Prediction meets causal inference: the role of treatment in clinical prediction models

Nan van Geloven, Sonja A Swanson, Chava L Ramspek, Kim Luijken, Merel van Diepen, Tim P Morris, Rolf H H Groenwold, Hans C van Houwelingen, Hein Putter, Saskia le Cessie, Nan van Geloven, Sonja A Swanson, Chava L Ramspek, Kim Luijken, Merel van Diepen, Tim P Morris, Rolf H H Groenwold, Hans C van Houwelingen, Hein Putter, Saskia le Cessie

Abstract

In this paper we study approaches for dealing with treatment when developing a clinical prediction model. Analogous to the estimand framework recently proposed by the European Medicines Agency for clinical trials, we propose a 'predictimand' framework of different questions that may be of interest when predicting risk in relation to treatment started after baseline. We provide a formal definition of the estimands matching these questions, give examples of settings in which each is useful and discuss appropriate estimators including their assumptions. We illustrate the impact of the predictimand choice in a dataset of patients with end-stage kidney disease. We argue that clearly defining the estimand is equally important in prediction research as in causal inference.

Keywords: Censoring; Clinical prediction model; Estimands; Predictimands; Treatment.

Figures

Fig. 1
Fig. 1
Graphical representation of the studied situation. Follow up on the event of interest may stop (a) or continue (b) after treatment initiation
Fig. 2
Fig. 2
Predicted mortality curves and 10 year mortality risks for patients aged 50 and 70 on hemodialysis. red: composite, green: while untreated/cumulative incidence, black: ignore treatment, solid blue: hypothetical—censor at treatment, dashed blue: hypothetical—modelling treatment, dotted blue: hypothetical—censor at treatment + IPW, dotdash blue: hypothetical—modelling treatment + IPW

