A practical method based on functional data analysis and single exponential smoothing to combine survival curves in meta-analysis: a simulation study.

*(English)*Zbl 1422.62305Summary: Aims: The best tool to incorporate the results of trials that include time to event outcomes is the individual patient data meta-analysis which is often neither practical nor possible. Other methods are not appropriate for meta-analysis of survival data since they cannot process single-arm trials, or are limited by distributional assumptions. We proposed a method, to dispel the shortcomings and pitfalls of other approaches.

Methods: At first, we use the early steps of functional data analysis (FDA) and a correction by single exponential smoothing (SES) to combine the survival curves. Then to compare two groups, a statistic similar to the Log-Rank is proposed. A simulation study was done to investigate statistical power and Type I error. Finally, we conduct our method on a clinical data example.

Results: In increasing hazard rate, the power of test statistic increased as the sample size increased in all failures rates, but it decreased as the failure rate increases. For low failure rate, it was more than 82%. It was less than 67% in failure rate 70%. In decreasing hazard rate, the power was high and increased as the sample size increases. For the failure rate of 10%, 30%, and 50% the statistical power is more than 80%.

Discussion: The proposed method is beneficial in combining the survival curves. The results agree to employ the proposed test statistic in determining the authenticity of the difference between groups in small or moderate failure rates, and moderate or high sample sizes, in all number of studies.

Methods: At first, we use the early steps of functional data analysis (FDA) and a correction by single exponential smoothing (SES) to combine the survival curves. Then to compare two groups, a statistic similar to the Log-Rank is proposed. A simulation study was done to investigate statistical power and Type I error. Finally, we conduct our method on a clinical data example.

Results: In increasing hazard rate, the power of test statistic increased as the sample size increased in all failures rates, but it decreased as the failure rate increases. For low failure rate, it was more than 82%. It was less than 67% in failure rate 70%. In decreasing hazard rate, the power was high and increased as the sample size increases. For the failure rate of 10%, 30%, and 50% the statistical power is more than 80%.

Discussion: The proposed method is beneficial in combining the survival curves. The results agree to employ the proposed test statistic in determining the authenticity of the difference between groups in small or moderate failure rates, and moderate or high sample sizes, in all number of studies.

##### MSC:

62N05 | Reliability and life testing |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

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\textit{S. Ghanbari} et al., Adv. Appl. Stat. 53, No. 2, 179--197 (2018; Zbl 1422.62305)

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##### References:

[1] | I. Ahmed, T. P. A. Debray, K. G. M. Moons and R. D Riley, Developing and validating risk prediction models in an individual participant data meta-analysis, BMC Med. Res. Methodol. 14(3) (2014), 15 pp. |

[2] | L. R. Arends, M. G. Hunink and T. Stijnen, Meta-analysis of summary survival curve data, Stat. Med. 27(22) (2008), 4381-4396. |

[3] | G. Bonadonna, G. N. Hortobagyi and P. Valagussa, Textbook of Breast Cancer: A Clinical Guide to Therapy, CRC Press, 2006. |

[4] | P. Čisar and S. M. Čisar, Optimization methods of EWMA statistics, Acta Polytechnica Hungarica 8(5) (2011), 73-87. 196 Saeed Ghanbari, Najaf Zare and Zahra Shayan · Zbl 1110.94010 |

[5] | M. J. Crowther, Simulating simple and complex survival data, United Kingdom Stata Users’ Group Meetings 2014, Stata Users Group, 2014. |

[6] | M. J. Crowther and P. C. Lambert, Simulating complex survival data, The Stata Journal 12(4) (2012), 674-687. |

[7] | M. J. Crowther and P. C. Lambert, Simulating biologically plausible complex survival data, Stat. Med. 32(23) (2013), 4118-4134. |

[8] | K. B. Dear, Iterative generalized least squares for meta-analysis of survival data at multiple times, Biometrics 50(4) (1994), 989-1002. · Zbl 0825.62791 |

[9] | T. Dehesh, N. Zare and S. M. T. Ayatollahi, The covariance adjustment approaches for combining incomparable Cox regressions caused by unbalanced covariates adjustment: a multivariate meta-analysis study, Comput. Math. Meth. Med. 2015 (2015), Article ID 801031, 11 pp. · Zbl 1335.92006 |

[10] | R. DerSimonian and R. Kacker, Random-effects model for meta-analysis of clinical trials: an update, Contemp. Clin. Trials 28(2) (2007), 105-114. |

