Network Meta-Analysis

Code

source("R/nma_functions.R")
dat <- load_pairwise_data()
nm_random <- run_model(dat, model_type = "simple", effect_model = "random")

Network plot

Code

netmeta::netgraph(
  nm_random,
  number.of.studies = TRUE,
  thickness = "number.of.studies",
  multiarm = TRUE,
  points = TRUE,
  cex.points = 4,
  cex = 0.8,
  plastic = FALSE,
  seq = sort(nm_random$trts)
)

Model summary

Code

summary(nm_random, backtransf = TRUE)

Original data:

           treat1        treat2      TE   seTE
study 1        BR             I -1.0210 0.1810
study 2       FCR         I + R -0.9940 0.1620
study 3       FCR         I + R -0.8200 0.1600
study 4       FCR     Ibr + Ven -1.1390 0.2380
study 5   Clb + O     Ibr + Ven -1.3100 0.1950
study 6   Clb + O       Ven + O -1.1710 0.1790
study 7   Clb + O       Ibr + O -1.3860 0.2270
study 8       Clb             I -1.8720 0.1810
study 9  Acal + O       Clb + O  1.9670 0.1770
study 10     Acal       Clb + O  1.4270 0.1610
study 11       BR  Zanubrutinib -1.2380 0.1640
study 12 FCR + BR       Ven + O -0.7550 0.1930
study 13 FCR + BR Ven + O + Ibr -1.2040 0.2310
study 14 FCR + BR       Ven + R -0.3570 0.0820
study 15       BR       Clb + O  0.6000 0.2000

Number of treatment arms (by study):
         narms
study 1      2
study 2      2
study 3      2
study 4      2
study 5      2
study 6      2
study 7      2
study 8      2
study 9      2
study 10     2
study 11     2
study 12     2
study 13     2
study 14     2
study 15     2

Results (common effects model):

           treat1        treat2     HR            95%-CI    Q leverage
study 1        BR             I 0.3602 [0.2526;  0.5136] 0.00     1.00
study 2       FCR         I + R 0.4042 [0.3233;  0.5052] 0.30     0.49
study 3       FCR         I + R 0.4042 [0.3233;  0.5052] 0.29     0.51
study 4       FCR     Ibr + Ven 0.3201 [0.2008;  0.5104] 0.00     1.00
study 5   Clb + O     Ibr + Ven 0.2698 [0.1841;  0.3954] 0.00     1.00
study 6   Clb + O       Ven + O 0.3101 [0.2183;  0.4404] 0.00     1.00
study 7   Clb + O       Ibr + O 0.2501 [0.1603;  0.3902] 0.00     1.00
study 8       Clb             I 0.1538 [0.1079;  0.2193] 0.00     1.00
study 9  Acal + O       Clb + O 7.1492 [5.0535; 10.1139] 0.00     1.00
study 10     Acal       Clb + O 4.1662 [3.0387;  5.7119] 0.00     1.00
study 11       BR  Zanubrutinib 0.2900 [0.2103;  0.3999] 0.00     1.00
study 12 FCR + BR       Ven + O 0.4700 [0.3220;  0.6861] 0.00     1.00
study 13 FCR + BR Ven + O + Ibr 0.3000 [0.1908;  0.4718] 0.00     1.00
study 14 FCR + BR       Ven + R 0.6998 [0.5959;  0.8218] 0.00     1.00
study 15       BR       Clb + O 1.8221 [1.2312;  2.6966] 0.00     1.00

Results (random effects model):

           treat1        treat2     HR            95%-CI
study 1        BR             I 0.3602 [0.2526;  0.5136]
study 2       FCR         I + R 0.4042 [0.3233;  0.5052]
study 3       FCR         I + R 0.4042 [0.3233;  0.5052]
study 4       FCR     Ibr + Ven 0.3201 [0.2008;  0.5104]
study 5   Clb + O     Ibr + Ven 0.2698 [0.1841;  0.3954]
study 6   Clb + O       Ven + O 0.3101 [0.2183;  0.4404]
study 7   Clb + O       Ibr + O 0.2501 [0.1603;  0.3902]
study 8       Clb             I 0.1538 [0.1079;  0.2193]
study 9  Acal + O       Clb + O 7.1492 [5.0535; 10.1139]
study 10     Acal       Clb + O 4.1662 [3.0387;  5.7119]
study 11       BR  Zanubrutinib 0.2900 [0.2103;  0.3999]
study 12 FCR + BR       Ven + O 0.4700 [0.3220;  0.6861]
study 13 FCR + BR Ven + O + Ibr 0.3000 [0.1908;  0.4718]
study 14 FCR + BR       Ven + R 0.6998 [0.5959;  0.8218]
study 15       BR       Clb + O 1.8221 [1.2312;  2.6966]

Number of studies: k = 15
Number of pairwise comparisons: m = 15
Number of treatments: n = 15
Number of designs: d = 14