References

    1. Hemingway H, Croft P, Perel P, et al. Prognosis research strategy (PROGRESS) 1: a framework for researching clinical outcomes. BMJ. 2013;346:e5595.
    1. Groenwold RH, Moons KG, Pajouheshnia R, Altman DG, Collins GS, Debray TP, Reitsma JB, Riley RD, Peelen LM. Explicit inclusion of treatment in prognostic modeling was recommended in observational and randomized settings. J Clin Epidemiol. 2016;78:90–100.
    1. Sperrin M, Martin GP, Pate A, Van Staa T, Peek N, Buchan I. Using marginal structural models to adjust for treatment drop-in when developing clinical prediction models. Stat Med. 2018;37:4142–4154.
    1. Pajouheshnia R, Damen JAAG, Groenwold RHH, Moons KGM, Peelen LM. Treatment use in prognostic model research: a systematic review of cardiovascular prognostic studies. Diagn Progn Res. 2017;1:15.
    1. Kim WR, Therneau TM, Benson JT, Kremers WK, Rosen CB, Gores GJ, Dickson ER. Deaths on the liver transplant waiting list: an analysis of competing risks. Hepatology. 2006;43(2):345–351.
    1. Staplin ND, Kimber AC, Collett D, Roderick PJ. Dependent censoring in piecewise exponential survival models. Stat Methods Med Res. 2015;24(3):325–341.
    1. Moons KGM, Altman DG, Reitsma JB, et al. Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): explanation and elaboration. Ann Intern Med. 2015;162:W1–W73.
    1. ICH E9 working group. ICH E9 (R1): addendum on estimands and sensitivity analysis in clinical trials to the guideline on statistical principles for clinical trials. EMA/CHMP/ICH/436221/2017. 2020 . Accessed 24 Feb 2020.
    1. Pajouheshnia R, Schuster NA, Groenwold RHH, Rutten FH, Moons KGM, Peelen LM. Accounting for time-dependent treatment use when developing a prognostic model from observational data: a review of methods. Stat Neerlandica. 2020;74(1):38–51.
    1. Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Stat Med. 2007;26:2389–2430.
    1. Justice AC, Covinsky KE, Berlin JA. Assessing the generalizability of prognostic information. Ann Intern Med. 1999;130(6):515–524.
    1. Hippisley-Cox J, Coupland C, Brindle P. Development and validation of QRISK3 risk prediction algorithms to estimate future risk of cardiovascular disease: prospective cohort study. BMJ. 2017;357:j2099.
    1. Peek N, Sperrin M, Mamas M, van Staa T, Buchan I. Hari Seldon, QRISK3, and the prediction paradox. BMJ. 2017;357:2099.
    1. Hicks KA, Mahaffey KW, Mehran R, Nissen SE, Wiviott SD, Dunn B, Solomon SD, Marler JR, Teerlink JR, Farb A, Morrow DA, Targum SL, Sila CA, Hai MTT, Jaff MR, Joffe HV, Cutlip DE, Desai AS, Lewis EF, Gibson CM, Landray MJ, Lincoff AM, White CJ, Brooks SS, Rosenfield K, Domanski MJ, Lansky AJ, McMurray JJV, Tcheng JE, Steinhubl SR, Burton P, Mauri L, O’Connor CM, Pfeffer MA, Hung HMJ, Stockbridge NL, Chaitman BR, Temple RJ. Standardized data collection for cardiovascular trials initiative (SCTI). 2017 Cardiovascular and Stroke Endpoint Definitions for Clinical Trials. Circulation. 2018;137:961–972.
    1. von Dadelszen P, Payne B, Li J, Ansermino JM, Broughton Pipkin F, Côté AM, Douglas MJ, Gruslin A, Hutcheon JA, Joseph KS, Kyle PM, Lee T, Loughna P, Menzies JM, Merialdi M, Millman AL, Moore MP, Moutquin JM, Ouellet AB, Smith GN, Walker JJ, Walley KR, Walters BN, Widmer M, Lee SK, Russell JA, Magee LA, PIERS Study Group. Prediction of adverse maternal outcomes in pre-eclampsia: development and validation of the fullPIERS model. Lancet. 2011;377(9761):219–27. 10.1016/S0140-6736(10)61351-7.
    1. Grunkemeier GL, Jin R, Eijkemans MJ, Takkenberg JJ. Actual and actuarial probabilities of competing risks: apples and lemons. Ann Thorac Surg. 2007;83:1586–1592.
    1. Young JG, Stensrud MJ, Tchetgen Tchetgen EJ, Hernán MA. A causal framework for classical statistical estimands in failure-time settings with competing events. Stat Med. 2020;39:1199–1236.
    1. Geskus RB. Data analysis with competing risks and intermediate states. New York: Chapman and Hall/CRC; 2015.
    1. Pfeiffer RM, Gail MH. Absolute risk: methods and applications in clinical management and public health. New York: Chapman and Hall/CRC; 2017.
    1. van Geloven N, Geskus RB, Mol BW, Zwinderman AH. Correcting for the dependent competing risk of treatment using inverse probability of censoring weighting and copulas in the estimation of natural conception chances. Stat Med. 2014;33:4671–4680.
    1. Fine JP, Gray RJ. A proportional hazards model for the subdistribution of a competing risk. J Am Stat Assoc. 1999;94:496–509.
