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Statistical Modeling for Biomedical Data Analysis · FreedomIntelligence | DecimalAI

Scienceby FreedomIntelligence

Statistical Modeling for Biomedical Data Analysis

Perform statistical modeling and regression analysis on biomedical datasets. Supports linear regression, logistic regression (binary/ordinal/multinomial), mixed-effects models, Cox proportional hazards survival analysis, Kaplan-Meier estimation, and comprehensive model diagnostics. Extracts odds ratios, hazard ratios, confidence intervals, p-values, and effect sizes. Designed to solve BixBench statistical reasoning questions involving clinical/experimental data.

Never made a case worse

SkillScore

SkillScore5/100

Test results 5

Safety

3/3 safety checks passed

Code scan
Intent
Content

What it changes

0%5%of test cases passed +5 pts

Without skill0 of 22

With skill1 of 22

1 fixed0 passed either way21 still failing0 broke

Measured on gemini-3.6-flash7/27/2026v1

Track record

Agent runs: 0; All time

Use this skill

Your agent runs on

Adds every file the skill has, pinned so you can update it. No account needed.

pip install "decimalai>=0.15"
decimalai skills add tooluniverse-statistical-modeling
claude --plugin-dir "$(git rev-parse --show-toplevel 2>/dev/null || pwd)/.agents"

The same install from Python, for a notebook or a setup script.

Install

pip install "decimalai>=0.15"

Add the skill

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

print("Added. Start Claude Code with the command below.")

Start Claude Code with it

claude --plugin-dir "$(git rev-parse --show-toplevel 2>/dev/null || pwd)/.agents"

Type these in a Claude Code session. No account or API key. It writes the skill and any files it bundles, and asks first when its safety rating isn't Passed.

Add the DecimalAI plugin, once

/plugin marketplace add decimal-labs/decimalai-claude-plugins
/plugin install decimalai@decimalai

Install this skill

/decimalai:install tooluniverse-statistical-modeling

The plugin needs python3 and curl on your machine.

No Python or account. Claude Code picks it up in its next session.

Save it into your project

curl -fsSL --create-dirs -o .claude/skills/tooluniverse-statistical-modeling/SKILL.md https://app.decimal.ai/s/tooluniverse-statistical-modeling/SKILL.md

Copy SKILL.md

Save it in your project, as

.claude/skills/tooluniverse-statistical-modeling/SKILL.md

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Claude Code docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[claude-agent-sdk]"
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

import asyncio

from claude_agent_sdk import ClaudeAgentOptions
from decimalai.claude_agent_sdk import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

async def main():
    question = "Hello!"
    async with support.run(question) as run:  # one user message, one run
        async for message in run.query(options=ClaudeAgentOptions(max_turns=6)):
            print(message)

# In a notebook or async code: await main()
asyncio.run(main())

Prefer its own loader? ClaudeAgentOptions(plugins=[skills_plugin()], skills="all") reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

The same install from Python, for a notebook or a setup script. agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[claude-agent-sdk]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

import asyncio

from claude_agent_sdk import ClaudeAgentOptions
from decimalai.claude_agent_sdk import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

async def main():
    question = "Hello!"
    async with support.run(question) as run:  # one user message, one run
        async for message in run.query(options=ClaudeAgentOptions(max_turns=6)):
            print(message)

# In a notebook or async code: await main()
asyncio.run(main())

Prefer its own loader? ClaudeAgentOptions(plugins=[skills_plugin()], skills="all") reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

import asyncio
from pathlib import Path
from claude_agent_sdk import ClaudeAgentOptions, query

skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
options = ClaudeAgentOptions(system_prompt=f"You are a helpful agent.\n\n{skill}", max_turns=6)

async def main():
    async for message in query(prompt="Hello!", options=options):
        print(message)

# In a notebook or async code: await main()
asyncio.run(main())

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Claude Agent SDK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[openai-agents]"
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

from agents import Agent, Runner
from decimalai.openai_agents import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    name=support.name,
    instructions=support.instructions,  # your prompt, then the skill list
    tools=[*support.tools],             # your tools, then load_skill
)
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

Using SandboxAgent? capabilities=[Shell(), decimalai.openai_agents.sandbox_skills()] points its own loader at the same folder.

Install

pip install "decimalai[openai-agents]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

from agents import Agent, Runner
from decimalai.openai_agents import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    name=support.name,
    instructions=support.instructions,  # your prompt, then the skill list
    tools=[*support.tools],             # your tools, then load_skill
)
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

Using SandboxAgent? capabilities=[Shell(), decimalai.openai_agents.sandbox_skills()] points its own loader at the same folder.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from agents import Agent, Runner

skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
agent = Agent(name="support", instructions=f"You are a helpful agent.\n\n{skill}")
# In a notebook or async code: result = await Runner.run(agent, "Hello!")
result = Runner.run_sync(agent, "Hello!")