[11] | C. C. Earle, B. Pham and G. A. Wells, An assessment of methods to combine published survival curves, Med. Decis. Making 20(1) (2000), 104-111. |

[12] | S. Ghanbari, S. M. Ayatollahi and N. Zare, Comparing role of two chemotherapy regimens, CMF and anthracycline-based, on breast cancer survival in the eastern Mediterranean region and Asia by multivariate mixed effects models: a metaanalysis, Asian Pac. J. Cancer Prev. 16(14) (2015), 5655-5661. |

[13] | P. Guyot, A. E. Ades, M. J. N. M. Ouwens and N. J Welton, Enhanced secondary analysis of survival data: reconstructing the data from published Kaplan-Meier survival curves, BMC Med. Res. Methodol. 12(9) (2012), 13 pp. |

[14] | R. J. Hyndman and G. Athanasopoulos, Forecasting: Principles and Practice, OTexts, 2014. |

[15] | D. Jackson, K. Rollins and P. Coughlin, A multivariate model for the metaanalysis of study level survival data at multiple times, Res. Synth. Methods 5(3) (2014), 264-272. |

[16] | J. P Jansen, Network meta-analysis of survival data with fractional polynomials, BMC Med. Res. Methodol. 11(61) (2011), 14 pp. |

[17] | D. Kleinbaum and M. Klein, Survival Analysis: A Self-learning Text, Springer, New York, 1996. · Zbl 1093.62090 |

[18] | P. F. Moodie, N. A. Nelson and G. G. Koch, A non-parametric procedure for evaluating treatment effect in the meta-analysis of survival data, Stat. Med. 23(7) (2004), 1075-1093. A Practical Method Based on Functional Data Analysis … 197 |

[19] | M. K. Parmar, V. Torri and L. Stewart, Extracting summary statistics to perform meta-analyses of the published literature for survival endpoints, Stat. Med. 17(24) (1998), 2815-2834. |

[20] | M. Pufulete, J. P. Higgins, C. A. Rogers, L. Dreyer, W. Hollingworth, M. Dayer, A. Nightingale, T. McDonagh and B. C. Reeves, Protocol for a systematic review and individual participant data meta-analysis of B-type natriuretic peptide-guided therapy for heart failure, Syst. Rev. 3 (2014), 41. |

[21] | J. O. Ramsay and B. W. Silverman, Applied Functional Data Analysis: Methods and Case Studies, Springer Series in Statistics, Springer-Verlag, New York, 2002. · Zbl 1011.62002 |

[22] | V. Rondeau, S. Michiels, B. Liquet and J.-P. Pignon, Investigating trial and treatment heterogeneity in an individual patient data meta-analysis of survival data by means of the penalized maximum likelihood approach, Stat. Med. 27(11) (2008), 1894-1910. |

[23] | P. Royston, Tools to simulate realistic censored survival-time distributions, Stata. J. 12(4) (2012), 639-654. |

[24] | P. Saramago, L. H. Chuang and M. O. Soares, Network meta-analysis of (individual patient) time to event data alongside (aggregate) count data, BMC Med. Res. Methodol. 14 (2014), 105. |

[25] | J. F. Tierney, L. A. Stewart, D. Ghersi, S. Burdett and M. R. Sydes, Practical methods for incorporating summary time-to-event data into meta-analysis, Trials 8 (2007), 16. |

[26] | X. Wan, L. Peng and Y. Li, A review and comparison of methods for recreating individual patient data from published Kaplan-Meier survival curves for economic evaluations: a simulation study, PLoS One 10(3) (2015), e0121353. |

[27] | A. Whitehead and J. Whitehead, A general parametric approach to the metaanalysis of randomized clinical trials, Stat. Med. 10(11) (1991), 1665-1677. |

[28] | P. R. Williamson, C. T. Smith, J. L. Hutton and A. G. Marson, Aggregate data meta-analysis with time-to-event outcomes, Stat. Med. 21(22) (2002), 3337-3351. |

[29] | N. Zare, S. Ghanbari and A. Salehi, Effects of two chemotherapy regimens, anthracycline-based and CMF, on breast cancer disease free survival in the eastern Mediterranean Region and Asia: a meta-analysis approach for survival curves, Asian Pac. J. Cancer Prev. 14(3) (2013), 2013-2017. |

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