Effect modification by time in evidence synthesis of time-to-event outcomes_Chinese Journal of Evidence-Based Medicine

Authors：

ZOU Xinyu ^1,2 ,  LI Sheyu ^1,2

1. Department of Endocrinology and Metabolism, West China Hospital, Sichuan University, Chengdu 610041, P. R. China;
2. Chinese Evidence-based Medicine Center/ MAGIC China Center/ Cochrane China, West China Hospital, Sichuan University, Chengdu 610041, P. R. China;

Corresponding author：

LI Sheyu, Email: lisheyu@gmail.com

Keywords：

Effect modification; Individual patient data; Meta-analysis; Time-to-event outcome; Time-dependent covariate; Time-dependent coefficient

DOI：

10.7507/1672-2531.202310033

Video：

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Abstract Full text Figures/Tables Video References Cited by

Time-to-event outcomes are a key component in survival analyses. Effect modification by time, also known as interaction between effect and time, can exist in time-to-event data and influence the analysis process. Our objective is to discuss the proper methods to conduct evidence synthesis of time-to-event data when effect modification by time exists.

Citation： ZOU Xinyu, LI Sheyu. Effect modification by time in evidence synthesis of time-to-event outcomes. Chinese Journal of Evidence-Based Medicine, 2024, 24(3): 364-372. doi: 10.7507/1672-2531.202310033 Copy