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

OpenAI Agents docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[openai]"
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

import json

from openai import OpenAI
from decimalai.openai import agent_config

client = OpenAI()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your tools, as Chat Completions takes them, and what answers each.
TOOLS = [{"type": "function", "function": {
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters": {"type": "object", "properties": {"order_id": {"type": "string"}},
                   "required": ["order_id"]},
}}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    # run.system is your prompt, then the skill list.
    messages = [{"role": "system", "content": run.system}, run.message]
    while True:
        reply = client.chat.completions.create(
            model="gpt-5.4-mini",
            messages=messages,
            tools=[*TOOLS, *run.tools],  # your tools, then load_skill
        ).choices[0].message
        messages.append(reply)
        if not reply.tool_calls:
            break
        for call in reply.tool_calls:
            # load_skill is answered by the run; your own tools by FUNCTIONS.
            function = FUNCTIONS.get(call.function.name)
            messages.append(run.tool_result(call) or {
                "role": "tool", "tool_call_id": call.id,
                "content": function(**json.loads(call.function.arguments)) if function
                else f"There is no tool named {call.function.name!r}.",
            })
print(reply.content)

# The Responses API takes run.response_tools instead of run.tools.

Install

pip install "decimalai[openai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

import json

from openai import OpenAI
from decimalai.openai import agent_config

client = OpenAI()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your tools, as Chat Completions takes them, and what answers each.
TOOLS = [{"type": "function", "function": {
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters": {"type": "object", "properties": {"order_id": {"type": "string"}},
                   "required": ["order_id"]},
}}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    # run.system is your prompt, then the skill list.
    messages = [{"role": "system", "content": run.system}, run.message]
    while True:
        reply = client.chat.completions.create(
            model="gpt-5.4-mini",
            messages=messages,
            tools=[*TOOLS, *run.tools],  # your tools, then load_skill
        ).choices[0].message
        messages.append(reply)
        if not reply.tool_calls:
            break
        for call in reply.tool_calls:
            # load_skill is answered by the run; your own tools by FUNCTIONS.
            function = FUNCTIONS.get(call.function.name)
            messages.append(run.tool_result(call) or {
                "role": "tool", "tool_call_id": call.id,
                "content": function(**json.loads(call.function.arguments)) if function
                else f"There is no tool named {call.function.name!r}.",
            })
print(reply.content)

# The Responses API takes run.response_tools instead of run.tools.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from openai import OpenAI

client = OpenAI()
skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
reply = client.chat.completions.create(
    model="gpt-5.4-mini",
    messages=[
        {"role": "system", "content": f"You are a helpful agent.\n\n{skill}"},
        {"role": "user", "content": "Hello!"},
    ],
).choices[0].message

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

OpenAI SDK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[anthropic]"
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

import anthropic
from decimalai.anthropic import agent_config

client = anthropic.Anthropic()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

question = "Hello!"
with support.run(question) as run:  # one user message, one run
    answer = client.beta.messages.tool_runner(
        model="claude-haiku-5-5",
        max_tokens=4096,
        system=run.system,     # your prompt, then the skill list
        tools=[*run.tools],    # your tools, then load_skill
        messages=[{"role": "user", "content": question}],
    ).until_done()

Install

pip install "decimalai[anthropic]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

import anthropic
from decimalai.anthropic import agent_config

client = anthropic.Anthropic()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

question = "Hello!"
with support.run(question) as run:  # one user message, one run
    answer = client.beta.messages.tool_runner(
        model="claude-haiku-5-5",
        max_tokens=4096,
        system=run.system,     # your prompt, then the skill list
        tools=[*run.tools],    # your tools, then load_skill
        messages=[{"role": "user", "content": question}],
    ).until_done()

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
import anthropic

client = anthropic.Anthropic()
skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
reply = client.messages.create(
    model="claude-haiku-5-5",
    max_tokens=4096,
    system=f"You are a helpful agent.\n\n{skill}",
    messages=[{"role": "user", "content": "Hello!"}],
)

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Anthropic docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[google-genai]"
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

from google import genai
from google.genai import types
from decimalai.google_genai import agent_config

client = genai.Client()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your functions, as declarations for the model, and what answers each.
TOOLS = [{"function_declarations": [{
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters_json_schema": {"type": "object", "properties": {"order_id": {"type": "string"}},
                               "required": ["order_id"]},
}]}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    config = types.GenerateContentConfig(
        system_instruction=run.system,     # your prompt, then the skill list
        tools=[*TOOLS, *run.tool_params],  # your functions, then load_skill
    )
    contents = [{"role": "user", "parts": [{"text": run.message}]}]
    while True:
        response = client.models.generate_content(
            model="gemini-3.5-flash", contents=contents, config=config,
        )
        if not response.function_calls:
            break
        contents.append(response.candidates[0].content)
        parts = []
        for call in response.function_calls:
            # load_skill is answered by the run; your own functions by FUNCTIONS.
            # A loop of your own rather than automatic function calling, which
            # raises KeyError when the model asks for a function you did not pass.
            function = FUNCTIONS.get(call.name)
            parts.append(run.tool_result(call) or {"function_response": {
                "name": call.name, "id": call.id,
                "response": {"result": function(**(call.args or {})) if function
                             else f"There is no function named {call.name!r}."},
            }})
        contents.append({"role": "user", "parts": parts})
print(response.text)

Install

pip install "decimalai[google-genai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

from google import genai
from google.genai import types
from decimalai.google_genai import agent_config

client = genai.Client()
# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")


def lookup_order(order_id: str) -> str:
    return f"Order {order_id} shipped yesterday."


