Statsmodels におけるメタ分析¶
Statsmodels にはメタ分析のための基本的な方法が含まれています。このノートブックでは現在の使用法を示します。
ステータス: 結果は R の meta および metafor パッケージと照合して確認されています。ただし、API はまだ実験的であり、変更される可能性があります。R の meta および metafor パッケージで利用できる追加の方法のいくつかは、現在サポートされていません。
メタ分析のサポートには 3 つの部分があります：
効果量関数: 現在、次のものが含まれています
effectsize_smdは標準化平均差の効果量とその標準誤差を計算します。effectsize_2proportionsはリスク差、（対数）リスク比、（対数）オッズ比、またはアークサイン平方根変換を使用して、2つの独立した比率を比較するための効果量を計算します。
combine_effectsは、全体の平均または効果の固定効果およびランダム効果の推定値を計算します。返される結果インスタンスには、フォレストプロット関数が含まれています。ランダム効果分散、tau-squared を推定するための補助関数
combine_effects における全体の効果量の推定は、WLS や GLM を使用して var_weights で行うこともできます。
最後に、現在のメタ分析関数には マンテル・ハンゼル（Mantel-Hanszel）法は含まれていません。ただし、固定効果の結果は、以下に示すように StratifiedTable を使用して直接計算することができます。
[1]:
%matplotlib inline
[2]:
import numpy as np
import pandas as pd
from scipy import stats, optimize
from statsmodels.regression.linear_model import WLS
from statsmodels.genmod.generalized_linear_model import GLM
from statsmodels.stats.meta_analysis import (
effectsize_smd,
effectsize_2proportions,
combine_effects,
_fit_tau_iterative,
_fit_tau_mm,
_fit_tau_iter_mm,
)
# increase line length for pandas
pd.set_option("display.width", 100)
例¶
[3]:
data = [
["Carroll", 94, 22, 60, 92, 20, 60],
["Grant", 98, 21, 65, 92, 22, 65],
["Peck", 98, 28, 40, 88, 26, 40],
["Donat", 94, 19, 200, 82, 17, 200],
["Stewart", 98, 21, 50, 88, 22, 45],
["Young", 96, 21, 85, 92, 22, 85],
]
colnames = ["study", "mean_t", "sd_t", "n_t", "mean_c", "sd_c", "n_c"]
rownames = [i[0] for i in data]
dframe1 = pd.DataFrame(data, columns=colnames)
rownames
[3]:
['Carroll', 'Grant', 'Peck', 'Donat', 'Stewart', 'Young']
[4]:
mean2, sd2, nobs2, mean1, sd1, nobs1 = np.asarray(
dframe1[["mean_t", "sd_t", "n_t", "mean_c", "sd_c", "n_c"]]
).T
rownames = dframe1["study"]
rownames.tolist()
[4]:
['Carroll', 'Grant', 'Peck', 'Donat', 'Stewart', 'Young']
[5]:
np.array(nobs1 + nobs2)
[5]:
array([120, 130, 80, 400, 95, 170], dtype=int64)
標準化された平均差の効果量を推定する¶
[6]:
eff, var_eff = effectsize_smd(mean2, sd2, nobs2, mean1, sd1, nobs1)
一段階のカイ二乗検定、DerSimonian-Laird法によるランダム効果分散τの推定¶
ランダム効果の方法オプション
method_re="chi2" または method_re="dl" は、どちらの名前も受け入れられます。これは一般にDerSimonian-Laird法として知られ、固定効果の推定から得られるピアソンのカイ二乗を基にしたモーメント推定量に基づいています。
[7]:
res3 = combine_effects(eff, var_eff, method_re="chi2", use_t=True, row_names=rownames)
