Epidemiological Data Analysis

If the question implies causation ("does X cause Y?") but only cross-sectional data is available, state the limitation explicitly and proceed with association language.

Step 2: Find and Evaluate Data

Use ToolUniverse to discover datasets and find what prior studies used:

# Search for relevant datasets — use find_tools to discover what's available
find_tools("dataset search")
find_tools("your domain keywords")  # e.g., "cancer genomics", "clinical trial", "survey health"

# Search literature for study precedents — papers cite their data sources
execute_tool("PubMed_search_articles", {"query": "[exposure] [outcome] [study design]", "max_results": 5})
execute_tool("EuropePMC_search_articles", {"query": "[exposure] [outcome] cohort", "limit": 5})

Evaluate dataset fitness: Does it have the exposure variable? The outcome? Key confounders (age, sex, plus domain-specific)? Adequate sample size?

Power analysis (run before committing to a dataset):

from scipy.stats import norm
import numpy as np

def sample_size_logistic(p0, OR, alpha=0.05, power=0.80):
    """Minimum N for logistic regression detecting OR at given power."""
    p1 = (p0 * OR) / (1 - p0 + p0 * OR)
    z_a, z_b = norm.ppf(1 - alpha/2), norm.ppf(power)
    n = ((z_a + z_b)**2 * (1/(p0*(1-p0)) + 1/(p1*(1-p1)))) / (np.log(OR))**2
    return int(np.ceil(n))

print(f"Need N={sample_size_logistic(0.10, 1.5)} for OR=1.5 with 10% baseline prevalence")

Step 3: Download and Prepare Data

Download data programmatically. Adapt the loading code to your data source's format.

import pandas as pd
import requests, io

# Generic download helper — adapt URL and format to your source
def download_and_parse(url, fmt="csv"):
    r = requests.get(url, timeout=120)
    content = io.BytesIO(r.content)
    if fmt == "xpt":
        return pd.read_sas(content, format="xport")
    elif fmt == "csv":
        return pd.read_csv(content)
    elif fmt == "tsv":
        return pd.read_csv(content, sep="\t")
    elif fmt == "stata":
        return pd.read_stata(content)
    elif fmt == "json":
        return pd.read_json(content)
    else:
        return pd.read_csv(content)  # default fallback

# Load and merge multiple files on shared ID column
df1 = download_and_parse(url1, fmt="xpt")
df2 = download_and_parse(url2, fmt="xpt")
df = df1.merge(df2, on="id_col", how="inner")

# Filter population (inclusion/exclusion criteria)
df = df[(df['age'] >= 20) & (df['age'] < 80)]

# Handle missing data
missing_pct = df.isnull().mean() * 100
print("Missing % per variable:\n", missing_pct[missing_pct > 0].sort_values(ascending=False))
# Decision: complete case if <5% missing; multiple imputation if 5-20%; drop variable if >20%

# Variable coding (adapt to your data)
df['age_group'] = pd.cut(df['age'], bins=[20,40,60,80], labels=['20-39','40-59','60-79'])
df['outcome_binary'] = (df['outcome_continuous'] >= threshold).astype(int)

Survey weights: Some surveys (NHANES, BRFSS, MEPS) require sampling weights for valid inference. Check the survey documentation. For weighted regression, use statsmodels.stats.weightstats or linearmodels.

REST API data: For sources like GDC (TCGA), ClinicalTrials.gov, or OpenTargets, paginate through the API:

all_records = []
offset = 0
while True:
    resp = requests.get(f"{api_url}?offset={offset}&limit=500", timeout=30)
    batch = resp.json().get("data", [])
    if not batch:
        break
    all_records.extend(batch)
    offset += len(batch)
df = pd.DataFrame(all_records)

Step 4: Descriptive Statistics (Table 1)

# Table 1: mean +/- SD for continuous, N(%) for categorical, by exposure group
continuous_vars = ['age', 'bmi']  # adapt to your variables
for var in continuous_vars:
    print(df.groupby('exposure_group')[var].agg(['mean', 'std', 'count']))

categorical_vars = ['sex', 'race']  # adapt to your variables
for var in categorical_vars:
    print(pd.crosstab(df['exposure_group'], df[var], normalize='index') * 100)

Check distributions: df[var].skew(), scipy.stats.shapiro(), histograms for outliers.

Step 5: Regression Analysis

Sequential adjustment strategy (build evidence for confounding):

import statsmodels.formula.api as smf
import numpy as np

# Model 1: Unadjusted
m1 = smf.logit('outcome ~ exposure', data=df).fit(disp=0)

# Model 2: + demographics
m2 = smf.logit('outcome ~ exposure + age + sex + race', data=df).fit(disp=0)

# Model 3: + clinical factors
m3 = smf.logit('outcome ~ exposure + age + sex + race + bmi + smoking + alcohol', data=df).fit(disp=0)

# Report ORs with 95% CI
for name, model in [('Unadjusted', m1), ('Demographics', m2), ('Fully adjusted', m3)]:
    or_val = np.exp(model.params['exposure'])
    ci = np.exp(model.conf_int().loc['exposure'])
    print(f"{name}: OR={or_val:.2f} (95% CI: {ci[0]:.2f}-{ci[1]:.2f}), p={model.pvalues['exposure']:.4f}")

