Complement-Targeted Therapies in Glioblastoma: A Systematic Review.
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The authors' code
Python · 513 lines · 17 KB · no license
- """
- Meta-analysis computations: pooled effect sizes, heterogeneity,
- forest plots, funnel plots, subgroup analysis, sensitivity analysis,
- Egger's test, SMD calculation, and HR pooling.
- """
- import logging
- from pathlib import Path
- from typing import Optional
- import numpy as np
- import pandas as pd
- import matplotlib.pyplot as plt
- from scipy import stats
- logger = logging.getLogger(__name__)
- # ---------------------------------------------------------------------------
- # Core pooling
- # ---------------------------------------------------------------------------
- def compute_pooled_effect(
- effects: np.ndarray,
- variances: np.ndarray,
- method: str = "random",
- ) -> dict:
- """
- Compute pooled effect size using inverse-variance weighting.
- DerSimonian-Laird for random effects.
- """
- effects = np.asarray(effects, dtype=float)
- variances = np.asarray(variances, dtype=float)
- mask = np.isfinite(effects) & np.isfinite(variances) & (variances > 0)
- effects = effects[mask]
- variances = variances[mask]
- if len(effects) < 2:
- return {"pooled_effect": float("nan"), "n_studies": len(effects),
- "error": "Need at least 2 studies"}
- weights_fixed = 1.0 / variances
- pooled_fixed = np.sum(weights_fixed * effects) / np.sum(weights_fixed)
- Q = np.sum(weights_fixed * (effects - pooled_fixed) ** 2)
- df = len(effects) - 1
- C = np.sum(weights_fixed) - np.sum(weights_fixed ** 2) / np.sum(weights_fixed)
- tau2 = max(0, (Q - df) / C) if C > 0 else 0
- I2 = max(0, (Q - df) / Q * 100) if Q > 0 else 0.0
- if method == "random":
- weights = 1.0 / (variances + tau2)
- else:
- weights = weights_fixed
- pooled = np.sum(weights * effects) / np.sum(weights)
- se_pooled = np.sqrt(1.0 / np.sum(weights))
- ci_lower = pooled - 1.96 * se_pooled
- ci_upper = pooled + 1.96 * se_pooled
- z = pooled / se_pooled if se_pooled > 0 else 0
- p_value = 2 * (1 - stats.norm.cdf(abs(z)))
- return {
- "pooled_effect": float(pooled),
- "se": float(se_pooled),
- "ci_lower": float(ci_lower),
- "ci_upper": float(ci_upper),
- "p_value": float(p_value),
- "z": float(z),
- "tau2": float(tau2),
- "I2": float(I2),
- "Q": float(Q),
- "Q_df": int(df),
- "Q_p": float(1 - stats.chi2.cdf(Q, df)) if df > 0 else 1.0,
- "method": method,
- "n_studies": int(len(effects)),
- }
- # ---------------------------------------------------------------------------
- # Hazard ratio pooling (log-HR scale)
- # ---------------------------------------------------------------------------
- def pool_hazard_ratios(
- hrs: np.ndarray,
- hr_ci_lowers: np.ndarray,
- hr_ci_uppers: np.ndarray,
- method: str = "random",
- ) -> dict:
- """
- Pool hazard ratios on the log scale.
- CIs are used to derive SE: SE(log HR) = (log(upper) - log(lower)) / (2 * 1.96)
- """
- hrs = np.asarray(hrs, dtype=float)
- lowers = np.asarray(hr_ci_lowers, dtype=float)
- uppers = np.asarray(hr_ci_uppers, dtype=float)
- mask = (hrs > 0) & (lowers > 0) & (uppers > 0) & np.isfinite(hrs)
- hrs = hrs[mask]
- lowers = lowers[mask]
- uppers = uppers[mask]
- if len(hrs) < 2:
- return {"pooled_hr": float("nan"), "n_studies": len(hrs),
- "error": "Need at least 2 studies with HR + CI"}
- log_hrs = np.log(hrs)
- se_log_hrs = (np.log(uppers) - np.log(lowers)) / (2 * 1.96)
- variances = se_log_hrs ** 2
- result = compute_pooled_effect(log_hrs, variances, method=method)
- result["pooled_hr"] = float(np.exp(result["pooled_effect"]))
- result["hr_ci_lower"] = float(np.exp(result["ci_lower"]))
- result["hr_ci_upper"] = float(np.exp(result["ci_upper"]))
- result["scale"] = "log-HR"
- return result
- def pool_hazard_ratios_with_se(
- hrs: np.ndarray,
- se_log_hrs: np.ndarray,
- method: str = "random",
- ) -> dict:
- """Pool HRs when SE of log(HR) is directly available."""
