Implementing meta-analysis based on linear or nonlinear multi-level models using SAS MIXED and SAS NLMIXED_Chinese Journal of Evidence-Based Medicine

Authors：

ZHENG Jianqing ^1,2 , LI Tingting ² , XIAO Lihua ² ,  CAI Qunrong ²

1. Clinical Research Center, The Second Affiliated Hospital of Fujian Medical University, Quanzhou, 362000, P.R.China;
2. Department of Radiation Therapy, The Second Affiliated Hospital of Fujian Medical University, Quanzhou, 362000, P.R.China;

Corresponding author：

CAI Qunrong, Email: caiqr_1969@163.com

Keywords：

Linear mixed effect model; Non-linear mixed effect model; Multilevel model; Meta-analysis

DOI：

10.7507/1672-2531.201911074

Video：

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Abstract Full text Figures/Tables Video References Cited by

Objective To introduce a meta-analysis of linear or nonlinear multilevel models using SAS MIXED and SAS NLMIXED.Methods A systematic review performed to evaluate the risk of local recurrence in patients with cervical cancer treated with radical chemoradiotherapy and adjuvant surgery published by Shim et al. was selected as an illustration. An SAS software was used to implement meta-analysis based on linear or nonlinear multi-level models, and programming codes were provided.Results In the absence of covariates, the OR combined effect values of PROC MIXED based on the bivariate random effects model and PROC NLMIXED of the nonlinear mixed effects model were 0.63 (95%CI 0.46 to 0.87, P=0.005 7) and 0.60 (95%CI 0.39 to 0.81, P=0.000 3), respectively. In the case of covariates, the bivariate random effects model and the nonlinear mixed effects model provided an effect value of OR=0.65 (95%CI 0.47 to 0.91, P=0.011) and 0.59 (95%CI 0.38 to 0.80, P=0.000 3). Covariate OR effect values were 2.70 (95%CI 0.16 to 45.23, P>0.05) and 1.86 (95%CI −0.07 to 3.79, P=0.06).Conclusions The meta-analysis results of the SAS NLMIXED nonlinear mixed-effects model are similar to those of the SAS MIXED linear mixed-effects model. PROC NLMIXED has powerful programming capability and nonlinear mixed-effects model has flexible modeling capabilities for sparse data. Therefore, PROC NLMIXED will play an increasingly important role in meta-analysis.

Citation： ZHENG Jianqing, LI Tingting, XIAO Lihua, CAI Qunrong. Implementing meta-analysis based on linear or nonlinear multi-level models using SAS MIXED and SAS NLMIXED. Chinese Journal of Evidence-Based Medicine, 2020, 20(3): 351-358. doi: 10.7507/1672-2531.201911074 Copy

1.	Sheu CF, Suzuki S. Meta-analysis using linear mixed models. Behav Res Meth Ins C, 2001, 33(2): 102.
2.	肖丽华, 郑建清, 黄碧芬, 等. 利用SAS软件实现基于多水平模型纵向数据的Meta分析. 中国循证医学杂志, 2019, 19(5): 614-621.
3.	郑建清, 黄碧芬, 吴敏, 等. 基于SAS NLMIXED的广义线性混合效应模型在发病率数据Meta分析中的应用. 中国循证儿科杂志, 2019, 14(2): 129-133.
4.	DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials, 1986, 7(3): 177-188.
5.	DerSimonian R, Laird N. Meta-analysis in clinical trials revisited. Contemp Clin Trials, 2015, 45(2015): 139-145.
6.	朱彩蓉, 刘忠华, 孙克宏, 等. 组合聚集数据与个体数据的多水平Meta分析模型. 四川大学学报(医学版), 2005, 36(6): 133-136.
7.	Thompson SG, Sharp SJ. Explaining heterogeneity in meta-analysis: a comparison of methods. Stat Med, 1999, 18(20): 2693-2708.
8.	程里礼, 雷鹏, 陶园, 等. 基于统计学角度:解读固定效应模型和随机效应模型. 中国循证心血管医学杂志, 2017, 9(3): 261-264.
9.	徐畅, 曾宪涛, Suhail D, et al. 选择QE或RE模型:一种带偏倚校正功能的加权方式在Meta分析中的应用. 中国循证医学杂志, 2016, 16(5): 612-616.
10.	Shim SH, Kim SN, Chae SH, et al. Impact of adjuvant hysterectomy on prognosis in patients with locally advanced cervical cancer treated with concurrent chemoradiotherapy: a meta-analysis. J Gynecol Oncol, 2018, 29(2): e25.
11.	王明高, 孟生旺. 贝叶斯非线性混合效应模型及其应用研究. 统计与信息论坛, 2016, 31(12): 10-16.
12.	Sheu CF, Chen CT, Su YH, et al. Using SAS PROC NLMIXED to fit item response theory models. Behav Res Methods, 2005, 37(2): 202-218.
13.	Harring JR, Blozis SA. Fitting correlated residual error structures in nonlinear mixed-effects models using SAS PROC NLMIXED. Behav Res Methods, 2014, 46(2): 372-384.
14.	李晓松, 刘巧兰, 倪宗瓒. Meta分析中两水平混合效应模型方法的探讨. 数理医药学杂志, 1999, 12(2): 97-98.
15.	Chu H, Nie L, Chen Y, et al. Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: methods for the absolute risk difference and relative risk. Stat Methods Med Res, 2012, 21(6): 621-633.
16.	Burdon J, Connolly P, Silva N, et al. A meta-analysis using a logit non-linear mixed effects model for ‘Hass’ avocado postharvest performance data. Postharvest Biol Tec, 2013, 86(2013): 134-140.