1.	Altman DG, Bland JM. Time to event (survival) data. BMJ, 1998, 317(7156): 468-469.
2.	Cox DR. Regression models and life-tables. J R Stat Soc Series B Stat Methodol, 1972, 34: 187-202.
3.	Dekker FW, de Mutsert R, van Dijk PC, et al. Survival analysis: time-dependent effects and time-varying risk factors. Kidney Int, 2008, 74(8): 994-997.
4.	Mok TS, Wu YL, Thongprasert S, et al. Gefitinib or carboplatin-paclitaxel in pulmonary adenocarcinoma. N Engl J Med, 2009, 361(10): 947-957.
5.	Haidich AB. Meta-analysis in medical research. Hippokratia, 2010, 14(Suppl 1): 29-37.
6.	Williamson PR, Smith CT, Hutton JL, et al. Aggregate data meta-analysis with time-to-event outcomes. Stat Med, 2002, 21(22): 3337-3351.
7.	Zou X, Shi Q, Vandvik PO, et al. Sodium-glucose cotransporter-2 inhibitors in patients with heart failure : a systematic review and meta-analysis. Ann Intern Med, 2022, 175(6): 851-861.
8.	Kleinbaum D, Klein M. Survival analysis: a self-learning text (3rd edition). New York: Springer, 2012.
9.	Kaplan EL, Meier P. Non parametric estimation from incomplete observations. J Am Stat Assoc, 1958, 53: 457-481.
10.	Rich JT, Neely JG, Paniello RC, et al. A practical guide to understanding Kaplan-Meier curves. Otolaryngol Head Neck Surg, 2010, 143(3): 331-336.
11.	Mantel N. Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemother Rep, 1966, 50(3): 163-170.
12.	Gehan EA. A generalized wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika, 1965, 52: 203-223.
13.	Tarone RE, Ware J. On distribution-free tests for equality of survival distributions. Biometrika, 1977, 64(1): 156-160.
14.	Peto R, Peto J. Asymptotically efficient rank invariant test procedures. J R Stat Soc Ser A, 1972, 135(2): 185-198.
15.	Harrington DP, Fleming TR. A class of rank test procedures for censored survival data. Biometrika, 1982, 69(3): 553-566.
16.	Bollschweiler E. Benefits and limitations of Kaplan-Meier calculations of survival chance in cancer surgery. Langenbecks Arch Surg, 2003, 388(4): 239-244.
17.	Crowther MJ, Lambert PC. A general framework for parametric survival analysis. Stat Med, 2014, 33(30): 5280-5297.
18.	Zhang Z. Parametric regression model for survival data: Weibull regression model as an example. Ann Transl Med, 2016, 4(24): 484.
19.	Ananthakrishnan R, Green S, Previtali A, et al. Critical review of oncology clinical trial design under non-proportional hazards. Crit Rev Oncol Hematol, 2021, 162: 103350.
20.	Hess KR. Graphical methods for assessing violations of the proportional hazards assumption in Cox regression. Stat Med, 1995, 14(15): 1707-1723.
21.	Ng'andu NH. An empirical comparison of statistical tests for assessing the proportional hazards assumption of Cox's model. Stat Med, 1997, 16(6): 611-626.
22.	Zhang Z, Reinikainen J, Adeleke KA, et al. Time-varying covariates and coefficients in Cox regression models. Ann Transl Med, 2018, 6(7): 121.
23.	Anderson JR, Cain KC, Gelber RD. Analysis of survival by tumor response. J Clin Oncol, 1983, 1(11): 710-719.
24.	Gleiss A, Oberbauer R, Heinze G. An unjustified benefit: immortal time bias in the analysis of time-dependent events. Transpl Int, 2018, 31(2): 125-130.
25.	Ascierto PA, Long GV. Progression-free survival landmark analysis: a critical endpoint in melanoma clinical trials. Lancet Oncol, 2016, 17(8): 1037-1039.
26.	Heymach JV, Harpole D, Mitsudomi T, et al. Perioperative durvalumab for resectable non-small-cell lung cancer. N Engl J Med, 2023, 389(18): 1672-1684.
27.	Kfoury M, Najean M, Lappara A, et al. Analysis of the association between prospectively collected immune-related adverse events and survival in patients with solid tumor treated with immune-checkpoint blockers, taking into account immortal-time bias. Cancer Treat Rev, 2022, 110: 102452.
28.	Ueyama HA, Miyamoto Y, Watanabe A, et al. Cardiac re-operation or transcatheter mitral valve replacement for patients with failed mitral prostheses. J Am Coll Cardiol, 2023.
29.	Sá MP, Jacquemyn X, Van den Eynde J, et al. Impact of prosthesis-patient mismatch after transcatheter aortic valve replacement: meta-analysis of Kaplan-Meier-derived individual patient data. JACC Cardiovasc Imaging, 2023, 16(3): 298-310.