- hrs = np.asarray(hrs, dtype=float)
- se_log_hrs = np.asarray(se_log_hrs, dtype=float)
- mask = (hrs > 0) & (se_log_hrs > 0) & np.isfinite(hrs)
- hrs = hrs[mask]
- se_log_hrs = se_log_hrs[mask]
- if len(hrs) < 2:
- return {"pooled_hr": float("nan"), "n_studies": len(hrs),
- "error": "Need at least 2 studies"}
- log_hrs = np.log(hrs)
- variances = se_log_hrs ** 2
- result = compute_pooled_effect(log_hrs, variances, method=method)
- result["pooled_hr"] = float(np.exp(result["pooled_effect"]))
- result["hr_ci_lower"] = float(np.exp(result["ci_lower"]))
- result["hr_ci_upper"] = float(np.exp(result["ci_upper"]))
- result["scale"] = "log-HR"
- return result
- # ---------------------------------------------------------------------------
- # Prediction interval
- # ---------------------------------------------------------------------------
- def prediction_interval(
- pooled_effect: float,
- se_pooled: float,
- tau2: float,
- k: int,
- ) -> dict:
- """
- Compute the 95% prediction interval for a new study.
- PI = pooled +/- t(k-2, 0.975) * sqrt(se^2 + tau^2)
- Requires k >= 3.
- """
- if k < 3:
- return {
- "pi_lower": float("nan"),
- "pi_upper": float("nan"),
- "error": "Need at least 3 studies for prediction interval",
- }
- t_crit = stats.t.ppf(0.975, df=k - 2)
- pi_se = np.sqrt(se_pooled ** 2 + tau2)
- return {
- "pi_lower": float(pooled_effect - t_crit * pi_se),
- "pi_upper": float(pooled_effect + t_crit * pi_se),
- "t_critical": float(t_crit),
- "pi_se": float(pi_se),
- }
- # ---------------------------------------------------------------------------
- # Standardized mean difference (SMD / Hedges' g)
- # ---------------------------------------------------------------------------
- def compute_smd(
- mean_t: float, sd_t: float, n_t: int,
- mean_c: float, sd_c: float, n_c: int,
- ) -> dict:
- """Compute Hedges' g (bias-corrected SMD) for a single study."""
- sp = np.sqrt(((n_t - 1) * sd_t ** 2 + (n_c - 1) * sd_c ** 2) / (n_t + n_c - 2))
- if sp == 0:
- return {"smd": 0, "se_smd": float("nan"), "variance": float("nan")}
- d = (mean_t - mean_c) / sp
- # Hedges' correction
- df = n_t + n_c - 2
- j = 1 - 3 / (4 * df - 1) if df > 1 else 1
- g = d * j
- var_g = (n_t + n_c) / (n_t * n_c) + g ** 2 / (2 * (n_t + n_c))
- se_g = np.sqrt(var_g)
- return {"smd": float(g), "se_smd": float(se_g), "variance": float(var_g)}
- def pool_smds(
- smds: np.ndarray,
- variances: np.ndarray,
- method: str = "random",
- ) -> dict:
- """Pool standardized mean differences."""
- result = compute_pooled_effect(smds, variances, method=method)
- result["metric"] = "SMD (Hedges' g)"
- return result
- # ---------------------------------------------------------------------------
- # Subgroup analysis
- # ---------------------------------------------------------------------------
- def subgroup_analysis(
- df: pd.DataFrame,
- effect_col: str,
- variance_col: str,
- group_col: str,
- method: str = "random",
- ) -> dict:
- """Run pooled analysis within each subgroup and test for differences."""
- results = {}
- for group, group_df in df.groupby(group_col):
- effects = group_df[effect_col].values
- variances = group_df[variance_col].values
- if len(effects) >= 2:
- results[str(group)] = compute_pooled_effect(effects, variances, method)
- results[str(group)]["n_studies"] = len(effects)
- # Test for subgroup differences (Q_between)
- if len(results) >= 2:
- pooled_effects = np.array([r["pooled_effect"] for r in results.values()])
- pooled_weights = np.array([1 / r["se"] ** 2 for r in results.values() if r["se"] > 0])
- if len(pooled_weights) >= 2:
- overall = np.sum(pooled_weights * pooled_effects[:len(pooled_weights)]) / np.sum(pooled_weights)
- Q_between = np.sum(pooled_weights * (pooled_effects[:len(pooled_weights)] - overall) ** 2)
- df_between = len(results) - 1
- p_between = 1 - stats.chi2.cdf(Q_between, df_between)
- results["_subgroup_test"] = {
- "Q_between": float(Q_between),
- "df": df_between,
- "p_value": float(p_between),
- }
- return results
- # ---------------------------------------------------------------------------
- # Sensitivity analysis (leave-one-out)
- # ---------------------------------------------------------------------------
- def leave_one_out(
- effects: np.ndarray,
- variances: np.ndarray,
- labels: list[str],
- method: str = "random",
- ) -> list[dict]:
- """Leave-one-out sensitivity analysis."""