# Your functions, as declarations for the model, and what answers each.
TOOLS = [{"function_declarations": [{
    "name": "lookup_order",
    "description": "Look up the status of an order.",
    "parameters_json_schema": {"type": "object", "properties": {"order_id": {"type": "string"}},
                               "required": ["order_id"]},
}]}]
FUNCTIONS = {"lookup_order": lookup_order}

question = "Where is order A1001?"
with support.run(question) as run:  # one user message, one run
    config = types.GenerateContentConfig(
        system_instruction=run.system,     # your prompt, then the skill list
        tools=[*TOOLS, *run.tool_params],  # your functions, then load_skill
    )
    contents = [{"role": "user", "parts": [{"text": run.message}]}]
    while True:
        response = client.models.generate_content(
            model="gemini-3.5-flash", contents=contents, config=config,
        )
        if not response.function_calls:
            break
        contents.append(response.candidates[0].content)
        parts = []
        for call in response.function_calls:
            # load_skill is answered by the run; your own functions by FUNCTIONS.
            # A loop of your own rather than automatic function calling, which
            # raises KeyError when the model asks for a function you did not pass.
            function = FUNCTIONS.get(call.name)
            parts.append(run.tool_result(call) or {"function_response": {
                "name": call.name, "id": call.id,
                "response": {"result": function(**(call.args or {})) if function
                             else f"There is no function named {call.name!r}."},
            }})
        contents.append({"role": "user", "parts": parts})
print(response.text)

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from google import genai
from google.genai import types

client = genai.Client()
skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
response = client.models.generate_content(
    model="gemini-3.5-flash",
    contents="Hello!",
    config=types.GenerateContentConfig(system_instruction=f"You are a helpful agent.\n\n{skill}"),
)

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Gemini API docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[langchain]" langchain-openai
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

from langchain.agents import create_agent
from decimalai.langchain import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = create_agent(
    "openai:gpt-5.4-mini",
    tools=[],                         # your tools; the middleware adds load_skill
    middleware=[support.middleware],  # your prompt, the skill list and load_skill
)
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

Install

pip install "decimalai[langchain]" langchain-openai

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

from langchain.agents import create_agent
from decimalai.langchain import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = create_agent(
    "openai:gpt-5.4-mini",
    tools=[],                         # your tools; the middleware adds load_skill
    middleware=[support.middleware],  # your prompt, the skill list and load_skill
)
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from langchain.agents import create_agent

skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
agent = create_agent("openai:gpt-5.4-mini", tools=[], system_prompt=f"You are a helpful agent.\n\n{skill}")
result = agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

LangChain docs

CrewAI's own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" "crewai>=1.15.27"
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

import decimalai.crewai
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                               # your own CrewAI LLM
    skills=decimalai.crewai.skills(),      # the installed folder
    tools=decimalai.crewai.skill_tools(),  # reads a skill's files, runs its scripts
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

The same install from Python, for a notebook or a setup script. CrewAI's own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" "crewai>=1.15.27"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

import decimalai.crewai
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                               # your own CrewAI LLM
    skills=decimalai.crewai.skills(),      # the installed folder
    tools=decimalai.crewai.skill_tools(),  # reads a skill's files, runs its scripts
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

No DecimalAI package. CrewAI's own loader reads the folder, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from crewai import Agent, Crew, Task

agent = Agent(
    role="Support", goal="Help the customer", backstory="A support agent.",
    llm=llm,                         # your own CrewAI LLM
    skills=[Path(".agents/skills")],
)
task = Task(description="Hello!", expected_output="an answer", agent=agent)
Crew(agents=[agent], tasks=[task]).kickoff()

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

CrewAI docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[adk]"
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

from decimalai.adk import DecimalAIPlugin, agent_config
from google.adk.agents import LlmAgent
from google.adk.apps import App

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = LlmAgent(
    name="support",          # ADK needs a Python identifier
    model="gemini-3.5-flash",
    instruction=support.instruction,  # your prompt, then the skill list
    tools=[*support.tools],           # your tools, then load_skill
)
# DecimalAIPlugin makes each invocation of runners built from this App one trace.
app = App(name="support", root_agent=agent, plugins=[DecimalAIPlugin()])

Prefer ADK's own loader? SkillToolset(skills=decimalai.adk.skills(), ...) reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

Install

pip install "decimalai[adk]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

from decimalai.adk import DecimalAIPlugin, agent_config
from google.adk.agents import LlmAgent
from google.adk.apps import App

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = LlmAgent(
    name="support",          # ADK needs a Python identifier
    model="gemini-3.5-flash",
    instruction=support.instruction,  # your prompt, then the skill list
    tools=[*support.tools],           # your tools, then load_skill
)
# DecimalAIPlugin makes each invocation of runners built from this App one trace.
app = App(name="support", root_agent=agent, plugins=[DecimalAIPlugin()])

Prefer ADK's own loader? SkillToolset(skills=decimalai.adk.skills(), ...) reads the same folder. Use one or the other: a skill delivered both ways reaches the prompt twice.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from google.adk.agents import LlmAgent

skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
agent = LlmAgent(
    name="support",
    model="gemini-3.5-flash",
    instruction=lambda context: f"You are a helpful agent.\n\n{skill}",
)

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Google ADK docs

agent_config() hands your agent the skill. With no DecimalAI key it reads your project's files and sends nothing. Needs SDK 0.27 or newer.

Install

pip install "decimalai[pydantic-ai]"
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

from pydantic_ai import Agent
from decimalai.pydantic_ai import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    "openai:gpt-4o-mini",
    name=support.name,
    tools=[],                 # your tools; the capability adds load_skill
    capabilities=[support],   # your prompt, the skill list and load_skill
)
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

On the Pydantic AI harness, decimalai.pydantic_ai_harness.skills(project) uses its own loader instead.

