986) Canadian Journal of Statistics, 14, pp. 257-262; Faucett, C.L., Thomas, D.C., Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach (1996) Statistics in Medicine, 15, pp. 1663-1685; Fonseca, M., Lucena, F., Veloso, V., Carvalho, M., Accuracy of a probabilistic record linkage strategy applied to identify deaths among cases reported to the Brazilian AIDS surveillance database (2010) Cad. Saúde Pública [online], 26, pp. 1431-1438; Geisser, S., Eddy, W., A predictive approach to model selection (1979) Journal of the American Statistical Association, 74, pp. 153-160; Gelfand, A., Dey, D., Bayesian model choice: asymptotic and exact calculations (1994) Journal of the Royal Statistical Society Series B, 56, pp. 501-514; Gelman, A., Prior distributions for variance parameters in hierarchical models (Comment on Article by Browne and Draper) (2006) Bayesian Analysis, 1, pp. 515-534; Gray, R., Tsiatis, A., A linear rank test for use when the main interest is in differences in cure rates (1989) Biometrics, 45, pp. 899-904; Griffin, J.E., Brown, P., (2007) Bayesian adaptive lassos with non-convex penalization, , Technical Report 07–02, University of Warwick; Gu, Y., Sinha, D., Banerjee, S., Analysis of cure rate survival data under proportional odds model (2011) Lifetime Data Analysis, 17, pp. 123-134; Jackman, S., Bayesian Analysis for the Social Sciences (2009) Wiley Series in Probability and Statistics, , John Wiley & Sons, Ltd; Kelsall, J., Wakefield, J., Discussion of “Bayesian models for spatially correlated disease and exposure data (1999) Sixth Valencia International Meeting on Bayesian Statistics, , by, Best, N. G., In, Bernardo, J., Berger, J., Dawid, A., Smith, A., (Eds.),, Oxford University Press, London, UK; Kim, S., Chen, M.-H., Dey, D., A new threshold regression model for survival data with a cure fraction (2011) Lifetime Data Analysis, 17, pp. 101-122; Klein, N., Kneib, T., Scale-dependent priors for variance parameters in structured additive distributional regression (2016) Bayesian Analysis, 11, pp. 1071-1106; Lang, S., Brezger, A., Bayesian P-splines (2004) Journal of Computational and Graphical Statistics, 13, pp. 183-212; Lunn, D., Thomas, A., Best, N., Spiegelhalter, D., WinBUGS— A Bayesian modelling framework: concepts, structure, and extensibility (2000) Statistics and Computing, 10, pp. 325-337; May, M., Gompels, M., Delpech, V., Impact on life expectancy of HIV-1 positive individuals of CD4+ cell count and viral load response to antiretroviral therapy (2014) AIDS, 28, pp. 1193-1202; McLain, A.C., Lum, K.J., Sundaram, R., A joint mixed effects dispersion model for menstrual cycle length and time-to-pregnancy (2012) Biometrics, 68, pp. 648-656; McManus, H., O'Connor, C., Boyd, M., Broom, J., Russell, D., Long-term survival in HIV positive patients with up to 15 years of antiretroviral therapy (2012) PLoS ONE, 7; Musoro, J.Z., Geskus, R.B., Zwinderman, A.H., A joint model for repeated events of different types and multiple longitudinal outcomes with application to a follow-up study of patients after kidney transplant (2015) Biometrical Journal, 57, pp. 185-200; Nakagawa, F., Lodwick, R., Smith, C., Smith, R., Cambiano, V., Projected life expectancy of people with HIV according to timing of diagnosis (2012) AIDS, 26, pp. 335-343; Pan, J., Bao, Y., Dai, H., Fang, H.-B., Joint longitudinal and survival-cure models in tumour xenograft experiments (2014) Statistics in Medicine, 33, pp. 3229-3240; Proust-Lima, C., Taylor, J.G.G., Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: a joint modeling approach (2009) Biostatistics, 10, pp. 535-549; Rao, C., (1973) Linear Statistical Inference and Its Applications, , (2nd edn.)., Wiley, New York, NY; Rizopoulos, D., Dynamic predictions and prospective accuracy in joint models for longitudinal and time-to-event data (2011) Biometrics, 67, pp. 819-829; Rizopoulos, D., Ghosh, P., A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event (2011) Statistics in Medicine, 30, pp. 1366-1380; Samji, H., Cescon, A., Hogg, R., Modur, S., Althoff, K.N., Closing the gap: increases in life expectancy among treated HIV-positive individuals in the United States and Canada (2013) PLoS ONE, 8; Souza-Jr, P.R.B., Szwarcwald, C.L., Castilho, E.A., Delay in introducing antiretroviral therapy in patients infected by HIV in Brazil, 2003–2006 (2007) Clinical Science, 62, pp. 579-584; Spiegelhalter, D., Thomas, A., Best, N., Lunn, D., (2003) WinBUGS Version 1.4 User Manual, , MRC Biostatistics Unit, Cambridge, UK; Stangl, D., Greenhouse, J., Assessing placebo response using Bayesian hierarchical survival models (1998) Lifetime Data Analysis, 4, pp. 5-28; Sweeting, M., Thompson, S., Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture (2011) Biometrical Journal, 53, pp. 750-763; Temple, R., Are surrogate markers adequate to assess cardiovascular disease drugs (1999) The Journal of the American Medical Association, 282, pp. 790-795; Tournoud, M., Ecochard, R., Application of the promotion time cure model with time-changing exposure to the study of HIV/AIDS and other infectious diseases (2007) Statistics in Medicine, 26, pp. 1008-1021; Tsodikov, A.D., Müller, W.A., Modeling carcinogenesis under a time-changing exposure (1998) Mathematical Biosciences, 152, pp. 179-191; Van Sighem, A., Gras, L., Reiss, P., Brinkman, K., de Wolf, F., Life expectancy of recently diagnosed asymptomatic HIV-infected patients approaches that of uninfected individuals (2010) AIDS, 24, pp. 1527-1535; Watanabe, S., Asymptotic equivalence of Bayes cross validation and widely applicable information criterion in singular learning theory (2010) Journal of Machine Learning Research, 11, pp. 3571-3591; Wulfsohn, M., Tsiatis, A., A joint model for survival and longitudinal data measured with error (1997) Biometrics, 53, pp. 330-339; Yakovlev, A., Asselain, B., Bardou, V.-J., Fourquet, A., Hoang, T., A simple stochastic model of tumor recurrence and its application to data on premenopausal breast cancer (1993) Biometrie et Analyse de Donnees Spatio-Temporelles, 12, pp. 66-82. , In, Société Française de Biométrie, ENSA Rennes, France; Yu, M., Law, N., Taylor, J., Sandler, H., Joint longitudinal-survival-cure models and their application to prostate cancer (2004) Statistica Sinica, 14, pp. 835-862; Zhang, S., Müller, P., Do, K.-A., A Bayesian semiparametric survival model with longitudinal markers (2010) Biometrics, 66, pp. 435-443