30.	Dafni U. Landmark analysis at the 25-year landmark point. Circ cardiovasc qual outcomes, 2011, 4(3): 363-371.
31.	Royston P, Parmar MK. The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Stat Med, 2011, 30(19): 2409-2421.
32.	Dehbi HM, Royston P, Hackshaw A. Life expectancy difference and life expectancy ratio: two measures of treatment effects in randomised trials with non-proportional hazards. BMJ, 2017, 357: j2250.
33.	Royston P, Parmar MK. Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Med Res Methodol, 2013, 13: 152.
34.	Pak K, Uno H, Kim DH, et al. Interpretability of cancer clinical trial results using restricted mean survival time as an alternative to the hazard ratio. JAMA Oncol, 2017, 3(12): 1692-1696.
35.	Kim DH, Uno H, Wei LJ. Restricted mean survival time as a measure to interpret clinical trial results. JAMA Cardiol, 2017, 2(11): 1179-1180.
36.	Ehrmann S, Barbier F, Demiselle J, et al. Inhaled amikacin to prevent ventilator-associated pneumonia. N Engl J Med, 2023, 389(22): 2052-2062.
37.	Owen RK, Lyons J, Akbari A, et al. Effect on life expectancy of temporal sequence in a multimorbidity cluster of psychosis, diabetes, and congestive heart failure among 1·7 million individuals in Wales with 20-year follow-up: a retrospective cohort study using linked data. Lancet Public Health, 2023, 8(7): e535-e545.
38.	Kloecker DE, Davies MJ, Khunti K, et al. Uses and limitations of the restricted mean survival time: illustrative examples from cardiovascular outcomes and mortality trials in type 2 diabetes. Ann Intern Med, 2020, 172(8): 541-552.
39.	Royston P, Parmar MK. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat Med, 2002, 21(15): 2175-2197.
40.	Jackson CH. flexsurv: A platform for parametric survival modeling in R. J Stat Softw, 2016, 70: i08.
41.	Stewart LA, Parmar MK. Meta-analysis of the literature or of individual patient data: is there a difference. Lancet, 1993, 341(8842): 418-422.
42.	Guyot P, Ades AE, Ouwens MJ, et al. Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol, 2012, 12: 9.
43.	Wei Y, Royston P. Reconstructing time-to-event data from published Kaplan-Meier curves. Stata J, 2017, 17(4): 786-802.
44.	Liu N, Zhou Y, Lee JJ. IPD from KM: reconstruct individual patient data from published Kaplan-Meier survival curves. BMC Med Res Methodol, 2021, 21(1): 111.
45.	Cumpston M, Li T, Page MJ, et al. Updated guidance for trusted systematic reviews: a new edition of the Cochrane handbook for systematic reviews of interventions. Cochrane Database Syst Rev, 2019, (10): ED000142.
46.	Wei Y, Royston P, Tierney JF, et al. Meta-analysis of time-to-event outcomes from randomized trials using restricted mean survival time: application to individual participant data. Stat Med, 2015, 34(21): 2881-2898.
47.	Weir IR, Tian L, Trinquart L. Multivariate meta-analysis model for the difference in restricted mean survival times. Biostatistics, 2021, 22(1): 82-96.
48.	El Hajra I, Sanduzzi-Zamparelli M, Sapena V, et al. Outcome of patients with HCC and liver dysfunction under immunotherapy: a systematic review and meta-analysis. Hepatology, 2023, 77(4): 1139-1149.
49.	Milioglou I, Motairek I, Deo S, et al. Time-varying cardiovascular outcomes of sodium-glucose cotransporter inhibitors in patients with type 2 diabetes: a post hoc analysis of pivotal trials using restricted mean survival time. Circ Cardiovasc Qual Outcomes, 2023, 16(3): e009491.
50.	Tan DJH, Ng CH, Tay PWL, et al. Risk of hepatocellular carcinoma with tenofovir vs entecavir treatment for chronic hepatitis B virus: a reconstructed individual patient data meta-analysis. JAMA Netw Open, 2022, 5(6): e2219407.
51.	Burke DL, Ensor J, Riley RD. Meta-analysis using individual participant data: one-stage and two-stage approaches, and why they may differ. Stat Med, 2017, 36(5): 855-875.
52.	Abo-Zaid G, Guo B, Deeks JJ, et al. Individual participant data meta-analyses should not ignore clustering. J Clin Epidemiol, 2013, 66(8): 865-873.
53.	Hougaard P. Frailty models for survival data. Lifetime Data Anal, 1995, 1(3): 255-273.
54.	Charvat H, Belot A. Mexhaz: an R package for fitting flexible hazard-based regression models for overall and excess mortality with a random effect. J Stat Softw, 2021, 98: 1-36.