- effects = np.asarray(effects, dtype=float)
- variances = np.asarray(variances, dtype=float)
- results = []
- for i in range(len(effects)):
- mask = np.ones(len(effects), dtype=bool)
- mask[i] = False
- r = compute_pooled_effect(effects[mask], variances[mask], method)
- r["excluded_study"] = labels[i]
- results.append(r)
- return results
- # ---------------------------------------------------------------------------
- # Publication bias: Egger's test
- # ---------------------------------------------------------------------------
- def eggers_test(effects: np.ndarray, se: np.ndarray) -> dict:
- """
- Egger's regression test for funnel plot asymmetry.
- Regresses standardized effect (effect/SE) on precision (1/SE).
- """
- effects = np.asarray(effects, dtype=float)
- se = np.asarray(se, dtype=float)
- mask = (se > 0) & np.isfinite(effects) & np.isfinite(se)
- effects = effects[mask]
- se = se[mask]
- if len(effects) < 3:
- return {"error": "Need at least 3 studies for Egger's test"}
- precision = 1.0 / se
- standardized = effects / se
- slope, intercept, r_value, p_value, std_err = stats.linregress(precision, standardized)
- return {
- "intercept": float(intercept),
- "slope": float(slope),
- "se_intercept": float(std_err),
- "t_value": float(intercept / std_err) if std_err > 0 else float("nan"),
- "p_value": float(p_value),
- "significant": p_value < 0.05,
- "interpretation": "Significant asymmetry detected" if p_value < 0.05
- else "No significant asymmetry",
- }
- # ---------------------------------------------------------------------------
- # Plots
- # ---------------------------------------------------------------------------
- def forest_plot(
- df: pd.DataFrame,
- effect_col: str = "effect_size",
- ci_lower_col: str = "ci_lower",
- ci_upper_col: str = "ci_upper",
- label_col: str = "study_id",
- pooled: Optional[dict] = None,
- title: str = "Forest Plot",
- xlab: str = "Effect Size",
- null_value: float = 0,
- save_path: Optional[str] = None,
- ) -> plt.Figure:
- """Generate a forest plot from study data."""
- df = df.dropna(subset=[effect_col]).copy()
- if df.empty:
- fig, ax = plt.subplots()
- ax.text(0.5, 0.5, "No data available", ha="center", va="center")
- return fig
- fig, ax = plt.subplots(figsize=(11, max(4, len(df) * 0.45 + 2)))
- y_positions = range(len(df))
- ax.hlines(y_positions, df[ci_lower_col], df[ci_upper_col], color="black", lw=1)
- ax.scatter(df[effect_col], y_positions, zorder=5, color="steelblue", s=50)
- ax.axvline(null_value, color="grey", linestyle="--", lw=0.8)
- ax.set_yticks(list(y_positions))
- ax.set_yticklabels(df[label_col])
- ax.set_xlabel(xlab)
- ax.set_title(title, fontsize=11, fontweight="bold")
- x_min = float(np.nanmin(df[ci_lower_col].values))
- x_max = float(np.nanmax(df[ci_upper_col].values))
- diamond_y = len(df) + 0.5
- if pooled and "pooled_effect" in pooled:
- pe = pooled["pooled_effect"]
- ci_l = pooled.get("ci_lower", pe)
- ci_u = pooled.get("ci_upper", pe)
- x_min = min(x_min, ci_l)
- x_max = max(x_max, ci_u)
- ax.scatter(pe, diamond_y, marker="D", color="red", s=100, zorder=5)
- ax.hlines(diamond_y, ci_l, ci_u, color="red", lw=2)
- i2 = pooled.get("I2", 0)
- ax.text(
- ci_u + (ci_u - ci_l) * 0.1, diamond_y,
- f"Pooled: {pe:.2f} [{ci_l:.2f}, {ci_u:.2f}]\n"
- f"I²={i2:.1f}%, p={pooled.get('p_value', 0):.4f}",
