Multilevel mixed effects parametric survival models using adaptive Gauss-Hermite quadrature with application to recurrent events and individual participant data meta-analysis

Statistics in Medicine

Volumn 33, Issue 22, 2014, Pages 3844-3858

  Crowther, Michael J ^a   Look, Maxime P ^b   Riley, Richard D ^c  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b ERASMUS MC CANCER INSTITUTE   (Netherlands)

^c UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Adaptive Gauss Hermite quadrature; Flexible parametric models; Mixed effects; Survival analysis

Indexed keywords

BREAST TUMOR; COMPUTER PROGRAM; FEMALE; HUMAN; KIDNEY DISEASE; META ANALYSIS (TOPIC); MORTALITY; MULTICENTER STUDY (TOPIC); PROGNOSIS; RECURRENT DISEASE; RISK ASSESSMENT; STATISTICAL MODEL; SURVIVAL; TIME;

BREAST NEOPLASMS; FEMALE; HUMANS; KIDNEY DISEASES; META-ANALYSIS AS TOPIC; MODELS, STATISTICAL; MULTICENTER STUDIES AS TOPIC; PROGNOSIS; RECURRENCE; RISK ASSESSMENT; SOFTWARE; SURVIVAL ANALYSIS; TIME FACTORS;

EID: 84906824383     PISSN: 02776715     EISSN: 10970258     Source Type: Journal    
DOI: 10.1002/sim.6191     Document Type: Article

References (44)