1. Altman DG, Bland JM. Time to event (survival) data. BMJ, 1998, 317(7156): 468-469.
2. Cox DR. Regression models and life-tables. J R Stat Soc Series B Stat Methodol, 1972, 34: 187-202.
3. Dekker FW, de Mutsert R, van Dijk PC, et al. Survival analysis: time-dependent effects and time-varying risk factors. Kidney Int, 2008, 74(8): 994-997.
4. Mok TS, Wu YL, Thongprasert S, et al. Gefitinib or carboplatin-paclitaxel in pulmonary adenocarcinoma. N Engl J Med, 2009, 361(10): 947-957.
5. Haidich AB. Meta-analysis in medical research. Hippokratia, 2010, 14(Suppl 1): 29-37.
6. Williamson PR, Smith CT, Hutton JL, et al. Aggregate data meta-analysis with time-to-event outcomes. Stat Med, 2002, 21(22): 3337-3351.
7. Zou X, Shi Q, Vandvik PO, et al. Sodium-glucose cotransporter-2 inhibitors in patients with heart failure : a systematic review and meta-analysis. Ann Intern Med, 2022, 175(6): 851-861.
8. Kleinbaum D, Klein M. Survival analysis: a self-learning text (3rd edition). New York: Springer, 2012.
9. Kaplan EL, Meier P. Non parametric estimation from incomplete observations. J Am Stat Assoc, 1958, 53: 457-481.
10. Rich JT, Neely JG, Paniello RC, et al. A practical guide to understanding Kaplan-Meier curves. Otolaryngol Head Neck Surg, 2010, 143(3): 331-336.
11. Mantel N. Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemother Rep, 1966, 50(3): 163-170.
12. Gehan EA. A generalized wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika, 1965, 52: 203-223.
13. Tarone RE, Ware J. On distribution-free tests for equality of survival distributions. Biometrika, 1977, 64(1): 156-160.
14. Peto R, Peto J. Asymptotically efficient rank invariant test procedures. J R Stat Soc Ser A, 1972, 135(2): 185-198.
15. Harrington DP, Fleming TR. A class of rank test procedures for censored survival data. Biometrika, 1982, 69(3): 553-566.
16. Bollschweiler E. Benefits and limitations of Kaplan-Meier calculations of survival chance in cancer surgery. Langenbecks Arch Surg, 2003, 388(4): 239-244.
17. Crowther MJ, Lambert PC. A general framework for parametric survival analysis. Stat Med, 2014, 33(30): 5280-5297.
18. Zhang Z. Parametric regression model for survival data: Weibull regression model as an example. Ann Transl Med, 2016, 4(24): 484.
19. Ananthakrishnan R, Green S, Previtali A, et al. Critical review of oncology clinical trial design under non-proportional hazards. Crit Rev Oncol Hematol, 2021, 162: 103350.
20. Hess KR. Graphical methods for assessing violations of the proportional hazards assumption in Cox regression. Stat Med, 1995, 14(15): 1707-1723.
21. Ng'andu NH. An empirical comparison of statistical tests for assessing the proportional hazards assumption of Cox's model. Stat Med, 1997, 16(6): 611-626.
22. Zhang Z, Reinikainen J, Adeleke KA, et al. Time-varying covariates and coefficients in Cox regression models. Ann Transl Med, 2018, 6(7): 121.
23. Anderson JR, Cain KC, Gelber RD. Analysis of survival by tumor response. J Clin Oncol, 1983, 1(11): 710-719.
24. Gleiss A, Oberbauer R, Heinze G. An unjustified benefit: immortal time bias in the analysis of time-dependent events. Transpl Int, 2018, 31(2): 125-130.
25. Ascierto PA, Long GV. Progression-free survival landmark analysis: a critical endpoint in melanoma clinical trials. Lancet Oncol, 2016, 17(8): 1037-1039.
26. Heymach JV, Harpole D, Mitsudomi T, et al. Perioperative durvalumab for resectable non-small-cell lung cancer. N Engl J Med, 2023, 389(18): 1672-1684.
27. Kfoury M, Najean M, Lappara A, et al. Analysis of the association between prospectively collected immune-related adverse events and survival in patients with solid tumor treated with immune-checkpoint blockers, taking into account immortal-time bias. Cancer Treat Rev, 2022, 110: 102452.
28. Ueyama HA, Miyamoto Y, Watanabe A, et al. Cardiac re-operation or transcatheter mitral valve replacement for patients with failed mitral prostheses. J Am Coll Cardiol, 2023.
29. Sá MP, Jacquemyn X, Van den Eynde J, et al. Impact of prosthesis-patient mismatch after transcatheter aortic valve replacement: meta-analysis of Kaplan-Meier-derived individual patient data. JACC Cardiovasc Imaging, 2023, 16(3): 298-310.
30. Dafni U. Landmark analysis at the 25-year landmark point. Circ cardiovasc qual outcomes, 2011, 4(3): 363-371.
31. Royston P, Parmar MK. The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Stat Med, 2011, 30(19): 2409-2421.
