Empirical comparison of methods for analyzing multiple time-to-event outcomes in a non-inferiority trial: a breast cancer study

BMC Medical Research Methodology

Mark N Levine²  Timothy J Whelan²  Jim A Julian³  Lehana Thabane¹  Sameer Parpia³ 

[1] Department of Clinical Epidemiology and Biostatistics, McMaster University, Hamilton, ON, Canada;Juravinski Cancer Centre, 699 Concession Street, Hamilton, ON, L8V 5C2, Canada;Ontario Clinical Oncology Group, Department of Oncology, McMaster University, 711 Concession Street – G (60) Wing 1st Floor, Hamilton, ON, L8V 1C3, Canada

关键词: Competing risks;    Frailty model;    Marginal model;    Correlation;    Cox model;    Non-inferiority;   

Others  :  1125970
DOI  :  10.1186/1471-2288-13-44

 received in 2012-11-17, accepted in 2013-03-12,  发布年份 2013

【 摘 要 】

Background

Subjects with breast cancer enrolled in trials may experience multiple events such as local recurrence, distant recurrence or death. These events are not independent; the occurrence of one may increase the risk of another, or prevent another from occurring. The most commonly used Cox proportional hazards (Cox-PH) model ignores the relationships between events, resulting in a potential impact on the treatment effect and conclusions. The use of statistical methods to analyze multiple time-to-event events has mainly been focused on superiority trials. However, their application to non-inferiority trials is limited. We evaluate four statistical methods for multiple time-to-event endpoints in the context of a non-inferiority trial.

Methods

Three methods for analyzing multiple events data, namely, i) the competing risks (CR) model, ii) the marginal model, and iii) the frailty model were compared with the Cox-PH model using data from a previously-reported non-inferiority trial comparing hypofractionated radiotherapy with conventional radiotherapy for the prevention of local recurrence in patients with early stage breast cancer who had undergone breast conserving surgery. These methods were also compared using two simulated examples, scenario A where the hazards for distant recurrence and death were higher in the control group, and scenario B. where the hazards of distant recurrence and death were higher in the experimental group. Both scenarios were designed to have a non-inferiority margin of 1.50.

Results

In the breast cancer trial, the methods produced primary outcome results similar to those using the Cox-PH model: namely, a local recurrence hazard ratio (HR) of 0.95 and a 95% confidence interval (CI) of 0.62 to 1.46. In Scenario A, non-inferiority was observed with the Cox-PH model (HR = 1.04; CI of 0.80 to 1.35), but not with the CR model (HR = 1.37; CI of 1.06 to 1.79), and the average marginal and frailty model showed a positive effect of the experimental treatment. The results in Scenario A contrasted with Scenario B with non-inferiority being observed with the CR model (HR = 1.10; CI of 0.87 to 1.39), but not with the Cox-PH model (HR = 1.46; CI of 1.15 to 1.85), and the marginal and frailty model showed a negative effect of the experimental treatment.

Conclusion

When subjects are at risk for multiple events in non-inferiority trials, researchers need to consider using the CR, marginal and frailty models in addition to the Cox-PH model in order to provide additional information in describing the disease process and to assess the robustness of the results. In the presence of competing risks, the Cox-PH model is appropriate for investigating the biologic effect of treatment, whereas the CR models yields the actual effect of treatment in the study.

【 授权许可】

   
2013 Parpia et al.; licensee BioMed Central Ltd.

【 图 表 】

Figure 1.

Figure 2.

Figure 3.

