在进行网状meta分析过程中，一些试验经常会出现罕见事件（Rare event）。尤其是在安全性评价中，由于一些不良事件发生率低、样本量不充足，导致试验组和对照组的事件发生例数少，甚至出现0事件。针对出现0事件的研究，常采用连续性校正法进行校正，具体做法为对零事件研究中的每个分类的事件数均添加 0.5，用以近似估算效应量。另外，还有Mantel-Haenszel（M-H）和Non-central hypergeometric两种处理方法（具体理论部分可参考下文）。
今天的文章主要介绍使用netmeta程序包实现三种处理罕见事件的NMA方法。
程序包及数据加载
library(netmeta) # 加载程序包
data(Gurusamy2011) # 自带数据集
head(Gurusamy2011) # 查看数据
study treatment death n
1 Findlay 2001 Control/Placebo 1 30
2 Findlay 2001 Aprotonin 0 33
3 Garcia-Huete 1997 Control/Placebo 3 41
4 Garcia-Huete 1997 Aprotonin 1 39
5 Porte 2000 Control/Placebo 4 48
6 Porte 2000 Aprotonin 5 89
p1 = pairwise(treatment,
death,
n,
studlab = study,
data = Gurusamy2011,
sm = "OR")
Inverse variance NMA
针对罕见事件，netmeta程序包的主要函数为netmetabin，其中最传统的方法为倒方差法（Inverse variance），通过设定method = "Inverse"来实现。
IV1 = netmetabin(p1,
ref = "Control/Placebo",
method = "Inverse",
comb.random = FALSE)
网络证据图绘制
netgraph(IV1,
seq = "optimal",
col = "#BFBFBF",
plastic = F,
points = TRUE,
pch = 21,
cex.points =10*sqrt(n.trts/max(n.trts)),
col.points = "#BFBFBF",
bg.points = "#5C8286",
multiarm = FALSE,
number.of.studies = TRUE)
森林图绘制
forest(IV1,
drop = TRUE,
col.square = "#5C8286",
sortvar = TE)
Mantel-Haenszel NMA
Mantel-Haenszel方法是netmeta程序包中处理罕见事件的默认方法。
MH1 = netmetabin(p1,
ref = "Control/Placebo")
森林图绘制
forest(MH1,
drop = TRUE,
col.square = "#5C8286",
sortvar = TE)
节点分割法
print(netsplit(MH1),
show = "both",
ci = TRUE,
overall = FALSE)
Separate indirect from direct design evidence (SIDDE)
Common effects model:
comparison k direct 95%-CI indir. 95%-CI.1 RoR 95%-CI.2 z p-value
Aprotonin:Control/Placebo 3 0.4728 [0.1538; 1.4537] 0.0792 [0.0060; 1.0390] 5.9692 [0.3599; 98.9933] 1.25 0.2125
Aprotonin:Tranexamic acid 2 0.1633 [0.0191; 1.3962] 0.9745 [0.1593; 5.9627] 0.1675 [0.0101; 2.7783] -1.25 0.2125
Tranexamic acid:Control/Placebo 3 0.4688 [0.1187; 1.8511] 2.8960 [0.2569; 32.6456] 0.1619 [0.0100; 2.6213] -1.28 0.2000
Legend:
comparison - Treatment comparison
k - Number of studies providing direct evidence
direct - Estimated treatment effect (OR) derived from direct evidence
indir. - Estimated treatment effect (OR) derived from indirect evidence
RoR - Ratio of Ratios (direct versus indirect)
z - z-value of test for disagreement (direct versus indirect)
p-value - p-value of test for disagreement (direct versus indirect)
Non-central hypergeometric NMA
Non-central hypergeometric方法主要通过设定method = "NCH"来实现。
NCH1 = netmetabin(p1,
ref = "Control/Placebo",
method = "NCH")
森林图绘制
forest (NCH1,
drop = TRUE,
col.square = "#5C8286",
sortvar = TE)
可以通过森林图对比上述三种方法的结果。
参考文献
1. Efthimiou O. Practical guide to the meta-analysis of rare events. Evid Based Ment Health. 2018;21(2):72-76
2. Efthimiou O, Rücker G, Schwarzer G, Higgins JPT, Egger M, Salanti G. Network meta-analysis of rare events using the Mantel-Haenszel method. Stat Med. 2019;38(16):2992-3012.