Model selection by outcome type:

• Continuous outcome: smf.ols()
• Binary outcome: smf.logit()
• Ordered categories: OrderedModel from statsmodels
• Time-to-event: CoxPHFitter from lifelines
• Count data: smf.poisson() or smf.negativebinomial()

Assumption checks:

from statsmodels.stats.outliers_influence import variance_inflation_factor

# Multicollinearity (VIF > 5 is concerning, > 10 is severe)
X = df[['age', 'bmi', 'exposure']].dropna()
for i, col in enumerate(X.columns):
    print(f"VIF {col}: {variance_inflation_factor(X.values, i):.1f}")

Step 6: Sensitivity Analyses

# Stratified analysis (effect modification)
for stratum_var in ['sex', 'age_group', 'race']:
    print(f"\n--- Stratified by {stratum_var} ---")
    for level, sub in df.groupby(stratum_var):
        if len(sub) < 50: continue
        try:
            m = smf.logit('outcome ~ exposure + age + bmi', data=sub).fit(disp=0)
            or_val = np.exp(m.params['exposure'])
            ci = np.exp(m.conf_int().loc['exposure'])
            print(f"  {level}: OR={or_val:.2f} ({ci[0]:.2f}-{ci[1]:.2f}), p={m.pvalues['exposure']:.3f}, N={len(sub)}")
        except: print(f"  {level}: model failed (N={len(sub)})")

# Exclude outliers (+/- 3 SD) and re-run
df_no_outliers = df[np.abs(stats.zscore(df['exposure'].dropna())) < 3]
m_robust = smf.logit('outcome ~ exposure + age + sex + bmi', data=df_no_outliers).fit(disp=0)

# Confounder-adjusted exposure (residual method, e.g., energy-adjusted nutrient intake)
# Use when exposure correlates strongly with a confounder (total calories, body size, etc.)
adj_model = smf.ols('exposure ~ confounder', data=df).fit()
df['exposure_adj'] = adj_model.resid

# Multiple comparisons note
n_tests = 5  # number of exposure-outcome pairs tested
bonferroni_threshold = 0.05 / n_tests

Step 7: Biological Interpretation (ToolUniverse Advantage)

This is where ToolUniverse adds value beyond any statistics package. After finding a statistical association, investigate the biological plausibility. Use find_tools to discover the right tools for your domain.

# 1. Literature evidence — search for mechanism connecting exposure to outcome
execute_tool("PubMed_search_articles", {"query": "[exposure] [outcome] mechanism", "max_results": 5})
execute_tool("EuropePMC_search_articles", {"query": "[exposure] [outcome] mouse model in vivo", "limit": 5})

# 2. Pathway/molecular context — discover tools for your exposure type
find_tools("[exposure type] pathway")       # e.g., "nutrient pathway", "drug target", "chemical toxicology"
find_tools("[outcome type] gene disease")   # e.g., "diabetes gene", "cancer survival", "cardiac risk"

# 3. Gene-disease evidence (if a gene/variant is involved)
find_tools("gene disease association")
find_tools("variant functional annotation")

# 4. Drug/chemical mechanisms (if a drug or chemical is the exposure)
find_tools("drug mechanism target")
find_tools("chemical gene interaction")

The pattern: Exposure X → (what molecular pathway?) → (what biological process?) → Outcome Y. Use ToolUniverse tools to fill in the middle steps. This converts a statistical association into a biologically plausible hypothesis.

Step 8: Visualization

Key plots to produce (use matplotlib):

• Forest plot: stratified ORs with 95% CI, vertical reference line at OR=1, log scale x-axis
• Dose-response curve: exposure quartile medians on x-axis vs outcome prevalence/mean on y-axis
• DAG: directed acyclic graph showing assumed causal structure (exposure, confounders, outcome)
• Scatter + regression line: for continuous outcomes with sns.regplot()

Step 9: Report Structure

Write the final report in this order:

1. Background: What is known, what gap this analysis addresses (cite PubMed searches from Step 7)
2. Methods: PECO, data source, inclusion/exclusion, variable definitions, statistical approach, sensitivity analyses
3. Results: Table 1, unadjusted and adjusted ORs/HRs, stratified results, dose-response, sensitivity checks
4. Discussion: Compare to prior literature (PubMed), biological plausibility (ToolUniverse pathway/mechanism findings), clinical significance of effect size
5. Limitations: Study design constraints, unmeasured confounding, selection bias, measurement error, generalizability

Key limitations to always state:

• Cross-sectional design cannot establish temporality (if applicable)
• Residual confounding from unmeasured variables
• Self-reported exposure data may have recall bias
• Survey weights may not fully account for non-response bias

Completeness Checklist

Before finalizing any epidemiological analysis:

• PECO defined and documented
• Study design matches the research question
• Sample size adequate (power analysis done)
• Missing data reported and handled
• Table 1 produced
• Unadjusted AND adjusted models reported
• Confounders justified (not just statistically selected)
• Assumptions checked (VIF, linearity, model fit)
• At least one sensitivity analysis performed
• Biological plausibility investigated via ToolUniverse
• Effect size interpreted in clinical context (not just p-value)
• Limitations explicitly stated