| name | scientific-meta-analysis |
| description | メタ解析スキル。固定効果・ランダム効果モデル（DerSimonian-Laird）、Forest プロット、
異質性評価（I²/Q 検定/τ²）、出版バイアス検出（Funnel プロット/Egger/Begg 検定）、
サブグループ解析、メタ回帰、累積メタ解析のテンプレートを提供。
|
Scientific Meta-Analysis
複数の独立した研究結果を統合し、全体的なエビデンスを定量化するためのスキル。
効果量（SMD / OR / RR / MD）の統合、異質性評価、出版バイアス検出のパイプラインを
提供する。
When to Use
- 複数の研究・実験結果を統合的に評価するとき
- 効果量（Hedges' g / Cohen's d / SMD）を算出するとき
- Forest プロット / Funnel プロットを描画するとき
- 研究間の異質性を定量化するとき（I² / Q / τ²）
- 出版バイアスの有無を検定するとき
Quick Start
1. 効果量の算出
import numpy as np
import pandas as pd
from scipy.stats import norm
def compute_effect_sizes(studies_df, effect_type="SMD"):
"""
各研究の効果量と分散を算出する。
effect_type:
"SMD" — Standardized Mean Difference (Hedges' g)
"MD" — Mean Difference (同スケール)
"OR" — Odds Ratio (log 変換)
"RR" — Risk Ratio (log 変換)
Input columns (SMD/MD):
mean1, sd1, n1, mean2, sd2, n2
Input columns (OR/RR):
events1, total1, events2, total2
"""
df = studies_df.copy()
if effect_type == "SMD":
pooled_sd = np.sqrt(
((df["n1"]-1)*df["sd1"]**2 + (df["n2"]-1)*df["sd2"]**2) /
(df["n1"] + df["n2"] - 2)
)
d = (df["mean1"] - df["mean2"]) / pooled_sd
J = 1 - 3 / (4*(df["n1"]+df["n2"]-2) - 1)
df["effect_size"] = d * J
df["variance"] = (df["n1"]+df["n2"])/(df["n1"]*df["n2"]) + \
df["effect_size"]**2 / (2*(df["n1"]+df["n2"]))
elif effect_type == "MD":
df["effect_size"] = df["mean1"] - df["mean2"]
df["variance"] = df["sd1"]**2/df["n1"] + df["sd2"]**2/df["n2"]
elif effect_type == "OR":
a = df["events1"]; b = df["total1"] - df["events1"]
c = df["events2"]; d_val = df["total2"] - df["events2"]
df["effect_size"] = np.log((a * d_val) / (b * c + 1e-10) + 1e-10)
df["variance"] = 1/a + 1/b + 1/c + 1/d_val
elif effect_type == "RR":
p1 = df["events1"] / df["total1"]
p2 = df["events2"] / df["total2"]
df["effect_size"] = np.log(p1 / (p2 + 1e-10) + 1e-10)
df["variance"] = (1-p1)/(df["events1"]+1e-10) + \
(1-p2)/(df["events2"]+1e-10)
df["se"] = np.sqrt(df["variance"])
df["ci_lower"] = df["effect_size"] - 1.96 * df["se"]
df["ci_upper"] = df["effect_size"] + 1.96 * df["se"]
df["weight"] = 1 / df["variance"]
return df
2. 固定効果 / ランダム効果モデル
def meta_analysis(studies_df, model="random"):
"""
メタ解析統合。
model:
"fixed" — 固定効果モデル (Inverse-Variance weighted)
"random" — ランダム効果モデル (DerSimonian-Laird)
Input: DataFrame with columns: study, effect_size, variance
"""
es = studies_df["effect_size"].values
var = studies_df["variance"].values
w = 1 / var
k = len(es)
theta_fixed = np.sum(w * es) / np.sum(w)
se_fixed = 1 / np.sqrt(np.sum(w))
Q = np.sum(w * (es - theta_fixed)**2)
df_Q = k - 1
p_Q = 1 - __import__("scipy").stats.chi2.cdf(Q, df_Q)
I2 = max(0, (Q - df_Q) / Q * 100) if Q > 0 else 0
if model == "random":
C = np.sum(w) - np.sum(w**2) / np.sum(w)
tau2 = max(0, (Q - df_Q) / C)
w_re = 1 / (var + tau2)
theta_random = np.sum(w_re * es) / np.sum(w_re)
se_random = 1 / np.sqrt(np.sum(w_re))