# TODO: we still need better information about conf_int of individual samples
# We don't have enough information in the model for individual confidence intervals
# if those are not based on normal distribution.
res3.conf_int_samples(nobs=np.array(nobs1 + nobs2))
print(res3.summary_frame())
eff sd_eff ci_low ci_upp w_fe w_re
Carroll 0.094524 0.182680 -0.267199 0.456248 0.123885 0.157529
Grant 0.277356 0.176279 -0.071416 0.626129 0.133045 0.162828
Peck 0.366546 0.225573 -0.082446 0.815538 0.081250 0.126223
Donat 0.664385 0.102748 0.462389 0.866381 0.391606 0.232734
Stewart 0.461808 0.208310 0.048203 0.875413 0.095275 0.137949
Young 0.185165 0.153729 -0.118312 0.488641 0.174939 0.182736
fixed effect 0.414961 0.064298 0.249677 0.580245 1.000000 NaN
random effect 0.358486 0.105462 0.087388 0.629583 NaN 1.000000
fixed effect wls 0.414961 0.099237 0.159864 0.670058 1.000000 NaN
random effect wls 0.358486 0.090328 0.126290 0.590682 NaN 1.000000
[8]:
res3.cache_ci
[8]:
{(0.05,
True): (array([-0.26719942, -0.07141628, -0.08244568, 0.46238908, 0.04820269,
-0.1183121 ]), array([0.45624817, 0.62612908, 0.81553838, 0.86638112, 0.87541326,
0.48864139]))}
[9]:
res3.method_re
[9]:
'chi2'
[10]:
fig = res3.plot_forest()
fig.set_figheight(6)
fig.set_figwidth(6)
[11]:
res3 = combine_effects(eff, var_eff, method_re="chi2", use_t=False, row_names=rownames)
# TODO: we still need better information about conf_int of individual samples
# We don't have enough information in the model for individual confidence intervals
# if those are not based on normal distribution.
res3.conf_int_samples(nobs=np.array(nobs1 + nobs2))
print(res3.summary_frame())
eff sd_eff ci_low ci_upp w_fe w_re
Carroll 0.094524 0.182680 -0.263521 0.452570 0.123885 0.157529
Grant 0.277356 0.176279 -0.068144 0.622857 0.133045 0.162828
Peck 0.366546 0.225573 -0.075569 0.808662 0.081250 0.126223
Donat 0.664385 0.102748 0.463002 0.865768 0.391606 0.232734
Stewart 0.461808 0.208310 0.053527 0.870089 0.095275 0.137949
Young 0.185165 0.153729 -0.116139 0.486468 0.174939 0.182736
fixed effect 0.414961 0.064298 0.288939 0.540984 1.000000 NaN
random effect 0.358486 0.105462 0.151785 0.565187 NaN 1.000000
fixed effect wls 0.414961 0.099237 0.220460 0.609462 1.000000 NaN
random effect wls 0.358486 0.090328 0.181446 0.535526 NaN 1.000000
ランダム効果分散τの反復型 Paule-Mandel 推定の使用¶
一般に Paule-Mandel 推定と呼ばれる方法は、収束するまで平均と分散の推定を反復する、ランダム効果分散のモーメント推定法です。
[12]:
res4 = combine_effects(
eff, var_eff, method_re="iterated", use_t=False, row_names=rownames
)
res4_df = res4.summary_frame()
print("method RE:", res4.method_re)
print(res4.summary_frame())
fig = res4.plot_forest()
method RE: iterated
eff sd_eff ci_low ci_upp w_fe w_re
Carroll 0.094524 0.182680 -0.263521 0.452570 0.123885 0.152619
Grant 0.277356 0.176279 -0.068144 0.622857 0.133045 0.159157
Peck 0.366546 0.225573 -0.075569 0.808662 0.081250 0.116228
Donat 0.664385 0.102748 0.463002 0.865768 0.391606 0.257767
Stewart 0.461808 0.208310 0.053527 0.870089 0.095275 0.129428
Young 0.185165 0.153729 -0.116139 0.486468 0.174939 0.184799
fixed effect 0.414961 0.064298 0.288939 0.540984 1.000000 NaN
random effect 0.366419 0.092390 0.185338 0.547500 NaN 1.000000