Common effects model

Treatment estimate (sm = 'HR', comparison: other treatments vs 'Acal'):
                  HR           95%-CI     z  p-value
Acal               .                .     .        .
Acal + O      1.7160 [1.0736; 2.7427]  2.26   0.0240
BR            0.4374 [0.2644; 0.7234] -3.22   0.0013
Clb           0.1867 [0.0918; 0.3801] -4.63 < 0.0001
Clb + O       0.2400 [0.1751; 0.3291] -8.86 < 0.0001
FCR           0.2848 [0.1442; 0.5625] -3.62   0.0003
FCR + BR      0.3639 [0.1987; 0.6662] -3.28   0.0011
I             1.2141 [0.6559; 2.2472]  0.62   0.5369
I + R         0.7046 [0.3443; 1.4422] -0.96   0.3381
Ibr + O       0.9598 [0.5563; 1.6561] -0.15   0.8829
Ibr + Ven     0.8896 [0.5419; 1.4603] -0.46   0.6436
Ven + O       0.7741 [0.4829; 1.2409] -1.06   0.2876
Ven + O + Ibr 1.2129 [0.5698; 2.5818]  0.50   0.6166
Ven + R       0.5200 [0.2781; 0.9722] -2.05   0.0405
Zanubrutinib  1.5083 [0.8302; 2.7404]  1.35   0.1773

Random effects model

Treatment estimate (sm = 'HR', comparison: other treatments vs 'Acal'):
                  HR           95%-CI     z  p-value
Acal               .                .     .        .
Acal + O      1.7160 [1.0736; 2.7427]  2.26   0.0240
BR            0.4374 [0.2644; 0.7234] -3.22   0.0013
Clb           0.1867 [0.0918; 0.3801] -4.63 < 0.0001
Clb + O       0.2400 [0.1751; 0.3291] -8.86 < 0.0001
FCR           0.2848 [0.1442; 0.5625] -3.62   0.0003
FCR + BR      0.3639 [0.1987; 0.6662] -3.28   0.0011
I             1.2141 [0.6559; 2.2472]  0.62   0.5369
I + R         0.7046 [0.3443; 1.4422] -0.96   0.3381
Ibr + O       0.9598 [0.5563; 1.6561] -0.15   0.8829
Ibr + Ven     0.8896 [0.5419; 1.4603] -0.46   0.6436
Ven + O       0.7741 [0.4829; 1.2409] -1.06   0.2876
Ven + O + Ibr 1.2129 [0.5698; 2.5818]  0.50   0.6166
Ven + R       0.5200 [0.2781; 0.9722] -2.05   0.0405
Zanubrutinib  1.5083 [0.8302; 2.7404]  1.35   0.1773

Quantifying heterogeneity / inconsistency:
tau^2 = 0; tau = 0; I^2 = 0%

Tests of heterogeneity (within designs) and inconsistency (between designs):
                   Q d.f. p-value
Total           0.58    1  0.4448
Within designs  0.58    1  0.4448
Between designs 0.00    0      --

Details of network meta-analysis methods:
- Frequentist graph-theoretical approach
- DerSimonian-Laird estimator for tau^2
- Calculation of I^2 based on Q

Forest plot

Code

forest(nm_random, backtransf = TRUE)

League table

Code

lt <- netmeta::netleague(nm_random, random = TRUE, common = FALSE, ci = TRUE,
                         backtransf = TRUE, bracket = "(", separator = " - ")
knitr::kable(as.data.frame(lt$random))