【 参考文献 】

• [1]Andersen PK, Borgan O, Gill RD, Keiding N: Statistical models based on counting processes. New York: Springer; 1993.
• [2]Cox D: Regrssion models and life-tables. J Roy Stat Soc B Meth 1972, 43:187-220.
• [3]Gooley TA, Leisenring W, Crowley J, Storer BE: Estimation of failure probabilities in the presence of competing risks: new representations of old estimators. Stat Med 1999, 18:695-706.
• [4]Kim HT: Cumulative incidence in competing risks data and competing risks regression analysis. Clin Cancer Res 2007, 13:559-565.
• [5]Williamson PR, Kolamunnage-Dona R, Tudur Smith C: The influence of competing-risks setting on the choice of hypothesis test for treatment effect. Biostatistics 2007, 8:689-694.
• [6]Tai B-C, Grundy RG, Machin D: On the importance of accounting for competing risks in paediatric cancer trials designed to delay or avoid radiotherapy: I. Basic concepts and first analyses. Int J Radiat Oncol Biol Phys 2010, 76:1493-1499.
• [7]Fine J, Gray R: A proportional hazards model for the sub-distribution of a competing risk. J Am Stat Assoc 1999, 94:496-509.
• [8]Wei LJ, Glidden DV: An overview of statistical methods for multiple failure time data in clinical trials. Stat Med 1997, 16:833-839.
• [9]Hougaard P: Analysis of Multivariate Survival Data. New York, NY: Springer; 2000.
• [10]Bakoyannis G, Touloumi G: Practical methods for competing risks data: A review. Stat Methods Med Res 2011, 3:257-272.
• [11]Whelan T, MacKenzie R, Julian J, Levine M, Shelley W, Grimard L, Lada B, Lukka H, Perera F, Fyles A, Laukkanen E, Gulavita S, Benk V, Szechtman B: Randomized trial of breast irradiation schedules after lumpectomy for women with lymph node-negative breast cancer. J Natl Cancer Inst 2002, 94:1143-1150.
• [12]Whelan TJ, Pignol J-P, Levine MN, Julian JA, MacKenzie R, Parpia S, Shelley W, Grimard L, Bowen J, Lukka H, Perera F, Fyles A, Schneider K, Gulavita S, Freeman C: Long-term results of hypofractionated radiation therapy for breast cancer. N Engl J Med 2010, 362:513-520.
• [13]Parmar M, Machin D: Survival Analysis: A Practical Approach. Chichester, UK: John Wiley and Sons; 1995.
• [14]Kalbfleisch J, Prentice R: The Statistical Analysis of Failure Time Data. New York, USA: John Wiley and Sons; 1980.
• [15]Parpia S, Julian JA, Thabane L, Lee AYY, Rickles FR, Levine MN: Competing events in patients with malignant disease who are at risk for recurrent venous thromboembolism. Contemp Clin Trials 2011, 32:829-833.
• [16]Ghosh D: Methods for analysis of multiple events in the presence of death. Control Clin Trials 2000, 21:115-126.
• [17]Lim HJ, Liu J, Melzer-Lange M: Comparison of methods for analyzing recurrent events data: application to the Emergency Department Visits of Pediatric Firearm Victims. Accid Anal Prev 2007, 39:290-299.
• [18]Metcalfe C, Thompson SG: Wei, Lin and Weissfeld’s marginal analysis of multivariate failure time data: should it be applied to a recurrent events outcome? Stat Methods Med Res 2007, 16:103-122.
• [19]Li QH, Lagakos SW: Use of the Wei-Lin-Weissfeld method for the analysis of a recurring and a terminating event. Stat Med 1997, 16:925-940.
• [20]Wienke A: Frailty Models in Survival Analysis. Boca Raton, FL: Chapman & Hall/CRC; 2010.
• [21]Therneau T, Grambsch P: Modeling Survival Data. New York, NY: Springer; 2000.
• [22]Duchateau L, Janssen P: Evolution of recurrent asthma event rate over time in frailty models. J Roy Stat Soc C Appl Stat 2003, 52:355-363.
• [23]Duchateau L, Janssen P: The Frailty Model. New York, NY: Springer; 2010.
• [24]Freidlin B, Korn EL: Testing treatment effects in the presence of competing risks. Stat Med 2005, 24:1703-1712.
• [25]Clayton D: A model for association in bivariate life tables and its application in epidemiological of familial studies tendency in chronic disease incidence. Biometrika 1978, 65:141-151.
• [26]Hougaard P: A Class of Multivariate Failure Time Distributions. Biometrika 1986, 73:671-678.
• [27]B-Choo T, Stavola BLD, Gruttola VD, Gebski V, Machin D: First-event or marginal estimation of cause-specific hazards for analysing correlated multivariate failure-time data ? Stat Med 2008, 27:922-936.
• [28]Pintilie M: Competing Risks: A Practical Perspective. Chichester, UK: John Wiley and Sons; 2006.
• [29]Koller MT, Raatz H, Steyerberg EW, Wolbers M: Competing risks and the clinical community: irrelevance or ignorance? Stat Med 2011, 31:1089-1097.
• [30]Tai B-C, Wee J, Machin D: Analysis and design of randomised clinical trials involving competing risks endpoints. Trials 2011, 12:127. BioMed Central Full Text
• [31]Allignol A, Schumacher M, Wanner C, Drechsler C, Beyersmann J: Understanding competing risks: a simulation point of view. BMC Med Res Methodol 2011, 11:86. BioMed Central Full Text
• [32]Liu L, Huang X: The use of Gaussian quadrature for estimation in frailty proportional hazards models. Stat Med 2008, 27:2665-2683.
• [33]Dixon SN, Darlington GA, Desmond AF: A competing risks model for correlated data based on the subdistribution hazard. Lifetime Data Anal 2011, 17:473-495.