Woche 3

Autor:in

Benedikt Schnur

Code

import math
from typing import Tuple
from collections import namedtuple
import plotly.graph_objects as go
import plotly.io as pio


BENE_COLORS_DARK: Tuple[str, ...] = (
    "#47476b",
    "#6B5706",
    "#206260",
    "#93003a",
    "#215F80",
    "#973C2B",
    "#008381",
    "#6d3d3d",
    "#595865",
)
pio.templates["bene"] = go.layout.Template(layout=go.Layout(colorway=BENE_COLORS_DARK))
pio.templates.default = "plotly_white+bene"

FourByFourTable = namedtuple("FourByFourTable", ["a", "b", "c", "d"])

def berechne_RR (four_x_four: FourByFourTable) -> float:
    return (four_x_four.a / (four_x_four.a + four_x_four.b)) / (four_x_four.c / (four_x_four.c + four_x_four.d))

def berechne_SE_ln_RR (four_x_four: FourByFourTable) -> float:
    return math.sqrt((four_x_four.b/(four_x_four.a*(four_x_four.a+four_x_four.b)))+(four_x_four.d/(four_x_four.c*(four_x_four.c+four_x_four.d))))

def berechne_95_CI (four_x_four: FourByFourTable) -> Tuple[float, float]:
    RR = berechne_RR(four_x_four)
    ln_RR = math.log(RR)
    SE_ln_RR = berechne_SE_ln_RR(four_x_four)
    z = 1.96  # 95% confidence interval
    lower_ln = ln_RR - z * SE_ln_RR
    upper_ln = ln_RR + z * SE_ln_RR
    lower_CI = math.exp(lower_ln)
    upper_CI = math.exp(upper_ln)
    return lower_CI, upper_CI

Aufgabe 2

Code

four_x_four = FourByFourTable(12, 288, 20, 180)

1. b

\(\widehat{SE}\):

Code

f"{berechne_SE_ln_RR(four_x_four):.2f}"

'0.35'

Code

"{:.2f}, {:.2f}".format(*berechne_95_CI(four_x_four))

'0.20, 0.80'

Code

RR = berechne_RR(four_x_four)
CI = berechne_95_CI(four_x_four)

four_x_four_half = FourByFourTable(6, 144, 10, 90)
RR_half = berechne_RR(four_x_four_half)
CI_half = berechne_95_CI(four_x_four_half)

four_x_four_10 = FourByFourTable(120, 2880, 200, 1800)
RR_10 = berechne_RR(four_x_four_10)
CI_10 = berechne_95_CI(four_x_four_10)

fig = go.Figure()
y_axis = ["n=2500", "n=500", "n=250"]
fig.add_trace(
    go.Scatter(
        x=[RR_10, RR, RR_half],
        y=y_axis,
        mode="markers",
        marker=dict(size=10, symbol="square"),
        error_x=dict(
            type="data",
            symmetric=False,
            array=[CI_10[1] - RR_10, CI[1] - RR, CI_half[1] - RR_half],
            arrayminus=[RR_10 - CI_10[0], RR - CI[0], RR_half - CI_half[0]],
        ),
    )
)
fig.add_vline(x=1)
fig.add_vline(x=0.7, line_dash="dash")
fig.add_vline(x=1.5, line_dash="dash")

fig.update_layout(xaxis=dict(range=[0, 2]), height=150)

fig.show()

Aufgabe 4

a

Code

ln_RR = [3.5175, 0.7129, 1.5581, 1.1410, 1.6332]
SE_ln_RR = [1.4210, 1.2122, 0.5533, 0.3818, 0.3436]
# Berechnung der Gewichte w_i
weights = [1 / (se ** 2) for se in SE_ln_RR]

# Berechnung von Summe(w_i * ln(RR)) und Summe(w_i)
sum_w_lnRR = sum(w * lnrr for w, lnrr in zip(weights, ln_RR))
sum_w = sum(weights)
# Berechnung des gepoolten ln(RR)
ln_RR_pool = sum_w_lnRR / sum_w
RR_pool = math.exp(ln_RR_pool)

f"{RR_pool:.2f}"

'4.33'

b

Code

f"{weights[4]:.2f}"

'8.47'

Aufgabe 5

a

Code

four_x_four = FourByFourTable(
    round(295 * 0.197),
    round(295 - (295 * 0.197)),
    round(143 * 0.194),
    round(143 - (143 * 0.194)),
)
four_x_four

FourByFourTable(a=58, b=237, c=28, d=115)

b

Code

RR = berechne_RR(four_x_four)

f"{RR:.2f}"

'1.00'

c

Code

CI = berechne_95_CI(four_x_four)

f"{CI[0]:.2f}, {CI[1]:.2f}"

'0.67, 1.50'