fixed effect wls 0.414961 0.099237 0.220460 0.609462 1.000000 NaN
random effect wls 0.366419 0.092390 0.185338 0.547500 NaN 1.000000
[ ]:
例：Kacker インタラボラトリ平均¶
この例では、効果量はラボでの測定値の平均です。複数のラボからの推定値を組み合わせて、全体の平均を推定します。
[13]:
eff = np.array([61.00, 61.40, 62.21, 62.30, 62.34, 62.60, 62.70, 62.84, 65.90])
var_eff = np.array(
[0.2025, 1.2100, 0.0900, 0.2025, 0.3844, 0.5625, 0.0676, 0.0225, 1.8225]
)
rownames = ["PTB", "NMi", "NIMC", "KRISS", "LGC", "NRC", "IRMM", "NIST", "LNE"]
[14]:
res2_DL = combine_effects(eff, var_eff, method_re="dl", use_t=True, row_names=rownames)
print("method RE:", res2_DL.method_re)
print(res2_DL.summary_frame())
fig = res2_DL.plot_forest()
fig.set_figheight(6)
fig.set_figwidth(6)
method RE: dl
eff sd_eff ci_low ci_upp w_fe w_re
PTB 61.000000 0.450000 60.118016 61.881984 0.057436 0.123113
NMi 61.400000 1.100000 59.244040 63.555960 0.009612 0.040314
NIMC 62.210000 0.300000 61.622011 62.797989 0.129230 0.159749
KRISS 62.300000 0.450000 61.418016 63.181984 0.057436 0.123113
LGC 62.340000 0.620000 61.124822 63.555178 0.030257 0.089810
NRC 62.600000 0.750000 61.130027 64.069973 0.020677 0.071005
IRMM 62.700000 0.260000 62.190409 63.209591 0.172052 0.169810
NIST 62.840000 0.150000 62.546005 63.133995 0.516920 0.194471
LNE 65.900000 1.350000 63.254049 68.545951 0.006382 0.028615
fixed effect 62.583397 0.107846 62.334704 62.832090 1.000000 NaN
random effect 62.390139 0.245750 61.823439 62.956838 NaN 1.000000
fixed effect wls 62.583397 0.189889 62.145512 63.021282 1.000000 NaN
random effect wls 62.390139 0.294776 61.710384 63.069893 NaN 1.000000
C:\Users\user\projects\statsmodels\venv\lib\site-packages\statsmodels\stats\meta_analysis.py:105: UserWarning: `use_t=True` requires `nobs` for each sample or `ci_func`. Using normal distribution for confidence interval of individual samples.
warnings.warn(msg)
[15]:
res2_PM = combine_effects(eff, var_eff, method_re="pm", use_t=True, row_names=rownames)
print("method RE:", res2_PM.method_re)
print(res2_PM.summary_frame())
fig = res2_PM.plot_forest()
fig.set_figheight(6)
fig.set_figwidth(6)
method RE: pm
eff sd_eff ci_low ci_upp w_fe w_re
PTB 61.000000 0.450000 60.118016 61.881984 0.057436 0.125857
NMi 61.400000 1.100000 59.244040 63.555960 0.009612 0.059656
NIMC 62.210000 0.300000 61.622011 62.797989 0.129230 0.143658
KRISS 62.300000 0.450000 61.418016 63.181984 0.057436 0.125857
LGC 62.340000 0.620000 61.124822 63.555178 0.030257 0.104850
NRC 62.600000 0.750000 61.130027 64.069973 0.020677 0.090122
IRMM 62.700000 0.260000 62.190409 63.209591 0.172052 0.147821
NIST 62.840000 0.150000 62.546005 63.133995 0.516920 0.156980
LNE 65.900000 1.350000 63.254049 68.545951 0.006382 0.045201
fixed effect 62.583397 0.107846 62.334704 62.832090 1.000000 NaN
random effect 62.407620 0.338030 61.628120 63.187119 NaN 1.000000
fixed effect wls 62.583397 0.189889 62.145512 63.021282 1.000000 NaN
random effect wls 62.407620 0.338030 61.628120 63.187120 NaN 1.000000
C:\Users\user\projects\statsmodels\venv\lib\site-packages\statsmodels\stats\meta_analysis.py:105: UserWarning: `use_t=True` requires `nobs` for each sample or `ci_func`. Using normal distribution for confidence interval of individual samples.