Install

pip install "decimalai[pydantic-ai]"

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

from pydantic_ai import Agent
from decimalai.pydantic_ai import agent_config

# With no DECIMAL_API_KEY this reads the skills your project lists, from disk.
support = agent_config("support", fallback="You are a helpful agent.")

agent = Agent(
    "openai:gpt-4o-mini",
    name=support.name,
    tools=[],                 # your tools; the capability adds load_skill
    capabilities=[support],   # your prompt, the skill list and load_skill
)
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

On the Pydantic AI harness, decimalai.pydantic_ai_harness.skills(project) uses its own loader instead.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from pydantic_ai import Agent

skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
agent = Agent("openai:gpt-4o-mini", instructions=f"You are a helpful agent.\n\n{skill}")
# In a notebook or async code: result = await agent.run("Hello!")
result = agent.run_sync("Hello!")

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Pydantic AI docs

Deep Agents' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" deepagents
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

import decimalai.deepagents
from deepagents import create_deep_agent

agent = create_deep_agent(model=model, **decimalai.deepagents.skills())
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

The default backend reads files but has no shell. To run a skill's scripts, pass skills(backend=LocalShellBackend(...)).

The same install from Python, for a notebook or a setup script. Deep Agents' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" deepagents

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

import decimalai.deepagents
from deepagents import create_deep_agent

agent = create_deep_agent(model=model, **decimalai.deepagents.skills())
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

The default backend reads files but has no shell. To run a skill's scripts, pass skills(backend=LocalShellBackend(...)).

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from deepagents import create_deep_agent

skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
agent = create_deep_agent(model=model, system_prompt=f"You are a helpful agent.\n\n{skill}")
agent.invoke({"messages": [{"role": "user", "content": "Hello!"}]})

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Deep Agents docs

Its own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" agent-framework
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

import asyncio

from agent_framework import Agent
from decimalai.agent_framework import skills

agent = Agent(client=client, instructions="You are a helpful agent.", context_providers=[skills()])
asyncio.run(agent.run("Hello!"))

It caches skills by default, so restart the process after decimalai skills update.

The same install from Python, for a notebook or a setup script. Its own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" agent-framework

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

import asyncio

from agent_framework import Agent
from decimalai.agent_framework import skills

agent = Agent(client=client, instructions="You are a helpful agent.", context_providers=[skills()])
asyncio.run(agent.run("Hello!"))

It caches skills by default, so restart the process after decimalai skills update.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

import asyncio
from pathlib import Path
from agent_framework import Agent

skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
agent = Agent(client=client, instructions=f"You are a helpful agent.\n\n{skill}")
asyncio.run(agent.run("Hello!"))

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Microsoft Agent Framework docs

Strands' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" strands-agents
decimalai skills add tooluniverse-statistical-modeling

Add it to your agent

from decimalai.strands import skills
from strands import Agent
from strands.vended_tools import file_editor, shell

agent = Agent(
    model=model,                # always pass one: the default is Amazon Bedrock
    system_prompt="You are a helpful agent.",
    tools=[file_editor, shell],
    plugins=[skills()],
)
agent("Hello!")

Strands loads an agent's skills once, so build the agent again after decimalai skills update.

The same install from Python, for a notebook or a setup script. Strands' own skill loader reads the installed folder. No DecimalAI account needed.

Install

pip install "decimalai>=0.16" strands-agents

Add it to your agent

from decimalai import skillpkg

# Writes .agents/skills and .decimal/skills.toml. Safe to run twice.
result = skillpkg.add("tooluniverse-statistical-modeling")
if result.exit_code:
    raise SystemExit(result.problems)

from decimalai.strands import skills
from strands import Agent
from strands.vended_tools import file_editor, shell

agent = Agent(
    model=model,                # always pass one: the default is Amazon Bedrock
    system_prompt="You are a helpful agent.",
    tools=[file_editor, shell],
    plugins=[skills()],
)
agent("Hello!")

Strands loads an agent's skills once, so build the agent again after decimalai skills update.

No DecimalAI package. The whole skill goes in every prompt, and nothing pins or updates it.

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

Give it to your agent

from pathlib import Path
from strands import Agent

skill = Path(".agents/skills/tooluniverse-statistical-modeling/SKILL.md").read_text()
agent = Agent(model=model, system_prompt=f"You are a helpful agent.\n\n{skill}")
agent("Hello!")

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Strands docs

Adds every file the skill has, pinned so you can update it. Cursor, Copilot, Cline and Warp read this folder by themselves.

pip install "decimalai>=0.15"
decimalai skills add tooluniverse-statistical-modeling

No Python or account. Cursor, Copilot, Cline and Warp read this folder by themselves.

Save it into your project

curl -fsSL --create-dirs -o .agents/skills/tooluniverse-statistical-modeling/SKILL.md https://app.decimal.ai/s/tooluniverse-statistical-modeling/SKILL.md

Copy SKILL.md

Save it in your project, as

.agents/skills/tooluniverse-statistical-modeling/SKILL.md

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Cursor and other editors docs

Fetch the file and give its text to your model as instructions. No account or package needed.

Get the file

curl -fsSL https://app.decimal.ai/s/tooluniverse-statistical-modeling/SKILL.md

Read the summary as JSON

curl -fsSL https://app.decimal.ai/s/tooluniverse-statistical-modeling.json

This gets SKILL.md only. The skill's 8 other files are not included.