PY - 2017

Y1 - 2017

N2 - A typical survival analysis with time-dependent covariates usually does not take into account the possible random fluctuations or the contamination by measurement errors of the variables. Ignoring these sources of randomness may cause bias in the estimates of the model parameters. One possible way for overcoming that limitation is to consider a longitudinal model for the time-varying covariates jointly with a survival model for the time to the event of interest, thereby taking advantage of the complementary information flowing between these two-model outcomes. We employ here a Bayesian hierarchical approach to jointly model spatial-clustered survival data with a fraction of long-term survivors along with the repeated measurements of CD4+ T lymphocyte counts for a random sample of 500 HIV/AIDS individuals collected in all the 27 states of Brazil during the period 2002–2006. The proposed Bayesian joint model comprises two parts: on the one hand, a flexible model using Penalized Splines to better capture the nonlinear behavior of the different CD4 profiles over time; on the other hand, a spatial cure model to cope with the set of long-term survivor individuals. Our findings show that joint models considering this set of patients were the ones with the best performance comparatively to the more traditional survival approach. Moreover, the use of spatial frailties allowed us to map the heterogeneity in the disease risk among the Brazilian states. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

AB - A typical survival analysis with time-dependent covariates usually does not take into account the possible random fluctuations or the contamination by measurement errors of the variables. Ignoring these sources of randomness may cause bias in the estimates of the model parameters. One possible way for overcoming that limitation is to consider a longitudinal model for the time-varying covariates jointly with a survival model for the time to the event of interest, thereby taking advantage of the complementary information flowing between these two-model outcomes. We employ here a Bayesian hierarchical approach to jointly model spatial-clustered survival data with a fraction of long-term survivors along with the repeated measurements of CD4+ T lymphocyte counts for a random sample of 500 HIV/AIDS individuals collected in all the 27 states of Brazil during the period 2002–2006. The proposed Bayesian joint model comprises two parts: on the one hand, a flexible model using Penalized Splines to better capture the nonlinear behavior of the different CD4 profiles over time; on the other hand, a spatial cure model to cope with the set of long-term survivor individuals. Our findings show that joint models considering this set of patients were the ones with the best performance comparatively to the more traditional survival approach. Moreover, the use of spatial frailties allowed us to map the heterogeneity in the disease risk among the Brazilian states. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

KW - Cure fraction

KW - Mixed models

KW - Repeated measures

KW - Spatial frailty

KW - Time-to-event analysis

U2 - 10.1002/bimj.201600159

DO - 10.1002/bimj.201600159

M3 - Article

C2 - 28464317

SN - 0323-3847

VL - 59

SP - 1166

EP - 1183

JO - Biometrical Journal

JF - Biometrical Journal

IS - 6

ER -