after work statistics - biometrie.charite.de · u n i v e r s i t Ä t s m e d i z i n b e r l i n...

U N I V E R S I T Ä T S M E D I Z I N B E R L I N

After Work Statistics

Maja Krajewska

Institute of Biometry and

Clinical Epidemiology

[email protected]

Institute of Biometry and Clinical EpidemiologyWe are…

• … open and helpful!

• … active in the statistical methodologic research and in

medical research

• …active in teaching in many ways

Our Service Unit Biometry

• Free biometrical consulting for all medical research

projects, registration online

• “Statistik-Ambulanz” (Walk-in service): Consultation

without prior registration every Tuesday from 9am to 12pm

• Training in biometrical topics and statistical software

• Responsibility for project biometry within cooperation

For further information visit us online:

https://biometrie.charite.de/

Contact: Univ.-Prof. Dr. Geraldine Rauch (Head of Institute),

Institut für Biometrie und Klinische Epidemiologie (iBikE)

Standort Mitte (Charité Campus Mitte)

Reinhardstraße 58, 10117 Berlin

Standort Mitte (Charité Campus Klinik)

Rahel-Hirsch-Weg 5, 10117 Berlin

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https://biometrie.charite.de/

Slots

& Topics

Slot Topic

1 So many tests! The agony of choice.

2 So many questions! Multiple testing.

3 So many patients? Sample size calculation.

4 What is it this odds ratio? Logistic regression.

5 Missing information? Dealing with missing data.

6 The right time? Survival analysis.

7 The variety of influences - Mixed models.

8 Who fits together? Patient matching.

1 So viele Tests! Die Qual der Wahl.

2 So viele Fragestellungen! Multiples Testen.

3 So viele Patienten? Fallzahlplanung.

4 Was ist dieses Odds Ratio? Logistische Regression.

5 Fehlende Information? Umgang mit fehlenden Daten.

6 Der richtige Zeitpunkt? Analyse von Ereigniszeiten.

7 Die Vielfalt der Einflüsse – Gemischte Modelle.

8 Wer passt zusammen? Matching von Patienten.

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U N I V E R S I T Ä T S M E D I Z I N B E R L I N

Who fits together?

Patient matching.

Maja Krajewska

Institute of Biometry and

Clinical Epidemiology

[email protected]

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Matching: Online Dating

• Goal: find a partner

• Question: who fits together?

?

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Example: Clinical trial

• Two groups (treatment vs. placebo)

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Treatment Pain relief

Connection?

6



7

Confounder

Connection?

Smoking

Treatment Pain relief

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Confounder

The outcome of a trial might be biased, if one does not

adjust for potential confounders and structural inequalities

between groups.

!

Key-Message 1:

Confounders can bias the outcome of a trial.

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• Soluation: stratification („structural equality“)

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Case control studies

Case control studies:

• Observational studies

• General concept:

– Recruitment of diseased patients

– Retrospective collection of risk factors

– Comparison with control group

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Diseased Not

diseased

Exposed Not exposed Exposed Not exposed

Tim

e

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Diseased Not

diseased

Example: Lung cancer and smoking

How to identify

appropriate

control group?

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Case control studies: choice of control groups

• It is not possible to randomize in case control studies

• Other methods are necessary, in order to obtain

structural equality in study groups

!

Key-Message 2:

Matching of patients is used in observational

studies (especially case control studies) in

order to obtain structural equality.

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• But:

!

Key-Message 3:

By the use of matching in a observational study

one does not accomplish the same quality as

of a randomized trial!

https://guides.library.vcu.edu/humphrey/journal-club

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• Information about gender, age,

interests…

?