warnings.warn(msg)
[ ]:
比率のメタ分析¶
次の例では、ランダム効果の分散τがゼロであると推定されます。その後、データの2つのカウントを変更し、2番目の例ではランダム効果の分散がゼロより大きくなります。
[16]:
import io
[17]:
ss = """\
study,nei,nci,e1i,c1i,e2i,c2i,e3i,c3i,e4i,c4i
1,19,22,16.0,20.0,11,12,4.0,8.0,4,3
2,34,35,22.0,22.0,18,12,15.0,8.0,15,6
3,72,68,44.0,40.0,21,15,10.0,3.0,3,0
4,22,20,19.0,12.0,14,5,5.0,4.0,2,3
5,70,32,62.0,27.0,42,13,26.0,6.0,15,5
6,183,94,130.0,65.0,80,33,47.0,14.0,30,11
7,26,50,24.0,30.0,13,18,5.0,10.0,3,9
8,61,55,51.0,44.0,37,30,19.0,19.0,11,15
9,36,25,30.0,17.0,23,12,13.0,4.0,10,4
10,45,35,43.0,35.0,19,14,8.0,4.0,6,0
11,246,208,169.0,139.0,106,76,67.0,42.0,51,35
12,386,141,279.0,97.0,170,46,97.0,21.0,73,8
13,59,32,56.0,30.0,34,17,21.0,9.0,20,7
14,45,15,42.0,10.0,18,3,9.0,1.0,9,1
15,14,18,14.0,18.0,13,14,12.0,13.0,9,12
16,26,19,21.0,15.0,12,10,6.0,4.0,5,1
17,74,75,,,42,40,,,23,30"""
df3 = pd.read_csv(io.StringIO(ss))
df_12y = df3[["e2i", "nei", "c2i", "nci"]]
# TODO: currently 1 is reference, switch labels
count1, nobs1, count2, nobs2 = df_12y.values.T
dta = df_12y.values.T
[18]:
eff, var_eff = effectsize_2proportions(*dta, statistic="rd")
[19]:
eff, var_eff
[19]:
(array([ 0.03349282, 0.18655462, 0.07107843, 0.38636364, 0.19375 ,
0.08609464, 0.14 , 0.06110283, 0.15888889, 0.02222222,
0.06550969, 0.11417337, 0.04502119, 0.2 , 0.15079365,
-0.06477733, 0.03423423]),
array([0.02409958, 0.01376482, 0.00539777, 0.01989341, 0.01096641,
0.00376814, 0.01422338, 0.00842011, 0.01639261, 0.01227827,
0.00211165, 0.00219739, 0.01192067, 0.016 , 0.0143398 ,
0.02267994, 0.0066352 ]))
[20]:
res5 = combine_effects(
eff, var_eff, method_re="iterated", use_t=False
) # , row_names=rownames)
res5_df = res5.summary_frame()
print("method RE:", res5.method_re)
print("RE variance tau2:", res5.tau2)
print(res5.summary_frame())
fig = res5.plot_forest()
fig.set_figheight(8)
fig.set_figwidth(6)
method RE: iterated
RE variance tau2: 0
eff sd_eff ci_low ci_upp w_fe w_re
0 0.033493 0.155240 -0.270773 0.337758 0.017454 0.017454
1 0.186555 0.117324 -0.043395 0.416505 0.030559 0.030559
2 0.071078 0.073470 -0.072919 0.215076 0.077928 0.077928
3 0.386364 0.141044 0.109922 0.662805 0.021145 0.021145
4 0.193750 0.104721 -0.011499 0.398999 0.038357 0.038357
5 0.086095 0.061385 -0.034218 0.206407 0.111630 0.111630
6 0.140000 0.119262 -0.093749 0.373749 0.029574 0.029574
7 0.061103 0.091761 -0.118746 0.240951 0.049956 0.049956
8 0.158889 0.128034 -0.092052 0.409830 0.025660 0.025660
9 0.022222 0.110807 -0.194956 0.239401 0.034259 0.034259
10 0.065510 0.045953 -0.024556 0.155575 0.199199 0.199199
11 0.114173 0.046876 0.022297 0.206049 0.191426 0.191426
12 0.045021 0.109182 -0.168971 0.259014 0.035286 0.035286
13 0.200000 0.126491 -0.047918 0.447918 0.026290 0.026290
14 0.150794 0.119749 -0.083910 0.385497 0.029334 0.029334
15 -0.064777 0.150599 -0.359945 0.230390 0.018547 0.018547
16 0.034234 0.081457 -0.125418 0.193887 0.063395 0.063395
fixed effect 0.096212 0.020509 0.056014 0.136410 1.000000 NaN
random effect 0.096212 0.020509 0.056014 0.136410 NaN 1.000000