summary_effect = theta_random
summary_se = se_random
else:
tau2 = 0
summary_effect = theta_fixed
summary_se = se_fixed
z = summary_effect / summary_se
p_val = 2 * (1 - norm.cdf(abs(z)))
return {
"model": model,
"summary_effect": summary_effect,
"se": summary_se,
"ci_lower": summary_effect - 1.96 * summary_se,
"ci_upper": summary_effect + 1.96 * summary_se,
"z_value": z,
"p_value": p_val,
"Q_statistic": Q,
"Q_p_value": p_Q,
"I_squared": I2,
"tau_squared": tau2,
"k_studies": k,
}
3. Forest プロット
import matplotlib.pyplot as plt
def forest_plot(studies_df, meta_result, effect_label="SMD",
figsize=(10, None)):
"""
Forest プロットを描画する。
studies_df: study, effect_size, ci_lower, ci_upper, weight
meta_result: meta_analysis() の出力
"""
k = len(studies_df)
if figsize[1] is None:
figsize = (figsize[0], max(4, k * 0.4 + 2))
fig, ax = plt.subplots(figsize=figsize)
y_positions = range(k, 0, -1)
for i, (_, row) in enumerate(studies_df.iterrows()):
y = list(y_positions)[i]
ax.plot([row["ci_lower"], row["ci_upper"]], [y, y],
"b-", linewidth=1.5)
size = row.get("weight", 1) / studies_df["weight"].max() * 200 + 20
ax.plot(row["effect_size"], y, "bs", markersize=np.sqrt(size),
markerfacecolor="steelblue")
ax.text(-0.05, y, row.get("study", f"Study {i+1}"),
ha="right", va="center", fontsize=9,
transform=ax.get_yaxis_transform())
y_summary = 0
diamond_x = [meta_result["ci_lower"], meta_result["summary_effect"],
meta_result["ci_upper"], meta_result["summary_effect"]]
diamond_y = [y_summary, y_summary + 0.3, y_summary, y_summary - 0.3]
ax.fill(diamond_x, diamond_y, color="red", alpha=0.7)
ax.text(-0.05, y_summary, "Summary",
ha="right", va="center", fontsize=9, fontweight="bold",
transform=ax.get_yaxis_transform())
ax.axvline(0, color="black", linestyle="-", linewidth=0.5)
ax.set_xlabel(effect_label)
ax.set_yticks([])
ax.set_title(f"Forest Plot (I²={meta_result['I_squared']:.1f}%, "
f"p={meta_result['p_value']:.4f})", fontweight="bold")
for i, (_, row) in enumerate(studies_df.iterrows()):
y = list(y_positions)[i]
ax.text(1.02, y, f"{row['effect_size']:.2f} [{row['ci_lower']:.2f}, "
f"{row['ci_upper']:.2f}]",
ha="left", va="center", fontsize=8,
transform=ax.get_yaxis_transform())
plt.tight_layout()
plt.savefig("figures/forest_plot.png", dpi=300, bbox_inches="tight")
plt.close()
4. 出版バイアス検出
4.1 Funnel プロット
def funnel_plot(studies_df, meta_result, figsize=(8, 6)):
"""
Funnel プロットを描画する。
非対称なら出版バイアスの存在を示唆。
"""
fig, ax = plt.subplots(figsize=figsize)
ax.scatter(studies_df["effect_size"], studies_df["se"],
c="steelblue", s=50, edgecolors="black", zorder=5)
ax.axvline(meta_result["summary_effect"], color="red", linestyle="--")
se_range = np.linspace(0, studies_df["se"].max() * 1.1, 100)
ax.plot(meta_result["summary_effect"] - 1.96 * se_range, se_range,
"gray", linestyle="--", alpha=0.5)
ax.plot(meta_result["summary_effect"] + 1.96 * se_range, se_range,