1. Simmonds MC, Higgins JPT, Stewart LA, Tierney JF, Clarke MJ, Thompson SG. Meta-analysis of individual patient data from randomized trials: a review of methods used in practice. Clinical Trials 2(3):209-217.
2. Tudur-Smith C, Williamson PR, Marson AG. Investigating heterogeneity in an individual patient data meta-analysis of time to event outcomes. Statistics in Medicine 2005; 24(9):1307-1319.
3. Bowden J, Tierney JF, Simmonds M, Copas AJ, Higgins JP. Individual patient data meta-analysis of time-to-event outcomes: one-stage versus two-stage approaches for estimating the hazard ratio under a random effects model. Research Synthesis Methods 2011; 2(3):150-162.
4. Crowther MJ, Riley RD, Staessen JA, Wang J, Gueyffier F, Lambert PC. Individual patient data meta-analysis of survival data using Poisson regression models. BMC Medical Research Methodology March 2012; 12(1):34.
5. Riley RD, Lambert PC, Abo-Zaid G. Meta-analysis of individual participant data: rationale, conduct, and reporting. BMJ 2010; 340: c221.
6. Komárek A, Lesaffre E, Legrand C. Baseline and treatment effect heterogeneity for survival times between centers using a random effects accelerated failure time model with flexible error distribution. Statistics in Medicine December 2007; 26(30):5457-5472.
7. Yamaguchi T, Ohashi Y, Matsuyama Y. Proportional hazards models with random effects to examine centre effects in multicentre cancer clinical trials. Statistical Methods in Medical Research 2002; 11(3):221-236.
8. Legrand C, Ducrocq V, Janssen P, Sylvester R, Duchateau L. A Bayesian approach to jointly estimate centre and treatment by centre heterogeneity in a proportional hazards model. Statistics in Medicine 2005; 24(24):3789-3804.
9. International conference on harmonisation of technical requirements for registration of pharmaceuticals for human use: statistical principles for clinical trials. Statistics in Medicine 1999; 18: 1905-1942.
10. Gutierrez RG. Parametric frailty and shared frailty survival models. The Stata Journal 2002; 2(1):22-44.
11. Rondeau V, Mazroui Y, Gonzalez JR. Frailtypack: an R package for the analysis of correlated survival data with frailty models using penalized likelihood estimation or parametrical estimation. Journal of Statistical Software 2012; 47(4).
12. Rondeau V, Commenges D, Joly P. Maximum penalized likelihood estimation in a gamma-frailty model. Lifetime Data Analysis June 2003; 9(2):139-153.
13. Rondeau V, Filleul L, Joly P. Nested frailty models using maximum penalized likelihood estimation. Statistics in Medicine December 2006; 25(23):4036-4052.
14. Rondeau V, Mathoulin-Pelissier S, Jacqmin-Gadda H, Brouste V, Soubeyran P. Joint frailty models for recurring events and death using maximum penalized likelihood estimation: application on cancer events. Biostatistics October 2007; 8(4):708-721.
15. Rondeau V, Michiels S, Liquet B, Pignon JP. Investigating trial and treatment heterogeneity in an individual patient data meta-analysis of survival data by means of the penalized maximum likelihood approach. Statistics in Medicine 2008; 27(11):1894-1910.
16. Nielsen GG, Gill RD, Andersen PK, SÃÿrensen TIA. A counting process approach to maximum likelihood estimation in frailty models. Scandinavian Journal of Statistics 1992; 19(1):25-43.
17. Guo G, Rodriguez G. Estimating a multivariate proportional hazards model for clustered data using the EM algorithm, with an application to child survival in Guatemala. Journal of the American Statistical Association 1992; 87(420):969-976.
18. Klein JP. Semiparametric estimation of random effects using the cox model based on the EM algorithm. Biometrics 1992; 48(3):795-806.
19. McGilchrist CA, Aisbett CW. Regression with frailty in survival analysis. Biometrics June 1991; 47(2):461-466.
20. Therneau TM, Grambsch PM. Modelling Survival Data: Extending the Cox Model. Springer, 2000.
21. Cox DR. Regression models and life-tables. Journal of the Royal Statistical Society. Series B (Methodological) 1972; 34(2):187-220.
22. King NB, Harper S, Young ME. Use of relative and absolute effect measures in reporting health inequalities: structured review. BMJ 2012; 345: e5774.
23. Royston P, Parmar MKB. Flexible parametric proportional hazards and proportional odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Statistics in Medicine 2002; 21(15):2175-2197.
24. Royston P, Lambert PC. Flexible Parametric Survival Analysis Using Stata: Beyond the Cox Model. Stata Press: College Station, Texas, 2011.
25. Lambert PC, Holmberg L, Sandin F, Bray F, Linklater KM, Purushotham A, Robinson D, Møller H. Quantifying differences in breast cancer survival between England and Norway. Cancer Epidemiology December 2011; 35(6):526-533.
26. Crowther MJ, Abrams KR, Lambert PC. Flexible parametric joint modelling of longitudinal and survival data. Statistics in Medicine December 2012; 31(30):4456-4471.
27. Miladinovic B, Kumar A, Mhaskar R, Kim S, Schonwetter R, Djulbegovic B. A flexible alternative to the Cox proportional hazards model for assessing the prognostic accuracy of hospice patient survival. PLoS One 2012; 7(10):e47804.
28. Rooney J, Byrne S, Heverin M, Corr B, Elamin M, Staines A, Goldacre B, Hardiman O. Survival analysis of irish amyotrophic lateral sclerosis patients diagnosed from 1995-2010. PLoS One 2013; 8(9):e74733.
29. Liu L, Huang X. The use of gaussian quadrature for estimation in frailty proportional hazards models. Statistics in Medicine June 2008; 27(14):2665-2683.
30. Kong X, Archer KJ, Moulton LH, Gray RH, Wang MC. Parametric frailty models for clustered data with arbitrary censoring: application to effect of male circumcision on hpv clearance. BMC Medical Research Methodology 2010; 10: 40.
31. Lambert PC, Royston P. Further development of flexible parametric models for survival analysis. The Stata Journal 2009; 9: 265-290.
32. Rutherford MJ, Crowther MJ, Lambert PC. The use of restricted cubic splines to approximate complex hazard functions in the analysis of time-to-event data: a simulation study. Journal of Statistical Computation and Simulation 2014.
33. Mok TS, Wu Y-L, Thongprasert S, Yang C-H, Chu D-T, Saijo N, Sunpaweravong P, Han B, Margono B, Ichinose Y, Nishiwaki Y, Ohe Y, Yang J-J, Chewaskulyong B, Jiang H, Duffield EL, Watkins CL, Armour AA, Fukuoka M. Gefitinib or carboplatin-paclitaxel in pulmonary adenocarcinoma. New England Journal of Medicine September 2009; 361(10):947-957.
34. Pinheiro JC, Bates DM. Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics 1995; 4(1):12-35.
35. Rabe-Hesketh S, Skrondal A, Pickles A. Reliable estimation of generalized linear mixed models using adaptive quadrature. The Stata Journal 2002; 2: 1-21.
36. Gould W, Pitblado J, Poi B. Maximum Likelihood Estimation with Stata, 4th edition. Stata Press: College Station, Texas, 2010.
37. Riley RD, Abrams KR, Sutton AJ, Lambert PC, Thompson JR. Bivariate random-effects meta-analysis and the estimation of between-study correlation. BMC Medical Research Methodology 2007; 7: 3.
38. Look MP, van Putten null WLJ, Duffy MJ, Harbeck N, Christensen IJ, Thomssen C, Kates R, Spyratos F, Fernö M, Eppenberger-Castori S, Sweep CGJF, Ulm K, Peyrat J-P, Martin P-M, Magdelenat H, Brünner N, Duggan C, Lisboa BW, Bendahl P-O, Quillien V, Daver A, Ricolleau G, Meijer-van Gelder ME, Manders P, Fiets WE, Blankenstein MA, Broët P, Romain S, Daxenbichler G, Windbichler G, Cufer T, Borstnar S, Kueng W, Beex LVAM, Klijn JGM, O'Higgins N, Eppenberger U, Jänicke F, Schmitt M, Foekens JA. Pooled analysis of prognostic impact of urokinase-type plasminogen activator and its inhibitor pai-1 in 8377 breast cancer patients. Journal of National Cancer Institute January 2002; 94(2):116-128.
39. Schmid CH, Stark PC, Berlin JA, Landais P, Lau J. Meta-regression detected associations between heterogeneous treatment effects and study-level, but not patient-level, factors. Journal of Clinical Epidemiology 2004; 57(7):683-697.
40. Higgins JPT, Thompsonm S G, Spiegelhalter DJ. A re-evaluation of random-effects meta-analysis. Journal of the Royal Statistical Society: Series A (Statistics in Society) 2009; 172(1):137-159.
41. Riley RD, Higgins JPT, Deeks JJ. Interpretation of random effects meta-analyses. BMJ 2011; 342: d549.
42. Thompson S, Kaptoge S, White I, Wood A, Perry P, Danesh J. Collaboration TERF. Statistical methods for the time-to-event analysis of individual participant data from multiple epidemiological studies. International Journal of Epidemiology 2010; 39: 1345-1359.
43. Latimer NR. Survival analysis for economic evaluations alongside clinical trials-extrapolation with patient-level data: inconsistencies, limitations, and a practical guide. Medical Decision Making August 2013; 33(6):743-754.
44. McGilchrist CA. REML estimation for survival models with frailty. Biometrics March 1993; 49(1):221-225.