fixed effect wls 0.096212 0.016521 0.063831 0.128593 1.000000 NaN
random effect wls 0.096212 0.016521 0.063831 0.128593 NaN 1.000000
正のランダム効果分散を持つデータへの変換¶
[21]:
dta_c = dta.copy()
dta_c.T[0, 0] = 18
dta_c.T[1, 0] = 22
dta_c.T
[21]:
array([[ 18, 19, 12, 22],
[ 22, 34, 12, 35],
[ 21, 72, 15, 68],
[ 14, 22, 5, 20],
[ 42, 70, 13, 32],
[ 80, 183, 33, 94],
[ 13, 26, 18, 50],
[ 37, 61, 30, 55],
[ 23, 36, 12, 25],
[ 19, 45, 14, 35],
[106, 246, 76, 208],
[170, 386, 46, 141],
[ 34, 59, 17, 32],
[ 18, 45, 3, 15],
[ 13, 14, 14, 18],
[ 12, 26, 10, 19],
[ 42, 74, 40, 75]], dtype=int64)
[22]:
eff, var_eff = effectsize_2proportions(*dta_c, statistic="rd")
res5 = combine_effects(
eff, var_eff, method_re="iterated", use_t=False
) # , row_names=rownames)
res5_df = res5.summary_frame()
print("method RE:", res5.method_re)
print(res5.summary_frame())
fig = res5.plot_forest()
fig.set_figheight(8)
fig.set_figwidth(6)
method RE: iterated
eff sd_eff ci_low ci_upp w_fe w_re
0 0.401914 0.117873 0.170887 0.632940 0.029850 0.038415
1 0.304202 0.114692 0.079410 0.528993 0.031529 0.040258
2 0.071078 0.073470 -0.072919 0.215076 0.076834 0.081017
3 0.386364 0.141044 0.109922 0.662805 0.020848 0.028013
4 0.193750 0.104721 -0.011499 0.398999 0.037818 0.046915
5 0.086095 0.061385 -0.034218 0.206407 0.110063 0.102907
6 0.140000 0.119262 -0.093749 0.373749 0.029159 0.037647
7 0.061103 0.091761 -0.118746 0.240951 0.049255 0.058097
8 0.158889 0.128034 -0.092052 0.409830 0.025300 0.033270
9 0.022222 0.110807 -0.194956 0.239401 0.033778 0.042683
10 0.065510 0.045953 -0.024556 0.155575 0.196403 0.141871
11 0.114173 0.046876 0.022297 0.206049 0.188739 0.139144
12 0.045021 0.109182 -0.168971 0.259014 0.034791 0.043759
13 0.200000 0.126491 -0.047918 0.447918 0.025921 0.033985
14 0.150794 0.119749 -0.083910 0.385497 0.028922 0.037383
15 -0.064777 0.150599 -0.359945 0.230390 0.018286 0.024884
16 0.034234 0.081457 -0.125418 0.193887 0.062505 0.069751
fixed effect 0.110252 0.020365 0.070337 0.150167 1.000000 NaN
random effect 0.117633 0.024913 0.068804 0.166463 NaN 1.000000
fixed effect wls 0.110252 0.022289 0.066567 0.153937 1.000000 NaN
random effect wls 0.117633 0.024913 0.068804 0.166463 NaN 1.000000
[23]:
res5 = combine_effects(eff, var_eff, method_re="chi2", use_t=False)
res5_df = res5.summary_frame()
print("method RE:", res5.method_re)
print(res5.summary_frame())
fig = res5.plot_forest()
fig.set_figheight(8)
fig.set_figwidth(6)
method RE: chi2
eff sd_eff ci_low ci_upp w_fe w_re
0 0.401914 0.117873 0.170887 0.632940 0.029850 0.036114
1 0.304202 0.114692 0.079410 0.528993 0.031529 0.037940
2 0.071078 0.073470 -0.072919 0.215076 0.076834 0.080779
3 0.386364 0.141044 0.109922 0.662805 0.020848 0.025973
4 0.193750 0.104721 -0.011499 0.398999 0.037818 0.044614
5 0.086095 0.061385 -0.034218 0.206407 0.110063 0.105901
6 0.140000 0.119262 -0.093749 0.373749 0.029159 0.035356
7 0.061103 0.091761 -0.118746 0.240951 0.049255 0.056098
8 0.158889 0.128034 -0.092052 0.409830 0.025300 0.031063