- va="center", fontsize=8,
- )
- text_x = x_max + (x_max - x_min) * 0.08
- ax.text(text_x, -0.55, "Effect (95% CI)", ha="left", va="center", fontsize=8, fontweight="bold")
- for y, (_, row) in zip(y_positions, df.iterrows()):
- ax.text(
- text_x,
- y,
- f"{row[effect_col]:.2f} [{row[ci_lower_col]:.2f}, {row[ci_upper_col]:.2f}]",
- va="center",
- fontsize=8,
- )
- ax.set_xlim(left=max(0, x_min - (x_max - x_min) * 0.08), right=text_x + (x_max - x_min) * 0.35)
- ax.set_ylim(diamond_y + 0.8, -0.75)
- fig.tight_layout()
- if save_path:
- fig.savefig(save_path, dpi=300, bbox_inches="tight")
- logger.info("Forest plot saved to %s", save_path)
- return fig
- def forest_plot_hr(
- df: pd.DataFrame,
- hr_col: str = "hazard_ratio",
- hr_lower_col: str = "hr_ci_lower",
- hr_upper_col: str = "hr_ci_upper",
- label_col: str = "study_id",
- pooled: Optional[dict] = None,
- title: str = "Forest Plot — Hazard Ratios",
- save_path: Optional[str] = None,
- ) -> plt.Figure:
- """Forest plot for hazard ratios (log scale x-axis)."""
- df = df.dropna(subset=[hr_col]).copy()
- if df.empty:
- fig, ax = plt.subplots()
- ax.text(0.5, 0.5, "No HR data available", ha="center", va="center")
- return fig
- fig, ax = plt.subplots(figsize=(11, max(4, len(df) * 0.45 + 2)))
- y_positions = range(len(df))
- hrs = df[hr_col].values
- lowers = df[hr_lower_col].values if hr_lower_col in df.columns else hrs * 0.5
- uppers = df[hr_upper_col].values if hr_upper_col in df.columns else hrs * 2.0
- ax.hlines(y_positions, lowers, uppers, color="black", lw=1)
- ax.scatter(hrs, y_positions, zorder=5, color="steelblue", s=50)
- ax.axvline(1.0, color="grey", linestyle="--", lw=0.8)
- ax.set_xscale("log")
- ax.set_yticks(list(y_positions))
- ax.set_yticklabels(df[label_col])
- ax.set_xlabel("Hazard Ratio (log scale)")
- ax.set_title(title, fontsize=11, fontweight="bold")
- ax.set_xticks([0.5, 1, 2, 3, 5, 10])
- ax.set_xticklabels(["0.5", "1", "2", "3", "5", "10"])
- x_max = float(np.nanmax(uppers))
- diamond_y = len(df) + 0.5
- if pooled and "pooled_hr" in pooled:
- phr = pooled["pooled_hr"]
- ci_l = pooled.get("hr_ci_lower", phr)
- ci_u = pooled.get("hr_ci_upper", phr)
- x_max = max(x_max, ci_u)
- ax.scatter(phr, diamond_y, marker="D", color="red", s=100, zorder=5)
- ax.hlines(diamond_y, ci_l, ci_u, color="red", lw=2)
- i2 = pooled.get("I2", 0)
- ax.text(
- ci_u * 1.1, diamond_y,
- f"Pooled HR: {phr:.2f} [{ci_l:.2f}, {ci_u:.2f}]\n"
- f"I²={i2:.1f}%, p={pooled.get('p_value', 0):.4f}",
- va="center", fontsize=8,
- )
- text_x = x_max * 1.35
- ax.text(text_x, -0.55, "HR (95% CI)", va="center", fontsize=8, fontweight="bold")
- for y, hr, lo, hi in zip(y_positions, hrs, lowers, uppers):
- ax.text(text_x, y, f"{hr:.2f} [{lo:.2f}, {hi:.2f}]", va="center", fontsize=8)
- ax.set_xlim(left=max(0.4, float(np.nanmin(lowers)) * 0.8), right=text_x * 1.5)
- ax.set_ylim(diamond_y + 0.8, -0.75)
- fig.tight_layout()
- if save_path:
- fig.savefig(save_path, dpi=300, bbox_inches="tight")
- logger.info("HR forest plot saved to %s", save_path)
- return fig
- def funnel_plot(
- effects: np.ndarray,
- se: np.ndarray,
- title: str = "Funnel Plot",
- xlab: str = "Effect Size",
- egger: Optional[dict] = None,
- save_path: Optional[str] = None,
- ) -> plt.Figure:
- """Generate a funnel plot with optional Egger's test annotation."""