"gray", linestyle="--", alpha=0.5)
ax.set_xlabel("Effect Size")
ax.set_ylabel("Standard Error")
ax.set_title("Funnel Plot", fontweight="bold")
ax.invert_yaxis()
plt.tight_layout()
plt.savefig("figures/funnel_plot.png", dpi=300, bbox_inches="tight")
plt.close()
4.2 Egger 検定
import statsmodels.api as sm
def egger_test(studies_df):
"""
Egger 回帰検定 — Funnel プロットの非対称性を統計的に検定。
y = effect_size / se
x = 1 / se
切片 ≠ 0 → 出版バイアスあり
"""
precision = 1 / studies_df["se"]
z_score = studies_df["effect_size"] / studies_df["se"]
X = sm.add_constant(precision)
model = sm.OLS(z_score, X).fit()
return {
"intercept": model.params["const"],
"intercept_se": model.bse["const"],
"intercept_p": model.pvalues["const"],
"publication_bias": model.pvalues["const"] < 0.05,
}
5. サブグループ解析
def subgroup_analysis(studies_df, subgroup_col, model="random"):
"""サブグループごとにメタ解析を行い、グループ間差を検定する。"""
subgroups = studies_df[subgroup_col].unique()
results = []
for sg in subgroups:
subset = studies_df[studies_df[subgroup_col] == sg]
if len(subset) >= 2:
ma = meta_analysis(subset, model=model)
ma["subgroup"] = sg
ma["k"] = len(subset)
results.append(ma)
results_df = pd.DataFrame(results)
overall = meta_analysis(studies_df, model=model)
Q_within = sum(r["Q_statistic"] for r in results)
Q_between = overall["Q_statistic"] - Q_within
df_between = len(results) - 1
p_between = 1 - __import__("scipy").stats.chi2.cdf(Q_between, df_between)
return {
"subgroup_results": results_df,
"Q_between": Q_between,
"df_between": df_between,
"p_between": p_between,
}
6. 累積メタ解析
def cumulative_meta_analysis(studies_df, sort_by="year", model="random"):
"""
研究を順に追加しながらメタ解析を実行する。
エビデンスの蓄積過程を可視化。
"""
sorted_df = studies_df.sort_values(sort_by)
cumulative_results = []
for i in range(2, len(sorted_df) + 1):
subset = sorted_df.iloc[:i]
ma = meta_analysis(subset, model=model)
ma["n_studies"] = i
ma["last_added"] = sorted_df.iloc[i-1].get("study", f"Study {i}")
cumulative_results.append(ma)
return pd.DataFrame(cumulative_results)
References
Output Files
| ファイル | 形式 |
|---|
results/meta_analysis_summary.csv | CSV |
results/effect_sizes.csv | CSV |
results/publication_bias_tests.csv | CSV |
results/subgroup_analysis.csv | CSV |
figures/forest_plot.png | PNG |
figures/funnel_plot.png | PNG |
figures/cumulative_meta.png | PNG |
利用可能ツール
ToolUniverse SMCP 経由で利用可能な外部ツール。
| カテゴリ | 主要ツール | 用途 |
|---|
| PubMed | PubMed_search_articles | メタアナリシス対象文献検索 |
| PubMed | PubMed_get_article | 論文メタデータ取得 |
| EuropePMC | EuropePMC_search_articles | ヨーロッパ文献検索 |
| Crossref | Crossref_search_works | 出版情報検索 |
参照スキル
| スキル | 連携 |
|---|
scientific-survival-clinical | ← 生存解析・値引 HR |
scientific-statistical-testing | ← 仮説検定・効果量算出 |
scientific-deep-research | ← 系統的文献検索 |
scientific-clinical-trials-analytics | ← 臨床試験結果の統合 |
scientific-academic-writing | → メタアナリシス論文化 |
依存パッケージ
scipy>=1.10
statsmodels>=0.14