	Acal	Acal + O	BR	Clb	Clb + O	FCR	FCR + BR	I	I + R	Ibr + O	Ibr + Ven	Ven + O	Ven + O + Ibr	Ven + R	Zanubrutinib
Acal	Acal	.	.	.	4.1662 (3.0387 - 5.7119)	.	.	.	.	.	.	.	.	.	.
Acal + O	0.5827 (0.3646 - 0.9314)	Acal + O	.	.	7.1492 (5.0535 - 10.1139)	.	.	.	.	.	.	.	.	.	.
BR	2.2864 (1.3823 - 3.7819)	3.9236 (2.3246 - 6.6224)	BR	.	1.8221 (1.2312 - 2.6966)	.	.	0.3602 (0.2526 - 0.5136)	.	.	.	.	.	.	0.2900 (0.2103 - 0.3999)
Clb	5.3548 (2.6311 - 10.8981)	9.1889 (4.4502 - 18.9738)	2.3420 (1.4181 - 3.8678)	Clb	.	.	.	0.1538 (0.1079 - 0.2193)	.	.	.	.	.	.	.
Clb + O	4.1662 (3.0387 - 5.7119)	7.1492 (5.0535 - 10.1139)	1.8221 (1.2312 - 2.6966)	0.7780 (0.4116 - 1.4706)	Clb + O	.	.	.	.	0.2501 (0.1603 - 0.3902)	0.2698 (0.1841 - 0.3954)	0.3101 (0.2183 - 0.4404)	.	.	.
FCR	3.5113 (1.7778 - 6.9353)	6.0255 (3.0050 - 12.0820)	1.5357 (0.7481 - 3.1527)	0.6557 (0.2728 - 1.5761)	0.8428 (0.4611 - 1.5404)	FCR	.	.	0.4042 (0.3233 - 0.5052)	.	0.3201 (0.2008 - 0.5104)	.	.	.	.
FCR + BR	2.7483 (1.5011 - 5.0318)	4.7162 (2.5327 - 8.7821)	1.2020 (0.6288 - 2.2978)	0.5132 (0.2262 - 1.1647)	0.6597 (0.3938 - 1.1051)	0.7827 (0.3539 - 1.7309)	FCR + BR	.	.	.	.	0.4700 (0.3220 - 0.6861)	0.3000 (0.1908 - 0.4718)	0.6998 (0.5959 - 0.8218)	.
I	0.8237 (0.4450 - 1.5245)	1.4134 (0.7510 - 2.6600)	0.3602 (0.2526 - 0.5136)	0.1538 (0.1079 - 0.2193)	0.1977 (0.1165 - 0.3354)	0.2346 (0.1052 - 0.5231)	0.2997 (0.1432 - 0.6273)	I	.	.	.	.	.	.	.
I + R	1.4192 (0.6934 - 2.9047)	2.4353 (1.1729 - 5.0566)	0.6207 (0.2923 - 1.3180)	0.2650 (0.1072 - 0.6551)	0.3406 (0.1791 - 0.6480)	0.4042 (0.3233 - 0.5052)	0.5164 (0.2264 - 1.1776)	1.7230 (0.7495 - 3.9611)	I + R	.	.	.	.	.	.
Ibr + O	1.0419 (0.6038 - 1.7976)	1.7878 (1.0170 - 3.1430)	0.4557 (0.2518 - 0.8245)	0.1946 (0.0895 - 0.4230)	0.2501 (0.1603 - 0.3902)	0.2967 (0.1402 - 0.6278)	0.3791 (0.1918 - 0.7492)	1.2649 (0.6338 - 2.5243)	0.7341 (0.3359 - 1.6045)	Ibr + O	.	.	.	.	.
Ibr + Ven	1.1241 (0.6848 - 1.8453)	1.9290 (1.1512 - 3.2322)	0.4916 (0.2844 - 0.8500)	0.2099 (0.0999 - 0.4411)	0.2698 (0.1841 - 0.3954)	0.3201 (0.2008 - 0.5104)	0.4090 (0.2152 - 0.7773)	1.3648 (0.7108 - 2.6205)	0.7921 (0.4723 - 1.3284)	1.0790 (0.6002 - 1.9397)	Ibr + Ven	.	.	.	.
Ven + O	1.2918 (0.8058 - 2.0707)	2.2167 (1.3534 - 3.6306)	0.5650 (0.3339 - 0.9561)	0.2412 (0.1166 - 0.4990)	0.3101 (0.2183 - 0.4404)	0.3679 (0.1831 - 0.7391)	0.4700 (0.3220 - 0.6861)	1.5683 (0.8315 - 2.9580)	0.9102 (0.4375 - 1.8935)	1.2399 (0.7036 - 2.1850)	1.1491 (0.6840 - 1.9305)	Ven + O	.	.	.
Ven + O + Ibr	0.8245 (0.3873 - 1.7550)	1.4148 (0.6557 - 3.0529)	0.3606 (0.1636 - 0.7949)	0.1540 (0.0604 - 0.3927)	0.1979 (0.0996 - 0.3931)	0.2348 (0.0942 - 0.5855)	0.3000 (0.1908 - 0.4718)	1.0010 (0.4209 - 2.3807)	0.5810 (0.2268 - 1.4880)	0.7914 (0.3492 - 1.7932)	0.7334 (0.3343 - 1.6090)	0.6383 (0.3538 - 1.1514)	Ven + O + Ibr	.	.
Ven + R	1.9232 (1.0286 - 3.5958)	3.3003 (1.7365 - 6.2723)	0.8411 (0.4315 - 1.6398)	0.3592 (0.1558 - 0.8279)	0.4616 (0.2689 - 0.7925)	0.5477 (0.2437 - 1.2309)	0.6998 (0.5959 - 0.8218)	2.3350 (1.0964 - 4.9728)	1.3552 (0.5851 - 3.1388)	1.8460 (0.9167 - 3.7172)	1.7109 (0.8826 - 3.3164)	1.4888 (0.9871 - 2.2457)	2.3326 (1.4428 - 3.7713)	Ven + R	.
Zanubrutinib	0.6630 (0.3649 - 1.2046)	1.1377 (0.6155 - 2.1028)	0.2900 (0.2103 - 0.3999)	0.1238 (0.0682 - 0.2247)	0.1591 (0.0959 - 0.2642)	0.1888 (0.0859 - 0.4151)	0.2412 (0.1170 - 0.4972)	0.8049 (0.4987 - 1.2992)	0.4672 (0.2060 - 1.0594)	0.6364 (0.3242 - 1.2492)	0.5898 (0.3126 - 1.1128)	0.5132 (0.2771 - 0.9507)	0.8041 (0.3426 - 1.8876)	0.3447 (0.1643 - 0.7232)	Zanubrutinib