Normalizing measurements

Biomedical Image Analysis in Python

Stephen Bailey

Instructor

Analysis workflow

group-workflow

Biomedical Image Analysis in Python

OASIS population

df.shape

(400, 5)

df.sample(5)

                age sex  alzheimers  brain_vol    skull_vol
    ID                                                        
    OAS1_0272   75   F        True    851.451  1411.125695
    OAS1_0112   69   F       False    894.801  1434.146892
    OAS1_0213   48   F       False    925.859  1412.781004
    OAS1_0311   22   F       False    980.163  1363.413762
    OAS1_0201   85   F       False    904.104  1420.631447
Biomedical Image Analysis in Python

Hypothesis testing

men-women

Biomedical Image Analysis in Python

Hypothesis testing

Null hypothesis: two populations' mean brain volumes ($\mu_{m}, \mu_{w}$) are equal.

$$ H_{null}: \mu_{w} = \mu_{m} $$ $$ H_{alt}\ : \mu_{w} \ne \mu_{m} $$

$$ t = \frac{\bar X - \mu}{s / \sqrt{n}} $$

Implemented in scipy.stats.ttest_ind()

Biomedical Image Analysis in Python

Hypothesis testing

brain_m = df.loc[df.sex == 'M', 'brain_vol']

brain_f = df.loc[df.sex == 'F', 'brain_vol']

from scipy.stats import ttest_ind
results = ttest_ind(brain_m, brain_f)

results.statistic
results.pvalue

10.20986
5.03913e-22

A large $t$-statistic and low $p$-value suggests that there is a significant difference!

Biomedical Image Analysis in Python

Correlated measurements

df[['brain_vol', 'skull_vol']].corr()

                'brain_vol' 'skull_vol'
    'brain_vol'      1.000       0.736
    'skull_vol'      0.736       1.000

brain-skull-scatterplot

Biomedical Image Analysis in Python

Normalization

df['brain_norm'] = df.brain_vol / df.skull_vol

brain_norm_m = df.loc[df.sex == 'M', 'brain_norm']
brain_norm_f = df.loc[df.sex == 'F', 'brain_norm']
results = ttest_ind(brain_norm_m, brain_norm_f)

results.statistic
results.pvalue

-0.94011
0.34769

Size, not gender likely drove original results.

Biomedical Image Analysis in Python

Many potential confounds in imaging

Image acquisition

  • Contrast
  • Resolution
  • Field of view

Subject / object

  • Age
  • Gender
  • Pathology

Context

  • Hospital
  • Radiologist
  • Equipment

Data Quality

  • Format
  • Artifacts
Biomedical Image Analysis in Python

Congratulations!

Image Workflow

Biomedical Image Analysis in Python

Good luck!

Biomedical Image Analysis in Python

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