Medical Statistics: Scripted

Contingency Table

A contingency table is a matrix formatted view of the frequency distribution of given variables.

2x2 Contingency Table

"""
Example Contingency Table:
---------------------------------
Outcome      Treatment Groups
_________________________________
            Test        Control
Positive     a             c
Negative     b             d
Total       a+b           c+d
---------------------------------
Key:
a = t_pos
b = t_neg
c = c_pos
d = c_neg
"""

Libraries

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

Proportion of positive outcomes under test condition

Used for treatment comparison to control

def p_test_subs(t_pos, t_neg):
    """
    Calculate proportion of positive outcomes under test condition
    :param t_pos: Positive results in Test group 
    :param t_neg: Negative results in Test group
    :return p_test: Proportion of subjects w/ positive outcome under treatment/test condition 
    """
    total = t_pos+t_neg
    p_test = t_pos/total
    return p_test

Proportion of positive outcomes under control condition

Used for treatment comparison to control

def p_control_subs(c_pos, c_neg):
    """
    Calculate proportion of positive outcomes under control condition
    :param c_pos: Positive results in Control group 
    :param c_neg: Negative results in Control group
    :return p_control: Proportion of subjects w/ positive outcome under control condition
    """
    total = c_pos+c_neg
    p_control = c_pos/total
    return p_control

Basic difference of proportions of positive results in test, control groups

def diff_proportions(p_test, p_control):
    """
    Calculate difference of proportions of positive results in test, control groups
    :param p_test: Proportion of positive outcome under test
    :param p_control: Proportion of positive outcome under control
    :return dop: Difference of proportions of p_test and p_control
    """
    dop = p_control - p_test
    return dop

Absolute risk difference of positive results in test, control groups

Used for clinical trials

def diff_proportions(p_test, p_control):
    """
    Calculate Absolute risk difference (ARD) of positive results in test, control groups
    :param p_test: Proportion of positive outcome under test
    :param p_control: Proportion of positive outcome under control
    :return ard: Absolute risk difference 
    """
    ard = np.abs(p_control - p_test)
    return ard

Relative Risk

Used for prospective studies

def relative_risk(p_test, p_control):
    """
    Calculates relative risk
    :param p_test: Proportion of positive outcome under test
    :param p_control: Proportion of positive outcome under control
    :return rr: Relative Risk(RR)  
    """
    rr = p_test/p_control
    return rr

Number needed to treat/harm (NNT)

Inverse of RR

def NNT(p_test, p_control):
    """
    Calculate Number needed to treat (NNT) of positive results in test, control groups
    :param p_test: Proportion of positive outcome under test
    :param p_control: Proportion of positive outcome under control
    :return nnt: number needed to treat
    """
    nnt = 1 / np.abs(p_test - p_control)
    return nnt

Odds Ratio (OR)

Ratio of occurences/non-occurence between test/control groups

def OddsRatio(p_test, p_control):
    """
    Calculates odds ratio
    :param p_test: Proportion of positive outcome under test
    :param p_control: Proportion of positive outcome under control
    :return odds_ratio: Ratio of odds of occurence/non-occurence for test and control groups 
    """
    test_group = p_test/(1-p_test)
    control_group = p_control/(1-p_control)
    odds_ratio = test_group/control_group
    return odds_ratio