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• Information about gender, age,

interests…

WANTED

Gender: M

Age: 25 – 40

Interests:

• Football

• Literature

• HipHop

• Statistics

X

XX

X

X

X

X

X

X

X

X

X

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• Exact matching: find person, that matches description perfectly

• → not always possible

• → find person, that is closest to description

Male Age 25 - 40 Football Literature HipHop Statistics

Yes Yes Yes No Yes No

No Yes Yes No Yes No

No No No Yes No Yes

No Yes No Yes Yes No

Yes No No Yes Yes No

Yes Yes Yes No Yes Yes

WANTED

Gender: M

Age: 25 – 40

Interests:

• Football

• Literature

• HipHop

• Statistics

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How to quantify?

Dependent variable:

• Compatibility (yes/no)

→ possible to write as logistic regression model

𝐶𝑜𝑚𝑝𝑎𝑡𝑖𝑏𝑖𝑙𝑖𝑡𝑦 ~ 𝑔𝑒𝑛𝑑𝑒𝑟 + 𝑎𝑔𝑒 + 𝑓𝑜𝑜𝑡𝑏𝑎𝑙𝑙 + 𝑙𝑖𝑡𝑒𝑟𝑎𝑡𝑢𝑟𝑒 + ℎ𝑖𝑝ℎ𝑜𝑝 + 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑠

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Recap: logistic regression

Odds for a specific value X = 𝑥 :

log𝑝

1 − 𝑝= log 𝑂𝑑𝑑𝑠 = 𝛼 + 𝛽 ∙ 𝑥

Odds = 𝑒𝛼+ 𝛽∙𝑥 = 𝑒𝛼 ∙ 𝑒 𝛽∙𝑥

p =𝑒𝛼+ 𝛽∙𝑥

1 + 𝑒𝛼+ 𝛽∙𝑥

Whats happens when we increace 𝑥 by 1?

Odds𝑥+1 = 𝑒𝛼+ 𝛽∙(𝑥+1) = 𝑒𝛼 ∙ 𝑒 𝛽∙𝑥+𝛽= 𝑒𝛼 ∙ 𝑒 𝛽∙𝑥∙ 𝑒 𝛽

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• Calculation of probability, that the person looking for a is compatible with

a candidate from the dating data bank and vice versa

80% & 94%

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Individual matching

• Exact matching

• As similar as possible

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• Propensity score matching

• General concept: logistic regression with „exposed

yes/no“ as the dependent variable

Individual matching

0.57

0.850.87 0.85

0.62

0.73

0.540.63

0.71

0.52

0.98

0.37

0.77

0.37

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Individuelles Matching

!

Key-Message 4:

When applying propensity score matching

patients and controls are matched based on

their probability of having been exposed to the

risk factor of interest!

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General concept: Matching

1. Calculation of “proximity” of patients and potential controlls

2. Application of a matching method

3. Examination fo the quality of the matched sample

4. Statistical analysis of the data using appropriate methods, that

account for matching

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Options:

• 1:1 matching

• 1:k matching

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Beware of over matching!

• Matching based on a variable that has no influence on outcome (just the

risk factor), unnecessary → does not provide infromation, increases

complexity

• Matching based on a variable on the causal pathway risk factor and

outcome → biases the effect of the risk factor

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!

Key-Message 5:

The number of controls per case and the

number of variables that are used for matching

must be chosen very carefully!

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Frequency matching

• Matching of groups

• General concept: Proportions of selected parameters

equal in both groups (e.g. 1/3 female)

Diseased Not

diseased

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Summary

• Matching is a method used to control for confounders in

observational studies

• Matching can not replace randomisation

• General concept: calculate similiarity („proximity“) of

patients and controls

• Individual matching or matching of groups möglich

• By using propensity score matching patients and controls

are matched based on their probability of having been

exposed to the risk factor

• Over matching can bias the analysis or cause unnecessary

effort, complexity and expenses

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Literature suggestion

• Kuss O, Blettner M, Börgermann J: Propensity

score: an alternative method of analyzing

treatment effects—part 23 of a series on

evaluation of scientific publications. Dtsch Arztebl

Int 2016; 113: 597–603.

DOI: 10.3238/arztebl.2016.0597

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after work statistics - biometrie.charite.de · u n i v e r s i t Ä t s m e d i z i n b e r l i n...

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