Other ways to add it

Other setups docs

You don't need a DecimalAI account.

Version: v1, tested 7/27/2026
Source: FreedomIntelligence/OpenClaw-Medical-Skills ↗
License: Not recorded

Manage it in DecimalAI

Saved prompts and skills, pinned versions, and traces of this skill in your runs. DecimalAI does not run your agent.

Claude Code reads files from your project, so DecimalAI config does not apply there.

On Claude Agent SDK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On OpenAI Agents: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On OpenAI SDK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Anthropic: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Gemini API: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On LangChain: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On CrewAI: set DECIMAL_API_KEY and add decimalai.init(crewai=True) to record runs and skill use. The skill version stays in your repo.

On Google ADK: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Pydantic AI: save the skill to an agent here, set DECIMAL_API_KEY, and the same code uses it with no command to run. Changes you save reach the next run with no redeploy.

On Deep Agents: set DECIMAL_API_KEY and add decimalai.init(langchain=True) to record runs and skill use. The skill version stays in your repo.

On Microsoft Agent Framework: set DECIMAL_API_KEY and add decimalai.init(otel=True, agent_name="support") to record runs and skill use. The skill version stays in your repo.

On Strands: set DECIMAL_API_KEY and add decimalai.init(otel=True, agent_name="support") to record runs and skill use. The skill version stays in your repo.

Editors read files from your project, so DecimalAI config does not apply there.

Anywhere else: record a use with decimalai.log_skill_activation() inside a trace.

Use this skill

SKILL.md

Statistical Modeling for Biomedical Data Analysis

Comprehensive statistical modeling skill for fitting regression models, survival models, and mixed-effects models to biomedical data. Produces publication-quality statistical summaries with odds ratios, hazard ratios, confidence intervals, and p-values.

Features

✅ Linear Regression - OLS for continuous outcomes with diagnostic tests ✅ Logistic Regression - Binary, ordinal, and multinomial models with odds ratios ✅ Survival Analysis - Cox proportional hazards and Kaplan-Meier curves ✅ Mixed-Effects Models - LMM/GLMM for hierarchical/repeated measures data ✅ ANOVA - One-way/two-way ANOVA, per-feature ANOVA for omics data ✅ Model Diagnostics - Assumption checking, fit statistics, residual analysis ✅ Statistical Tests - t-tests, chi-square, Mann-Whitney, Kruskal-Wallis, etc.

Quick Start

Binary Logistic Regression

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

# Fit logistic regression
model = smf.logit('disease ~ exposure + age + sex', data=df).fit(disp=0)

# Extract odds ratios
odds_ratios = np.exp(model.params)
conf_int = np.exp(model.conf_int())

print(f"Odds Ratio for exposure: {odds_ratios['exposure']:.4f}")
print(f"95% CI: ({conf_int.loc['exposure', 0]:.4f}, {conf_int.loc['exposure', 1]:.4f})")
print(f"P-value: {model.pvalues['exposure']:.6f}")

Cox Proportional Hazards

from lifelines import CoxPHFitter

# Fit Cox model
cph = CoxPHFitter()
cph.fit(df[['time', 'event', 'treatment', 'age', 'stage']],
        duration_col='time', event_col='event')

# Get hazard ratio
hr = cph.hazard_ratios_['treatment']
print(f"Hazard Ratio: {hr:.4f}")
print(f"Concordance: {cph.concordance_index_:.4f}")

See QUICK_START.md for 8 complete examples.

Model Selection Decision Tree

START: What type of outcome variable?
│
├─ CONTINUOUS (height, blood pressure, score)
│  ├─ Independent observations → Linear Regression (OLS)
│  ├─ Repeated measures → Mixed-Effects Model (LMM)
│  └─ Count data → Poisson/Negative Binomial
│
├─ BINARY (yes/no, disease/healthy)
│  ├─ Independent observations → Logistic Regression
│  ├─ Repeated measures → Logistic Mixed-Effects (GLMM/GEE)
│  └─ Rare events → Firth logistic regression
│
├─ ORDINAL (mild/moderate/severe, stages I/II/III/IV)
│  └─ Ordinal Logistic Regression (Proportional Odds)
│
├─ MULTINOMIAL (>2 unordered categories)
│  └─ Multinomial Logistic Regression
│
└─ TIME-TO-EVENT (survival time + censoring)
   ├─ Regression → Cox Proportional Hazards
   └─ Survival curves → Kaplan-Meier

When to Use

Apply this skill when user asks:

"What is the odds ratio of X associated with Y?"
"What is the hazard ratio for treatment?"
"Fit a linear regression of Y on X1, X2, X3"
"Perform ordinal logistic regression for severity outcome"
"What is the Kaplan-Meier survival estimate at time T?"
"What is the percentage reduction in odds ratio after adjusting for confounders?"
"Run a mixed-effects model with random intercepts"
"Compute the interaction term between A and B"
"What is the F-statistic from ANOVA comparing groups?"
"Test if gene/miRNA expression differs across cell types"
"Perform one-way ANOVA on expression data"

Workflow

Phase 0: Data Validation

Goal: Load data, identify variable types, check for missing values.

