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Published in: Lifetime Data Analysis 3/2019

17-11-2018

Dealing with death when studying disease or physiological marker: the stochastic system approach to causality

Author: Daniel Commenges

Published in: Lifetime Data Analysis | Issue 3/2019

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Abstract

The stochastic system approach to causality is applied to situations where the risk of death is not negligible. This approach grounds causality on physical laws, distinguishes system and observation and represents the system by multivariate stochastic processes. The particular role of death is highlighted, and it is shown that local influences must be defined on the random horizon of time of death. We particularly study the problem of estimating the effect of a factor V on a process of interest Y, taking death into account. We unify the cases where Y is a counting process (describing an event) and the case where Y is quantitative; we examine the case of observations in continuous and discrete time and we study the issue of whether the mechanism leading to incomplete data can be ignored. Finally, we give an example of a situation where we are interested in estimating the effect of a factor (blood pressure) on cognitive ability in elderly.

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Appendix
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Literature
go back to reference Aalen OO, Borgan O, Gjessing H (2008) Survival and event history analysis: a process point of view. Springer, New YorkMATH Aalen OO, Borgan O, Gjessing H (2008) Survival and event history analysis: a process point of view. Springer, New YorkMATH
go back to reference Aalen OO, Cook RJ, Røysland K (2015) Does cox analysis of a randomized survival study yield a causal treatment effect? Lifetime Data Anal 21(4):579–593MathSciNetMATH Aalen OO, Cook RJ, Røysland K (2015) Does cox analysis of a randomized survival study yield a causal treatment effect? Lifetime Data Anal 21(4):579–593MathSciNetMATH
go back to reference Aalen OO, Røysland K, Gran JM, Kouyos R, Lange T (2016) Can we believe the dags? a comment on the relationship between causal dags and mechanisms. Stat Methods Med Res 25(5):2294–2314MathSciNet Aalen OO, Røysland K, Gran JM, Kouyos R, Lange T (2016) Can we believe the dags? a comment on the relationship between causal dags and mechanisms. Stat Methods Med Res 25(5):2294–2314MathSciNet
go back to reference Abell JG, Kivimäki M, Dugravot A, Tabak AG, Fayosse A, Shipley M, Sabia S, Singh-Manoux A (2018) Association between systolic blood pressure and dementia in the Whitehall II cohort study: role of age, duration, and threshold used to define hypertension. Eur Heart J 33(1):3119–3125 Abell JG, Kivimäki M, Dugravot A, Tabak AG, Fayosse A, Shipley M, Sabia S, Singh-Manoux A (2018) Association between systolic blood pressure and dementia in the Whitehall II cohort study: role of age, duration, and threshold used to define hypertension. Eur Heart J 33(1):3119–3125
go back to reference Andersen PK, Keiding N (2002) Multi-state models for event history analysis. Stat Methods Med Res 11(2):91–115MATH Andersen PK, Keiding N (2002) Multi-state models for event history analysis. Stat Methods Med Res 11(2):91–115MATH
go back to reference Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical methods based on counting processes. Springer, New YorkMATH Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical methods based on counting processes. Springer, New YorkMATH
go back to reference Asparouhov T, Hamaker EL, Muthén B (2017) Dynamic structural equation models. Struct Equ Model Multidiscip J 25:359–388MathSciNet Asparouhov T, Hamaker EL, Muthén B (2017) Dynamic structural equation models. Struct Equ Model Multidiscip J 25:359–388MathSciNet
go back to reference Commenges D, Gégout-Petit A (2007) Likelihood for generally coarsened observations from multistate or counting process models. Scand J Stat 34(2):432–450MathSciNetMATH Commenges D, Gégout-Petit A (2007) Likelihood for generally coarsened observations from multistate or counting process models. Scand J Stat 34(2):432–450MathSciNetMATH