32. Dehbi HM, Royston P, Hackshaw A. Life expectancy difference and life expectancy ratio: two measures of treatment effects in randomised trials with non-proportional hazards. BMJ, 2017, 357: j2250.
33. Royston P, Parmar MK. Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. BMC Med Res Methodol, 2013, 13: 152.
34. Pak K, Uno H, Kim DH, et al. Interpretability of cancer clinical trial results using restricted mean survival time as an alternative to the hazard ratio. JAMA Oncol, 2017, 3(12): 1692-1696.
35. Kim DH, Uno H, Wei LJ. Restricted mean survival time as a measure to interpret clinical trial results. JAMA Cardiol, 2017, 2(11): 1179-1180.
36. Ehrmann S, Barbier F, Demiselle J, et al. Inhaled amikacin to prevent ventilator-associated pneumonia. N Engl J Med, 2023, 389(22): 2052-2062.
37. Owen RK, Lyons J, Akbari A, et al. Effect on life expectancy of temporal sequence in a multimorbidity cluster of psychosis, diabetes, and congestive heart failure among 1·7 million individuals in Wales with 20-year follow-up: a retrospective cohort study using linked data. Lancet Public Health, 2023, 8(7): e535-e545.
38. Kloecker DE, Davies MJ, Khunti K, et al. Uses and limitations of the restricted mean survival time: illustrative examples from cardiovascular outcomes and mortality trials in type 2 diabetes. Ann Intern Med, 2020, 172(8): 541-552.
39. Royston P, Parmar MK. Flexible parametric proportional-hazards and proportional-odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects. Stat Med, 2002, 21(15): 2175-2197.
40. Jackson CH. flexsurv: A platform for parametric survival modeling in R. J Stat Softw, 2016, 70: i08.
41. Stewart LA, Parmar MK. Meta-analysis of the literature or of individual patient data: is there a difference. Lancet, 1993, 341(8842): 418-422.
42. Guyot P, Ades AE, Ouwens MJ, et al. Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves. BMC Med Res Methodol, 2012, 12: 9.
43. Wei Y, Royston P. Reconstructing time-to-event data from published Kaplan-Meier curves. Stata J, 2017, 17(4): 786-802.
44. Liu N, Zhou Y, Lee JJ. IPD from KM: reconstruct individual patient data from published Kaplan-Meier survival curves. BMC Med Res Methodol, 2021, 21(1): 111.
45. Cumpston M, Li T, Page MJ, et al. Updated guidance for trusted systematic reviews: a new edition of the Cochrane handbook for systematic reviews of interventions. Cochrane Database Syst Rev, 2019, (10): ED000142.
46. Wei Y, Royston P, Tierney JF, et al. Meta-analysis of time-to-event outcomes from randomized trials using restricted mean survival time: application to individual participant data. Stat Med, 2015, 34(21): 2881-2898.
47. Weir IR, Tian L, Trinquart L. Multivariate meta-analysis model for the difference in restricted mean survival times. Biostatistics, 2021, 22(1): 82-96.
48. El Hajra I, Sanduzzi-Zamparelli M, Sapena V, et al. Outcome of patients with HCC and liver dysfunction under immunotherapy: a systematic review and meta-analysis. Hepatology, 2023, 77(4): 1139-1149.
49. Milioglou I, Motairek I, Deo S, et al. Time-varying cardiovascular outcomes of sodium-glucose cotransporter inhibitors in patients with type 2 diabetes: a post hoc analysis of pivotal trials using restricted mean survival time. Circ Cardiovasc Qual Outcomes, 2023, 16(3): e009491.
50. Tan DJH, Ng CH, Tay PWL, et al. Risk of hepatocellular carcinoma with tenofovir vs entecavir treatment for chronic hepatitis B virus: a reconstructed individual patient data meta-analysis. JAMA Netw Open, 2022, 5(6): e2219407.
51. Burke DL, Ensor J, Riley RD. Meta-analysis using individual participant data: one-stage and two-stage approaches, and why they may differ. Stat Med, 2017, 36(5): 855-875.
52. Abo-Zaid G, Guo B, Deeks JJ, et al. Individual participant data meta-analyses should not ignore clustering. J Clin Epidemiol, 2013, 66(8): 865-873.
53. Hougaard P. Frailty models for survival data. Lifetime Data Anal, 1995, 1(3): 255-273.
54. Charvat H, Belot A. Mexhaz: an R package for fitting flexible hazard-based regression models for overall and excess mortality with a random effect. J Stat Softw, 2021, 98: 1-36.

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Effect modification by time in evidence synthesis of time-to-event outcomes

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