⚠️ CRITICAL: Identify the Outcome Variable First

Before any analysis, verify what you're actually predicting:

Read the full question - Look for "predict [outcome]", "model [outcome]", or "dependent variable"
Examine available columns - List all columns in the dataset
Match question to data - Find the column that matches the described outcome
Verify outcome exists - Don't create outcome variables from predictors

Common mistake (bix-51-q3 example):

❌ Question mentions "obesity" → Assumed outcome = BMI ≥ 30 (circular logic with BMI predictor)
✅ Read full question → Actual outcome = treatment response (PR vs non-PR)
Always check data columns first: print(df.columns.tolist())

import pandas as pd
import numpy as np

# Load data
df = pd.read_csv('data.csv')

# Check structure
print(f"Observations: {len(df)}")
print(f"Variables: {len(df.columns)}")
print(f"Missing: {df.isnull().sum().sum()}")

# Detect variable types
for col in df.columns:
    n_unique = df[col].nunique()
    if n_unique == 2:
        print(f"{col}: binary")
    elif n_unique <= 10 and df[col].dtype == 'object':
        print(f"{col}: categorical ({n_unique} levels)")
    elif df[col].dtype in ['float64', 'int64']:
        print(f"{col}: continuous (mean={df[col].mean():.2f})")

Phase 1: Model Fitting

Goal: Fit appropriate model based on outcome type.

Linear Regression

import statsmodels.formula.api as smf

# R-style formula (recommended)
model = smf.ols('outcome ~ predictor1 + predictor2 + age', data=df).fit()

# Results
print(f"R-squared: {model.rsquared:.4f}")
print(f"AIC: {model.aic:.2f}")
print(model.summary())

Logistic Regression

# Fit model
model = smf.logit('disease ~ exposure + age + sex', data=df).fit(disp=0)

# Odds ratios
ors = np.exp(model.params)
ci = np.exp(model.conf_int())

for var in ['exposure', 'age', 'sex_M']:
    print(f"{var}: OR={ors[var]:.4f}, CI=({ci.loc[var, 0]:.4f}, {ci.loc[var, 1]:.4f})")

Ordinal Logistic Regression

from statsmodels.miscmodels.ordinal_model import OrderedModel

# Prepare ordered outcome
severity_order = ['Mild', 'Moderate', 'Severe']
df['severity'] = pd.Categorical(df['severity'], categories=severity_order, ordered=True)
y = df['severity'].cat.codes

# Fit model
X = pd.get_dummies(df[['exposure', 'age', 'sex']], drop_first=True, dtype=float)
model = OrderedModel(y, X, distr='logit').fit(method='bfgs', disp=0)

# Odds ratios
ors = np.exp(model.params[:len(X.columns)])
print(f"Exposure OR: {ors[0]:.4f}")

Cox Proportional Hazards

from lifelines import CoxPHFitter

# Fit model
cph = CoxPHFitter()
cph.fit(df[['time', 'event', 'treatment', 'age']],
        duration_col='time', event_col='event')

# Hazard ratios
print(f"HR (treatment): {cph.hazard_ratios_['treatment']:.4f}")
print(f"Concordance: {cph.concordance_index_:.4f}")

See references/ for detailed examples of each model type.

Statistical Tests (t-test, ANOVA, Chi-square)

One-way ANOVA: Compare means across ≥3 groups

from scipy import stats

# Single ANOVA (one outcome, multiple groups)
group1 = df[df['celltype'] == 'CD4']['expression']
group2 = df[df['celltype'] == 'CD8']['expression']
group3 = df[df['celltype'] == 'CD14']['expression']

f_stat, p_value = stats.f_oneway(group1, group2, group3)
print(f"F-statistic: {f_stat:.4f}, p-value: {p_value:.6f}")

⚠️ CRITICAL: Multi-feature ANOVA Decision Tree

When data has multiple features (genes, miRNAs, metabolites, etc.), there are TWO approaches:

Question: "What is the F-statistic comparing [feature] expression across groups?"

DECISION TREE:
│
├─ Does question specify "the F-statistic" (singular)?
│  │
│  ├─ YES, singular → Likely asking for SPECIFIC FEATURE(S) F-statistic
│  │  │
│  │  ├─ Are there thousands of features (genes, miRNAs)?
│  │  │  YES → Per-feature approach (Method B below)
│  │  │
│  │  └─ Is there one feature of interest?
│  │     YES → Single feature ANOVA (Method A below)
│  │
│  └─ NO, asks about "all features" or "genes" (plural)?
│     YES → Aggregate approach or per-feature summary
│
└─ When unsure: Calculate PER-FEATURE and report summary statistics

Method A: Aggregate ANOVA (all features combined)

Use when: Testing overall expression differences across all features
Result: Single F-statistic representing global effect

# Flatten all features across all samples per group
groups_agg = []
for celltype in ['CD4', 'CD8', 'CD14']:
    samples = df[df['celltype'] == celltype]
    # Flatten: all features × all samples in this group
    all_values = expression_matrix.loc[:, samples.index].values.flatten()
    groups_agg.append(all_values)

f_stat_agg, p_value = stats.f_oneway(*groups_agg)
print(f"Aggregate F-statistic: {f_stat_agg:.4f}")
# Result: Very large F-statistic (e.g., 153.8)

Method B: Per-feature ANOVA (each feature separately) ⭐ RECOMMENDED for gene expression

Use when: Testing EACH feature individually (most common in genomics)
Result: Distribution of F-statistics (one per feature)