go back to reference Commenges D, Gégout-Petit A (2009) A general dynamical statistical model with causal interpretation. J R Stat Soc Ser B (Stat Methodol) 71(3):719–736MathSciNetMATH Commenges D, Gégout-Petit A (2009) A general dynamical statistical model with causal interpretation. J R Stat Soc Ser B (Stat Methodol) 71(3):719–736MathSciNetMATH
go back to reference Commenges D, Jacqmin-Gadda H (2015) Dynamical biostatistical models, vol 86. CRC Press, Boca RatonMATH Commenges D, Jacqmin-Gadda H (2015) Dynamical biostatistical models, vol 86. CRC Press, Boca RatonMATH
go back to reference Commenges D, Joly P, Gégout-Petit A, Liquet B (2007) Choice between semi-parametric estimators of Markov and non-Markov multi-state models from coarsened observations. Scand J Stat 34(1):33–52MathSciNetMATH Commenges D, Joly P, Gégout-Petit A, Liquet B (2007) Choice between semi-parametric estimators of Markov and non-Markov multi-state models from coarsened observations. Scand J Stat 34(1):33–52MathSciNetMATH
go back to reference Commenges D, Gégout-Petit A (2005) Likelihood inference for incompletely observed stochastic processes: ignorability conditions. arXiv:math/0507151 Commenges D, Gégout-Petit A (2005) Likelihood inference for incompletely observed stochastic processes: ignorability conditions. arXiv:​math/​0507151
go back to reference Commenges D, Gégout-Petit A (2015) The stochastic system approach for estimating dynamic treatments effect. Lifetime Data Anal 21:1–18MathSciNetMATH Commenges D, Gégout-Petit A (2015) The stochastic system approach for estimating dynamic treatments effect. Lifetime Data Anal 21:1–18MathSciNetMATH
go back to reference Dantan E, Joly P, Dartigues J-F, Jacqmin-Gadda H (2011) Joint model with latent state for longitudinal and multistate data. Biostatistics 12(4):723–736MATH Dantan E, Joly P, Dartigues J-F, Jacqmin-Gadda H (2011) Joint model with latent state for longitudinal and multistate data. Biostatistics 12(4):723–736MATH
go back to reference Di Serio C (1997) The protective impact of a covariate on competing failures with an example from a bone marrow transplantation study. Lifetime Data Anal 3(2):99–122MATH Di Serio C (1997) The protective impact of a covariate on competing failures with an example from a bone marrow transplantation study. Lifetime Data Anal 3(2):99–122MATH
go back to reference Didelez V (2008) Graphical models for marked point processes based on local independence. J R Stat Soc Ser B (Stat Methodol) 70(1):245–264MathSciNetMATH Didelez V (2008) Graphical models for marked point processes based on local independence. J R Stat Soc Ser B (Stat Methodol) 70(1):245–264MathSciNetMATH
go back to reference Dufouil C, Brayne C, Clayton D (2004) Analysis of longitudinal studies with death and drop-out: a case study. Stat Med 23(14):2215–2226 Dufouil C, Brayne C, Clayton D (2004) Analysis of longitudinal studies with death and drop-out: a case study. Stat Med 23(14):2215–2226
go back to reference Farewell D, Huang C, Didelez V (2017) Ignorability for general longitudinal data. Biometrika 104(2):317–326MathSciNetMATH Farewell D, Huang C, Didelez V (2017) Ignorability for general longitudinal data. Biometrika 104(2):317–326MathSciNetMATH
go back to reference Fosen J, Ferkingstad E, Borgan Ø, Aalen OO (2006) Dynamic path analysis-a new approach to analyzing time-dependent covariates. Lifetime Data Anal 12(2):143–167MathSciNetMATH Fosen J, Ferkingstad E, Borgan Ø, Aalen OO (2006) Dynamic path analysis-a new approach to analyzing time-dependent covariates. Lifetime Data Anal 12(2):143–167MathSciNetMATH
go back to reference Frangakis CE, Rubin DB (2002) Principal stratification in causal inference. Biometrics 58(1):21–29MathSciNetMATH Frangakis CE, Rubin DB (2002) Principal stratification in causal inference. Biometrics 58(1):21–29MathSciNetMATH
go back to reference Ganiayre J, Commenges D, Letenneur L (2008) A latent process model for dementia and psychometric tests. Lifetime Data Anal 14(2):115–133MathSciNetMATH Ganiayre J, Commenges D, Letenneur L (2008) A latent process model for dementia and psychometric tests. Lifetime Data Anal 14(2):115–133MathSciNetMATH
go back to reference Gégout-Petit A, Commenges D (2010) A general definition of influence between stochastic processes. Lifetime Data Anal 16(1):33–44MathSciNetMATH Gégout-Petit A, Commenges D (2010) A general definition of influence between stochastic processes. Lifetime Data Anal 16(1):33–44MathSciNetMATH