- effects = np.asarray(effects, dtype=float)
- se = np.asarray(se, dtype=float)
- fig, ax = plt.subplots(figsize=(8, 6))
- ax.scatter(effects, se, color="steelblue", alpha=0.7, edgecolors="black", lw=0.5)
- ax.set_xlabel(xlab)
- ax.set_ylabel("Standard Error")
- ax.invert_yaxis()
- mean_effect = np.nanmean(effects)
- ax.axvline(mean_effect, color="grey", linestyle="--", lw=0.8)
- # Pseudo-CI lines
- se_range = np.linspace(0.001, np.nanmax(se) * 1.1, 100)
- ax.plot(mean_effect - 1.96 * se_range, se_range, "k--", lw=0.5, alpha=0.5)
- ax.plot(mean_effect + 1.96 * se_range, se_range, "k--", lw=0.5, alpha=0.5)
- if egger:
- p = egger.get("p_value", 1)
- ax.text(
- 0.02, 0.98,
- f"Egger's test: p={p:.4f}\n{egger.get('interpretation', '')}",
- transform=ax.transAxes, va="top", fontsize=9,
- bbox=dict(boxstyle="round", facecolor="wheat", alpha=0.5),
- )
- fig.tight_layout()
- if save_path:
- fig.savefig(save_path, dpi=300, bbox_inches="tight")
- logger.info("Funnel plot saved to %s", save_path)
- return fig
meta.py, no license · at the source
Overview
Abstract
Background/
Reproduced under the paper's license (CC BY), from the paper cited above.
Repository
Its files are read in the Code ↔ Paper reader above.
OSF w2fh3
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
- 27 September 2026: the link answers (HTTP 200)
1 file
- meta.py, Python, 513 lines
The paper's code and data availability statement is in the Data section.
Tracing map
Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.
What the map holds:
- 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
- 1 script, each with its path and the digest of its content;
- no match between paragraphs and code yet;
- neither the text of the paper nor the code itself.
Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.
Data
No dataset and no data link were found in the paper.
Data Availability Statement
All data supporting the findings of this systematic review are available within the article and its Supplementary Materials. The per-study extraction dataset, risk-of-bias assessments, and Python code for descriptive and exploratory analyses are provided as Supplementary Data and have been deposited in the Open Science Framework (OSF) repository (DOI: https://
Reproduced under the paper's license (CC BY), from the paper cited above.
Versions
The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.
Version 1, 27 September 2026: the first record
Recorded: type, language, journal, volume, issue, pages, dates, 2 authors, 5 keywords, 1 funder, 53 references.
Cite
This paper
Walton, C. M., & Strickland, B. A. (2026). Complement-Targeted Therapies in Glioblastoma: A Systematic Review. Biomedicines, 14(8), 1702. https://
BibTeX
@article{walton2026compl
author = {Walton, Chase M. and Strickland, Ben A.},
title = {{Complement-Targeted Therapies in Glioblastoma: A Systematic Review}},
journal = {Biomedicines},
year = {2026},
month = jul,
volume = {14},
number = {8},
pages = {1702},
publisher = {Multidisciplinary Digital Publishing Institute (MDPI)},
issn = {2227-9059},
doi = {10.3390/
url = {https://
pmid = {42652085},
pmcid = {PMC13510105}
}
RIS
TY - JOUR
AU - Walton, Chase M.
AU - Strickland, Ben A.
TI - Complement-Targeted Therapies in Glioblastoma: A Systematic Review
T2 - Biomedicines
J2 - Biomedicines
PY - 2026
DA - 2026/
VL - 14
IS - 8
SP - 1702
SN - 2227-9059
PB - Multidisciplinary Digital Publishing Institute (MDPI)
DO - 10.3390/
UR - https://
LA - en
ER -
CSL-JSON
{
"id": "10.3390/
"type": "article-journal",
"title": "Complement-Targeted Therapies in Glioblastoma: A Systematic Review",
"container-title": "Biomedicines",
"author": [
{
"family": "Walton",
"given": "Chase M."
},
{
"family": "Strickland",
"given": "Ben A."
}
],
"container-title-short":
"volume": "14",
"issue": "8",
"page": "1702",
"DOI": "10.3390/
"PMID": "42652085",
"PMCID": "PMC13510105",
"ISSN": "2227-9059",
"publisher": "Multidisciplinary Digital Publishing Institute (MDPI)",
"URL": "https://
"language": "en",
"issued": {
"date-parts": [
[
2026,
7,
29
]
]
}
}
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