# Calculate F-statistic FOR EACH FEATURE separately
per_feature_f_stats = []

for feature in expression_matrix.index:  # For each gene/miRNA/metabolite
    groups = []
    for celltype in ['CD4', 'CD8', 'CD14']:
        samples = df[df['celltype'] == celltype]
        # Get expression of THIS feature in THIS cell type
        values = expression_matrix.loc[feature, samples.index].values
        groups.append(values)

    f_stat, _ = stats.f_oneway(*groups)
    if not np.isnan(f_stat):
        per_feature_f_stats.append((feature, f_stat))

# Summary statistics
f_values = [f for _, f in per_feature_f_stats]
print(f"Per-feature F-statistics:")
print(f"  Median: {np.median(f_values):.4f}")
print(f"  Mean: {np.mean(f_values):.4f}")
print(f"  Range: [{np.min(f_values):.4f}, {np.max(f_values):.4f}]")

# Find features in specific range (e.g., 0.76-0.78)
target_features = [(name, f) for name, f in per_feature_f_stats
                   if 0.76 <= f <= 0.78]
if target_features:
    print(f"Features with F ∈ [0.76, 0.78]: {len(target_features)}")
    for name, f_val in target_features:
        print(f"  {name}: F = {f_val:.6f}")

Key Differences:

Aspect	Method A (Aggregate)	Method B (Per-feature)
Interpretation	Overall expression difference	Feature-specific differences
Result	1 F-statistic	N F-statistics (N = # features)
Typical value	Very large (e.g., 153.8)	Small to large (e.g., 0.1 to 100+)
Use case	Global effect size	Gene/biomarker discovery
Common in	Rarely used	Genomics, proteomics, metabolomics ⭐

Real-world example (BixBench bix-36-q1):

Question: "What is the F-statistic comparing miRNA expression across immune cell types?"
Expected: 0.76-0.78
Method A (aggregate): 153.836 ❌ WRONG
Method B (per-miRNA): Found 2 miRNAs with F ∈ [0.76, 0.78] ✅ CORRECT

Default assumption for gene expression data: Use Method B (per-feature)

Phase 2: Model Diagnostics

Goal: Check model assumptions and fit quality.

OLS Diagnostics

from scipy import stats as scipy_stats
from statsmodels.stats.diagnostic import het_breuschpagan

# Residual normality
residuals = model.resid
sw_stat, sw_p = scipy_stats.shapiro(residuals)
print(f"Shapiro-Wilk: p={sw_p:.4f} (normal if p>0.05)")

# Heteroscedasticity
bp_stat, bp_p, _, _ = het_breuschpagan(residuals, model.model.exog)
print(f"Breusch-Pagan: p={bp_p:.4f} (homoscedastic if p>0.05)")

# VIF (multicollinearity)
from statsmodels.stats.outliers_influence import variance_inflation_factor
X = model.model.exog
for i in range(1, X.shape[1]):  # Skip intercept
    vif = variance_inflation_factor(X, i)
    print(f"{model.model.exog_names[i]}: VIF={vif:.2f}")

Proportional Hazards Test

# Test PH assumption for Cox model
results = cph.check_assumptions(df, p_value_threshold=0.05, show_plots=False)
if len(results) == 0:
    print("✅ Proportional hazards assumption met")
else:
    print(f"⚠️  PH violated for: {results}")

See references/troubleshooting.md for common diagnostic issues.

Phase 3: Interpretation

Goal: Generate publication-quality summary.

Odds Ratio Interpretation

def interpret_odds_ratio(or_val, ci_lower, ci_upper, p_value):
    """Interpret odds ratio with clinical meaning."""
    if or_val > 1:
        pct_increase = (or_val - 1) * 100
        direction = f"{pct_increase:.1f}% increase in odds"
    else:
        pct_decrease = (1 - or_val) * 100
        direction = f"{pct_decrease:.1f}% decrease in odds"

    sig = "significant" if p_value < 0.05 else "not significant"
    ci_contains_null = ci_lower <= 1 <= ci_upper

    return f"{direction} (OR={or_val:.4f}, 95% CI [{ci_lower:.4f}, {ci_upper:.4f}], p={p_value:.6f}, {sig})"

Common BixBench Patterns

Pattern 1: Odds Ratio from Ordinal Regression

Question: "What is the odds ratio of disease severity associated with exposure?"

Solution:

Identify ordinal outcome (mild/moderate/severe)
Fit ordinal logistic regression (proportional odds model)
Extract OR = exp(coefficient for exposure)
Report with CI and p-value

Pattern 2: Percentage Reduction in Odds

Question: "What is the percentage reduction in OR after adjusting for confounders?"

Solution:

# Unadjusted model
model_crude = smf.logit('outcome ~ exposure', data=df).fit(disp=0)
or_crude = np.exp(model_crude.params['exposure'])

# Adjusted model
model_adj = smf.logit('outcome ~ exposure + age + sex', data=df).fit(disp=0)
or_adj = np.exp(model_adj.params['exposure'])

# Percentage reduction
pct_reduction = (or_crude - or_adj) / or_crude * 100
print(f"Percentage reduction: {pct_reduction:.1f}%")

Pattern 3: Interaction Effects

Question: "What is the odds ratio for the interaction between A and B?"

Solution:

# Fit model with interaction
model = smf.logit('outcome ~ A * B + age', data=df).fit(disp=0)

# Interaction OR
interaction_coef = model.params['A:B']
interaction_or = np.exp(interaction_coef)
print(f"Interaction OR: {interaction_or:.4f}")

Pattern 4: Survival Analysis

Question: "What is the hazard ratio for treatment?"