go back to reference Gill RD, Van Der Laan MJ, Robins JM (1997) Coarsening at random: characterizations, conjectures, counter-examples. In: Proceedings of the FirstSeattle symposium in biostatistics. Springer, pp 255–294 Gill RD, Van Der Laan MJ, Robins JM (1997) Coarsening at random: characterizations, conjectures, counter-examples. In: Proceedings of the FirstSeattle symposium in biostatistics. Springer, pp 255–294
go back to reference Greenland S (2003) Quantifying biases in causal models: classical confounding vs collider-stratification bias. Epidemiology 14(3):300–306 Greenland S (2003) Quantifying biases in causal models: classical confounding vs collider-stratification bias. Epidemiology 14(3):300–306
go back to reference Gruger J, Kay R, Schumacher M (1991) The validity of inferences based on incomplete observations in disease state models. Biometrics 47:595–605 Gruger J, Kay R, Schumacher M (1991) The validity of inferences based on incomplete observations in disease state models. Biometrics 47:595–605
go back to reference Jazwinski H (1970) Stochastic process and filtering theory. Academic, CambridgeMATH Jazwinski H (1970) Stochastic process and filtering theory. Academic, CambridgeMATH
go back to reference Joffe M (2011) Principal stratification and attribution prohibition: good ideas taken too far. Int J Biostat 7(1) article: 35 Joffe M (2011) Principal stratification and attribution prohibition: good ideas taken too far. Int J Biostat 7(1) article: 35
go back to reference Joly P, Commenges D, Helmer C, Letenneur L (2002) A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia. Biostatistics 3(3):433–443MATH Joly P, Commenges D, Helmer C, Letenneur L (2002) A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia. Biostatistics 3(3):433–443MATH
go back to reference Kalman RE, Bucy RS (1961) New results in linear filtering and prediction theory. J Basic Eng 83(1):95–108MathSciNet Kalman RE, Bucy RS (1961) New results in linear filtering and prediction theory. J Basic Eng 83(1):95–108MathSciNet
go back to reference Kurland BF, Johnson LL, Egleston BL, Diehr PH (2009) Longitudinal data with follow-up truncated by death: match the analysis method to research aims. Stat Sci Rev J Inst Math Stat 24(2):211MathSciNetMATH Kurland BF, Johnson LL, Egleston BL, Diehr PH (2009) Longitudinal data with follow-up truncated by death: match the analysis method to research aims. Stat Sci Rev J Inst Math Stat 24(2):211MathSciNetMATH
go back to reference Pearl J (2011) Principal stratification-a goal or a tool? Int J Biostat 7(1), article: 20 Pearl J (2011) Principal stratification-a goal or a tool? Int J Biostat 7(1), article: 20
go back to reference Pearl J (2000) Causality: Models, reasoning, and inference. Cambridge University Press, CambridgeMATH Pearl J (2000) Causality: Models, reasoning, and inference. Cambridge University Press, CambridgeMATH
go back to reference Prague M, Commenges D, Drylewicz J, Thiébaut R (2012) Treatment monitoring of HIV-infected patients based on mechanistic models. Biometrics 68:902–911MathSciNetMATH Prague M, Commenges D, Drylewicz J, Thiébaut R (2012) Treatment monitoring of HIV-infected patients based on mechanistic models. Biometrics 68:902–911MathSciNetMATH
go back to reference Prague M, Commenges D, Gran JM, Ledergerber B, Young J, Furrer H, Thiébaut R (2017) Dynamic models for estimating the effect of HAART on CD4 in observational studies: application to the aquitaine cohort and the Swiss HIV Cohort Study. Biometrics 73(1):294–304MathSciNetMATH Prague M, Commenges D, Gran JM, Ledergerber B, Young J, Furrer H, Thiébaut R (2017) Dynamic models for estimating the effect of HAART on CD4 in observational studies: application to the aquitaine cohort and the Swiss HIV Cohort Study. Biometrics 73(1):294–304MathSciNetMATH
go back to reference Proust C, Jacqmin-Gadda H, Taylor JMG, Ganiayre J, Commenges D (2006) A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data. Biometrics 62(4):1014–1024MathSciNetMATH Proust C, Jacqmin-Gadda H, Taylor JMG, Ganiayre J, Commenges D (2006) A nonlinear model with latent process for cognitive evolution using multivariate longitudinal data. Biometrics 62(4):1014–1024MathSciNetMATH