1. Sheu CF, Suzuki S. Meta-analysis using linear mixed models. Behav Res Meth Ins C, 2001, 33(2): 102.
2. 肖丽华, 郑建清, 黄碧芬, 等. 利用SAS软件实现基于多水平模型纵向数据的Meta分析. 中国循证医学杂志, 2019, 19(5): 614-621.
3. 郑建清, 黄碧芬, 吴敏, 等. 基于SAS NLMIXED的广义线性混合效应模型在发病率数据Meta分析中的应用. 中国循证儿科杂志, 2019, 14(2): 129-133.
4. DerSimonian R, Laird N. Meta-analysis in clinical trials. Control Clin Trials, 1986, 7(3): 177-188.
5. DerSimonian R, Laird N. Meta-analysis in clinical trials revisited. Contemp Clin Trials, 2015, 45(2015): 139-145.
6. 朱彩蓉, 刘忠华, 孙克宏, 等. 组合聚集数据与个体数据的多水平Meta分析模型. 四川大学学报(医学版), 2005, 36(6): 133-136.
7. Thompson SG, Sharp SJ. Explaining heterogeneity in meta-analysis: a comparison of methods. Stat Med, 1999, 18(20): 2693-2708.
8. 程里礼, 雷鹏, 陶园, 等. 基于统计学角度:解读固定效应模型和随机效应模型. 中国循证心血管医学杂志, 2017, 9(3): 261-264.
9. 徐畅, 曾宪涛, Suhail D, et al. 选择QE或RE模型:一种带偏倚校正功能的加权方式在Meta分析中的应用. 中国循证医学杂志, 2016, 16(5): 612-616.
10. Shim SH, Kim SN, Chae SH, et al. Impact of adjuvant hysterectomy on prognosis in patients with locally advanced cervical cancer treated with concurrent chemoradiotherapy: a meta-analysis. J Gynecol Oncol, 2018, 29(2): e25.
11. 王明高, 孟生旺. 贝叶斯非线性混合效应模型及其应用研究. 统计与信息论坛, 2016, 31(12): 10-16.
12. Sheu CF, Chen CT, Su YH, et al. Using SAS PROC NLMIXED to fit item response theory models. Behav Res Methods, 2005, 37(2): 202-218.
13. Harring JR, Blozis SA. Fitting correlated residual error structures in nonlinear mixed-effects models using SAS PROC NLMIXED. Behav Res Methods, 2014, 46(2): 372-384.
14. 李晓松, 刘巧兰, 倪宗瓒. Meta分析中两水平混合效应模型方法的探讨. 数理医药学杂志, 1999, 12(2): 97-98.
15. Chu H, Nie L, Chen Y, et al. Bivariate random effects models for meta-analysis of comparative studies with binary outcomes: methods for the absolute risk difference and relative risk. Stat Methods Med Res, 2012, 21(6): 621-633.
16. Burdon J, Connolly P, Silva N, et al. A meta-analysis using a logit non-linear mixed effects model for ‘Hass’ avocado postharvest performance data. Postharvest Biol Tec, 2013, 86(2013): 134-140.

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