Solution:

Load survival data (time, event, covariates)
Fit Cox proportional hazards model
Extract HR = exp(coefficient)
Report with CI and concordance index

Pattern 5: Multi-feature ANOVA (Gene Expression)

Question: "What is the F-statistic comparing miRNA expression across cell types?"

Solution:

Identify that data has multiple features (genes/miRNAs)
Use per-feature ANOVA (NOT aggregate)
Calculate F-statistic for EACH feature separately
If question asks for "the F-statistic" (singular):
- Check if specific features match expected range
- Report those feature(s) F-statistics
If question asks for summary: report median/mean/distribution

Critical: For gene expression data, default to per-feature ANOVA. Aggregate ANOVA gives F-statistics ~200× larger and is rarely correct.

See references/bixbench_patterns.md for 15+ question patterns.

Statsmodels vs Scikit-learn

Use Case	Library	Reason
Inference (p-values, CIs, ORs)	statsmodels	Full statistical output
Prediction (accuracy, AUC)	scikit-learn	Better prediction tools
Mixed-effects models	statsmodels	Only option
Regularization (LASSO, Ridge)	scikit-learn	Better optimization
Survival analysis	lifelines	Specialized library

General rule: Use statsmodels for BixBench questions (they ask for p-values, ORs, HRs).

Python Package Requirements

statsmodels>=0.14.0
scikit-learn>=1.3.0
lifelines>=0.27.0
pandas>=2.0.0
numpy>=1.24.0
scipy>=1.10.0

File Structure

tooluniverse-statistical-modeling/
├── SKILL.md                          # This file
├── QUICK_START.md                    # 8 quick examples
├── EXAMPLES.md                       # Legacy examples (kept for reference)
├── TOOLS_REFERENCE.md                # ToolUniverse tool catalog
├── test_skill.py                     # Comprehensive test suite
├── references/
│   ├── logistic_regression.md        # Detailed logistic examples
│   ├── ordinal_logistic.md           # Ordinal logit guide
│   ├── cox_regression.md             # Survival analysis guide
│   ├── linear_models.md              # OLS and mixed-effects
│   ├── bixbench_patterns.md          # 15+ question patterns
│   └── troubleshooting.md            # Diagnostic issues
└── scripts/
    ├── format_statistical_output.py  # Format results for reporting
    └── model_diagnostics.py          # Automated diagnostics

Key Principles

Data-first approach - Always inspect and validate data before modeling
Model selection by outcome type - Use decision tree above
Assumption checking - Verify model assumptions (linearity, proportional hazards, etc.)
Complete reporting - Always report effect sizes, CIs, p-values, and model fit statistics
Confounder awareness - Adjust for confounders when specified or clinically relevant
Reproducible analysis - All code must be deterministic and reproducible
Robust error handling - Graceful handling of convergence failures, separation, collinearity
Round correctly - Match the precision requested (typically 2-4 decimal places)

Completeness Checklist

Before finalizing any statistical analysis:

References

statsmodels: https://www.statsmodels.org/
lifelines: https://lifelines.readthedocs.io/
scikit-learn: https://scikit-learn.org/
Ordinal models: statsmodels.miscmodels.ordinal_model.OrderedModel

ToolUniverse Integration

While this skill is primarily computational, ToolUniverse tools can provide data:

Use Case	Tools
Clinical trial data	`clinical_trials_search`
Drug safety outcomes	`FAERS_calculate_disproportionality`
Gene-disease associations	`OpenTargets_target_disease_evidence`
Biomarker data	`fda_pharmacogenomic_biomarkers`

See TOOLS_REFERENCE.md for complete tool catalog.

Support

For detailed examples and troubleshooting:

Logistic regression: references/logistic_regression.md
Ordinal models: references/ordinal_logistic.md
Survival analysis: references/cox_regression.md
Linear/mixed models: references/linear_models.md
BixBench patterns: references/bixbench_patterns.md
Diagnostics: references/troubleshooting.md

When it activates

Automatically, when a task matches. Use when asked to fit regression

About this skill

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FreedomIntelligence / OpenClaw-Medical-Skills

skills/tooluniverse-statistical-modeling/SKILL.md

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Imported 8/1/2026Version v1Bundled 8 files · scripts

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Use this skill

Statistical Modeling for Biomedical Data Analysis

Features

Quick Start

Binary Logistic Regression

Cox Proportional Hazards

Model Selection Decision Tree

When to Use

Workflow

Phase 0: Data Validation

Phase 1: Model Fitting

Linear Regression

Logistic Regression

Ordinal Logistic Regression

Cox Proportional Hazards

Statistical Tests (t-test, ANOVA, Chi-square)

Phase 2: Model Diagnostics

OLS Diagnostics

Proportional Hazards Test

Phase 3: Interpretation

Odds Ratio Interpretation

Common BixBench Patterns

Pattern 1: Odds Ratio from Ordinal Regression

Pattern 2: Percentage Reduction in Odds

Pattern 3: Interaction Effects

Pattern 4: Survival Analysis

Pattern 5: Multi-feature ANOVA (Gene Expression)

Statsmodels vs Scikit-learn

Python Package Requirements

File Structure

Key Principles

Completeness Checklist

References

ToolUniverse Integration

Support

When it activates

SkillSafety

Source

Related skills

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