go back to reference Proust-Lima C, Dartigues J-F, Jacqmin-Gadda H (2016) Joint modeling of repeated multivariate cognitive measures and competing risks of dementia and death: a latent process and latent class approach. Stat Med 35(3):382–398MathSciNet Proust-Lima C, Dartigues J-F, Jacqmin-Gadda H (2016) Joint modeling of repeated multivariate cognitive measures and competing risks of dementia and death: a latent process and latent class approach. Stat Med 35(3):382–398MathSciNet
go back to reference Proust-Lima C, Philipps V, Liquet B (2015) Estimation of extended mixed models using latent classes and latent processes: the R package lcmm. arXiv:1503.00890 Proust-Lima C, Philipps V, Liquet B (2015) Estimation of extended mixed models using latent classes and latent processes: the R package lcmm. arXiv:​1503.​00890
go back to reference Rizopoulos D (2010) JM: An R package for the joint modelling of longitudinal and time-to-event data. J Stat Softw (Online) 35(9):1–33 Rizopoulos D (2010) JM: An R package for the joint modelling of longitudinal and time-to-event data. J Stat Softw (Online) 35(9):1–33
go back to reference Rouanet A, Joly P, Dartigues J-F, Proust-Lima C, Jacqmin-Gadda H (2016) Joint latent class model for longitudinal data and interval-censored semi-competing events: application to dementia. Biometrics 72(4):1123–1135MathSciNetMATH Rouanet A, Joly P, Dartigues J-F, Proust-Lima C, Jacqmin-Gadda H (2016) Joint latent class model for longitudinal data and interval-censored semi-competing events: application to dementia. Biometrics 72(4):1123–1135MathSciNetMATH
go back to reference Rubin DB (2006) Causal inference through potential outcomes and principal stratification: application to studies with censoring due to death. Stat Sci 21:299–309MathSciNetMATH Rubin DB (2006) Causal inference through potential outcomes and principal stratification: application to studies with censoring due to death. Stat Sci 21:299–309MathSciNetMATH
go back to reference Tchetgen EJT, Glymour MM, Shpitser I, Weuve J (2012) Rejoinder: to weight or not to weight? On the relation between inverse-probability weighting and principal stratification for truncation by death. Epidemiology 23(1):132–137 Tchetgen EJT, Glymour MM, Shpitser I, Weuve J (2012) Rejoinder: to weight or not to weight? On the relation between inverse-probability weighting and principal stratification for truncation by death. Epidemiology 23(1):132–137
go back to reference VanderWeele TJ (2011) Principal stratification-uses and limitations. Int J Biostat 7(1):1–14MathSciNet VanderWeele TJ (2011) Principal stratification-uses and limitations. Int J Biostat 7(1):1–14MathSciNet
go back to reference Wang C, Scharfstein DO, Colantuoni E, Girard TD, Yan Y (2017) Inference in randomized trials with death and missingness. Biometrics 73(2):431–440MathSciNetMATH Wang C, Scharfstein DO, Colantuoni E, Girard TD, Yan Y (2017) Inference in randomized trials with death and missingness. Biometrics 73(2):431–440MathSciNetMATH
go back to reference Weuve J, Proust-Lima C, Power MC, Gross AL, Hofer SM, Thiébaut R, Chêne G, Glymour MM, Dufouil C, Initiative M et al (2015) Guidelines for reporting methodological challenges and evaluating potential bias in dementia research. Alzheimer’s Dement 11(9):1098–1109 Weuve J, Proust-Lima C, Power MC, Gross AL, Hofer SM, Thiébaut R, Chêne G, Glymour MM, Dufouil C, Initiative M et al (2015) Guidelines for reporting methodological challenges and evaluating potential bias in dementia research. Alzheimer’s Dement 11(9):1098–1109
go back to reference Wimsatt WC (1994) The ontology of complex systems: levels of organization, perspectives, and causal thickets. Can J Philos 20:207–274 Wimsatt WC (1994) The ontology of complex systems: levels of organization, perspectives, and causal thickets. Can J Philos 20:207–274
go back to reference Yang F, Ding P (2018) Using survival information in truncation by death problems without the monotonicity assumption. Biometrics (in press) Yang F, Ding P (2018) Using survival information in truncation by death problems without the monotonicity assumption. Biometrics (in press)
Metadata
Title
Dealing with death when studying disease or physiological marker: the stochastic system approach to causality
Author
Daniel Commenges
Publication date
17-11-2018
Publisher
Springer US
Published in
Lifetime Data Analysis / Issue 3/2019
Print ISSN: 1380-7870
Electronic ISSN: 1572-9249
DOI
https://doi.org/10.1007/s10985-018-9454-3

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