9 0.022222 0.110807 -0.194956 0.239401 0.033778 0.040357
10 0.065510 0.045953 -0.024556 0.155575 0.196403 0.154854
11 0.114173 0.046876 0.022297 0.206049 0.188739 0.151236
12 0.045021 0.109182 -0.168971 0.259014 0.034791 0.041435
13 0.200000 0.126491 -0.047918 0.447918 0.025921 0.031761
14 0.150794 0.119749 -0.083910 0.385497 0.028922 0.035095
15 -0.064777 0.150599 -0.359945 0.230390 0.018286 0.022976
16 0.034234 0.081457 -0.125418 0.193887 0.062505 0.068449
fixed effect 0.110252 0.020365 0.070337 0.150167 1.000000 NaN
random effect 0.115580 0.023557 0.069410 0.161751 NaN 1.000000
fixed effect wls 0.110252 0.022289 0.066567 0.153937 1.000000 NaN
random effect wls 0.115580 0.024241 0.068068 0.163093 NaN 1.000000
var_weights を使用した固定効果分析の再現¶
combine_effects は加重平均推定値を計算し、これは var_weights を使用したGLMまたはWLSを使用して再現できます。GLM.fit の scale オプションは、固定効果メタ分析を固定で、またはHKSJ/WLSスケールで再現するために使用できます。[24]:
from statsmodels.genmod.generalized_linear_model import GLM
[25]:
eff, var_eff = effectsize_2proportions(*dta_c, statistic="or")
res = combine_effects(eff, var_eff, method_re="chi2", use_t=False)
res_frame = res.summary_frame()
print(res_frame.iloc[-4:])
eff sd_eff ci_low ci_upp w_fe w_re
fixed effect 0.428037 0.090287 0.251076 0.604997 1.0 NaN
random effect 0.429520 0.091377 0.250425 0.608615 NaN 1.0
fixed effect wls 0.428037 0.090798 0.250076 0.605997 1.0 NaN
random effect wls 0.429520 0.091595 0.249997 0.609044 NaN 1.0
We need to fix scale=1 in order to replicate standard errors for the usual meta-analysis.
[26]:
weights = 1 / var_eff
mod_glm = GLM(eff, np.ones(len(eff)), var_weights=weights)
res_glm = mod_glm.fit(scale=1.0)
print(res_glm.summary().tables[1])
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 0.4280 0.090 4.741 0.000 0.251 0.605
==============================================================================
[27]:
# check results
res_glm.scale, res_glm.conf_int() - res_frame.loc[
"fixed effect", ["ci_low", "ci_upp"]
].values
[27]:
(array(1.), array([[-5.55111512e-17, 0.00000000e+00]]))
メタ分析でHKSJ分散調整を使用することは、ピアソンのカイ二乗を使用してスケールを推定することと同等であり、これはガウス分布ファミリーのデフォルトでもあります。
[28]:
res_glm = mod_glm.fit(scale="x2")
print(res_glm.summary().tables[1])
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 0.4280 0.091 4.714 0.000 0.250 0.606
==============================================================================
[29]:
# check results
res_glm.scale, res_glm.conf_int() - res_frame.loc[
"fixed effect", ["ci_low", "ci_upp"]
].values
[29]:
(1.0113358914264383, array([[-0.00100017, 0.00100017]]))
マンテル・ハンゼルオッズ比の使用（分割表を用いて）¶
マンテル・ハンゼル法を使用した対数オッズ比の固定効果は、StratifiedTableを使用して直接計算することができます。
StratifiedTableと共に使用するために、2 x 2 x k の分割表を作成する必要があります。
[30]:
t, nt, c, nc = dta_c
counts = np.column_stack([t, nt - t, c, nc - c])
ctables = counts.T.reshape(2, 2, -1)
ctables[:, :, 0]
[30]:
array([[18, 1],
[12, 10]], dtype=int64)
[31]:
counts[0]
[31]:
array([18, 1, 12, 10], dtype=int64)
[32]:
dta_c.T[0]
[32]:
array([18, 19, 12, 22], dtype=int64)
[33]:
import statsmodels.stats.api as smstats