    1. Scheike TH, Zhang MJ, Gerds TA. Predicting cumulative incidence probability by direct binomial regression. Biometrika. 2008;95:205–220.
    1. Nicolaie MA, van Houwelingen JC, Putter H. Vertical modelling: a pattern mixture approach for competing risks modelling. Stat Med. 2010;29:1190–1205.
    1. Sachs MC, Discacciati A, Everhov ÅH, Olén O, Gabriel EE. Ensemble prediction of time-to-event outcomes with competing risks: a case-study of surgical complications in Crohn’s disease. J R Stat Soc Ser C (Appl Stat) 2019;68:1431–1446.
    1. Hernán MA, Robins JM. Causal inference: what if. Boca Raton: Chapman and Hall/CRC; 2020.
    1. Pearl J. On the consistency rule in causal inference: axiom, definition, assumption, or theorem? Epidemiology. 2010;21:872–875.
    1. Zheng M, Klein P. Estimates of marginal survival for dependent competing risks based on an assumed copula. Biometrika. 1995;82:127–138.
    1. Escarela G, Carriere JF. Fitting competing risks with an assumed copula. Stat Methods Med Res. 2003;12:333–349.
    1. Hsu CH, Taylor JMG. Nonparametric comparison of two survival functions with dependent censoring via nonparametric multiple imputation. Stat Med. 2009;28:462–475.
    1. Jackson D, White IR, Seaman S, et al. Relaxing the independent censoring assumption in the Cox proportional hazards model using multiple imputation. Stat Med. 2014;33:4681–4694.
    1. Robins JM, Finkelstein DM. Correcting for noncompliance and dependent censoring in an AIDS clinical trial with inverse probability of censoring weighted (IPCW) log rank tests. Biometrics. 2000;56:779–788.
    1. Cole SR, Hernán MA. Constructing inverse probability weights for marginal structural models. Am J Epidemiol. 2008;168:656–664.
    1. Matsuyama Y, Yamaguchi T. Estimation of the marginal survival time in the presence of dependent competing risks using inverse probability of censoring weighted (IPCW) methods. Pharm Stat. 2008;7:202–214.
    1. Howe CJ, Cole SR, Chmiel JS, et al. Limitation of inverse probability of censoring weights in estimating survival in the presence of strong selection bias. Am J Epidemiol. 2011;173:569–577.
    1. Goetgeluk S, Vansteelandt S, Goetghebeur E. Estimation of controlled direct effects. J R Stat Soc B. 2009;70:1049–1066.
    1. Robins JM, Hernán MA, Brumback B. Marginal structural models and causal inference in epidemiology. Epidemiology. 2000;11:550–560.
    1. Ramspek CL, Voskamp PW, van Ittersum FJ, Krediet RT, Dekker FW, van Diepen M. Prediction models for the mortality risk in chronic dialysis patients: a systematic review and independent external validation study. Clin Epidemiol. 2017;9:451–464.
    1. Hoekstra T, Hemmelder MH, van Ittersum FJ. RENINE annual report 2015. . Accessed 15 Oct 2019.
    1. R Core Team. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing, 2017. .
    1. Efron B. The efficiency of Cox’s likelihood function for censored data. J Am Stat Assoc. 1977;72:557–565.
    1. Hernán MA, Hsu J, Healy B. A second chance to get causal inference right: a classification of data science tasks. Chance. 2019;32:42–49.
    1. Pajouheshnia R. Prognostic research in treated populations (Doctoral dissertation); 2018. Retrieved from .
    1. Cook RJ, Lawless JF. The statistical analysis of recurrent events. New York: Springer; 2007.
    1. Saha P, Heagerty PJ. Time-dependent predictive accuracy in the presence of competing risks. Biometrics. 2010;66(4):999–1011.
    1. Schoop R, Beyersmann J, Schumacher M, Binder H. Quantifying the predictive accuracy of time-to-event models in the presence of competing risks. Biom J. 2011;53(1):88–112.
    1. Zhang Z, Cortese G, Combescure C, Marshall R, Lee M, Lim HJ, Haller B. written on behalf of AME big-data clinical trial collaborative group. Overview of model validation for survival regression model with competing risks using melanoma study data. Ann Transl Med. 2018;6(16):325.
    1. Pajouheshnia R, Peelen LM, Moons KGM, Reitsma JB, Groenwold RHH. Accounting for treatment use when validating a prognostic model: a simulation study. BMC Med Res Methodol. 2017;17(1):103.
    1. Andersen PK, Keiding N. Interpretability and importance of functionals in competing risks and multistate models. Stat Med. 2011;31:1074–1088.
    1. Lash TL, Fox MP, Fink AK. Applying quantitative bias analysis to epidemiologic data. Berlin: Springer; 2011.

Source: PubMed

Sponsoren und Mitarbeiter

Krankheiten

Drogeninterventionen

3
Abonnieren