[34]:
st = smstats.StratifiedTable(ctables.astype(np.float64))
プールされたログオッズ比と標準誤差をRのメタパッケージと比較する
[35]:
st.logodds_pooled, st.logodds_pooled - 0.4428186730553189 # R meta
[35]:
(0.4428186730553187, -2.220446049250313e-16)
[36]:
st.logodds_pooled_se, st.logodds_pooled_se - 0.08928560091027186 # R meta
[36]:
(0.08928560091027186, 0.0)
[37]:
st.logodds_pooled_confint()
[37]:
(0.2678221109331691, 0.6178152351774683)
[38]:
print(st.test_equal_odds())
pvalue 0.34496419319878713
statistic 17.64707987033203
[39]:
print(st.test_null_odds())
pvalue 6.615053645964153e-07
statistic 24.724136624311814
層別クロス集計表への変換を確認する
各テーブルの行の合計は、処置群とコントロール群の実験における標本サイズです。
[40]:
ctables.sum(1)
[40]:
array([[ 19, 34, 72, 22, 70, 183, 26, 61, 36, 45, 246, 386, 59,
45, 14, 26, 74],
[ 22, 35, 68, 20, 32, 94, 50, 55, 25, 35, 208, 141, 32,
15, 18, 19, 75]], dtype=int64)
[41]:
nt, nc
[41]:
(array([ 19, 34, 72, 22, 70, 183, 26, 61, 36, 45, 246, 386, 59,
45, 14, 26, 74], dtype=int64),
array([ 22, 35, 68, 20, 32, 94, 50, 55, 25, 35, 208, 141, 32,
15, 18, 19, 75], dtype=int64))
Rメタパッケージの結果
> res_mb_hk = metabin(e2i, nei, c2i, nci, data=dat2, sm="OR", Q.Cochrane=FALSE, method="MH", method.tau="DL", hakn=FALSE, backtransf=FALSE)
> res_mb_hk
logOR 95%-CI %W(fixed) %W(random)
1 2.7081 [ 0.5265; 4.8896] 0.3 0.7
2 1.2567 [ 0.2658; 2.2476] 2.1 3.2
3 0.3749 [-0.3911; 1.1410] 5.4 5.4
4 1.6582 [ 0.3245; 2.9920] 0.9 1.8
5 0.7850 [-0.0673; 1.6372] 3.5 4.4
6 0.3617 [-0.1528; 0.8762] 12.1 11.8
7 0.5754 [-0.3861; 1.5368] 3.0 3.4
8 0.2505 [-0.4881; 0.9892] 6.1 5.8
9 0.6506 [-0.3877; 1.6889] 2.5 3.0
10 0.0918 [-0.8067; 0.9903] 4.5 3.9
11 0.2739 [-0.1047; 0.6525] 23.1 21.4
12 0.4858 [ 0.0804; 0.8911] 18.6 18.8
13 0.1823 [-0.6830; 1.0476] 4.6 4.2
14 0.9808 [-0.4178; 2.3795] 1.3 1.6
15 1.3122 [-1.0055; 3.6299] 0.4 0.6
16 -0.2595 [-1.4450; 0.9260] 3.1 2.3
17 0.1384 [-0.5076; 0.7844] 8.5 7.6
Number of studies combined: k = 17
logOR 95%-CI z p-value
Fixed effect model 0.4428 [0.2678; 0.6178] 4.96 < 0.0001
Random effects model 0.4295 [0.2504; 0.6086] 4.70 < 0.0001
Quantifying heterogeneity:
tau^2 = 0.0017 [0.0000; 0.4589]; tau = 0.0410 [0.0000; 0.6774];
I^2 = 1.1% [0.0%; 51.6%]; H = 1.01 [1.00; 1.44]
Test of heterogeneity:
Q d.f. p-value
16.18 16 0.4404
Details on meta-analytical method:
- Mantel-Haenszel method
- DerSimonian-Laird estimator for tau^2
- Jackson method for confidence interval of tau^2 and tau
> res_mb_hk$TE.fixed
[1] 0.4428186730553189
> res_mb_hk$seTE.fixed
[1] 0.08928560091027186
> c(res_mb_hk$lower.fixed, res_mb_hk$upper.fixed)
[1] 0.2678221109331694 0.6178152351774684
[42]:
print(st.summary())
Estimate LCB UCB
-----------------------------------------
Pooled odds 1.557 1.307 1.855
Pooled log odds 0.443 0.268 0.618
Pooled risk ratio 1.270
Statistic P-value
-----------------------------------
Test of OR=1 24.724 0.000
Test constant OR 17.647 0.345
-----------------------
Number of tables 17
Min n 32
Max n 527
Avg n 139
Total n 2362
-----------------------
最終更新日:
2025年01月28日