correlation and regression - etusivu | …...correlation and regression vanja radišić biljak...

CORRELATION AND REGRESSION

Vanja Radišić Biljak

Department of medical laboratory diagnostics, University Hospital „Sveti Duh”, Zagreb, Croatia

MedCalc

Example 1

Is there an association between White Blood Cell (WBC) count and

concentration of C-reactive protein (CRP) in a group of University Hospital

„Sveti Duh” Emergency Department patients with a suspicion of acute

appendicitis?

What is the question about the data?

Are these groups

different?

Are these groups

associated?

Can I predict one variable

by knowing the other?

Tests for

statistical

differences

Correlation Regression

Correlation

• Statistical procedure applied to investigate association between two

variables

• Numerically expressed as coefficient of correlation (r)

• Level of significance (P)

Positive correlation

• Increase of x → Increase of y

• Decrease of x → Decrease of y

0 < r ≤ 1

x

y

Negative correlation

-1 ≤ r < 0

Increase of x → Decrease of y

Decrease of x → Increase of y

y

x

No correlation

• Increase of x → ? of y

• Decrease of x → ? of y

y

x

Association but no correlation

• Correlation can be calculated only if there is LINEAR association

y y

x x

Types of correlation

• Pearson (rp) and Spearman correlation (rs)

1. Sample size < 30 Spearman correlation

2. Type of data At least one ordinal

data Spearman correlation

3. Normality

Both variables do not

follow normal

distribution

Spearman correlation

Pearson correlation

Example 1




appendicitis?

Example 1





3. Normality


follow normal

distribution


Pearson correlation

Example 1




appendicitis?

Example 1


1. Sample size = 120 < 30 Spearman correlation



3. Normality


follow normal

distribution


Pearson correlation

Example 1




appendicitis?

Example 1




appendicitis?

Quantitative (numerical) data

Example 1



2. Numerical data At least one ordinal


3. Normality


follow normal

distribution


Pearson correlation

Example 1





3. Reject normality


follow normal

distribution


Pearson correlation

Example 1





3. Reject normality

Both variables do

not follow normal

distribution


Pearson correlation

Example 1





3. Reject normality


follow normal

distribution


Pearson correlation

MedCalc

Coefficient of correlation (r)

Coefficient of correlation (r) Interpretation

0-0.24 No association

0.25-0.49 Poor association

0.50-0.74 Moderate to good association

0.75-1.00 Very good to excellent

association

r can be interpreted only if P < level of significance (0.05)

There is statistically significant positive poor

association between WBC and CRP in a group of

University Hospital „Sveti Duh” Emergency Department

patients with a suspicion of acute appendicitis.

Coefficient of determination (D)

• D = r2

• Indicates how well data fit a statistical model

• r = 0.85; D = 0.7225

• 72% of data are associated

• r = 0.25; D = 0.0625

• 6.25% of data are associated

There is statistically significant positive poor

association between WBC and CRP in a group of



r2=0,2162

22% of data are associated

Example 2

Is there an association between White Blood Cell (WBC) count and Mean

Platelet Volume (MPV) in a group of University Hospital „Sveti Duh”

Emergency Department patients with a suspicion of acute appendicitis?

Example 2





3. Normality


follow normal

distribution


Pearson correlation

Example 2

Is there an association between White Blood Cell (WBC) count and Mean

Platelet Volume (MPV) in a group of University Hospital „Sveti Duh”

Emergency Department patients with a suspicion of acute appendicitis?


Example 2





3. Normality


follow normal

distribution


Pearson correlation

Example 2





3. Accept normality


follow normal

distribution


Pearson correlation

MedCalc







association


We cannot interpret association between WBC and

MPV in a group of University Hospital „Sveti Duh”

Emergency Department patients with a suspicion of

acute appendicitis, as the P value is not significant.

Example 3

Is there an association between platelet (PLT) count and Mean Platelet

Volume (MPV) in a group of University Hospital „Sveti Duh” Emergency

Department patients with a suspicion of acute appendicitis?

Example 3





3. Normality


follow normal

distribution


Pearson correlation

Example 3





3. Accept normality


follow normal

distribution


Pearson correlation







association


There is statistically significant negative poor

association between Plt and MPV in a group of



There is statistically significant negative poor

association between Plt and MPV in a group of



r2=0,248

25% of data are associated

Example 4

Can we predict MPV values if we know Plt count in a group of University

Hospital „Sveti Duh” Emergency Department patients with a suspicion of acute

appendicitis?

What is the question about the data?

Are these groups

different?

Are these groups

associated?

Can I predict one variable

by knowing the other?

Tests for

statistical

differences

Correlation Regression

Regression

• Dependent variable is numeric

• Calculating value of dependent

variable

• Dependent variable is categorical

(binomial)

• Calculating the odds of an event

• Presence/Existence of disease

• Cut-off value

Linear Logistic

Example 4

Can we predict MPV if we know PLT count in a group of University Hospital


appendicitis?


Example 4



variable


(binomial)



• Cut-off value

Linear Logistic

Linear regression

• Linear regression can be calculated ONLY if there is correlation between

variables

• Independent variable (x)

• Dependent variable (y)

• Dependent variable (y) is calculated from the independent variable (x) using

mathematical operation

Linear regression equation

Equation

y = a + bx

Intercept = a

1

1

Slope = b

x

y

Independent

variable

Dependent

variable

www.mathisfun.com

MedCalc

Example 4

Confidence limits

95% confidence

interval for slope and

intercept

y = a + bx

Example 4

Example 4

only 25% of data follow calulated equation

Residuals

• Difference between

measured and calculated

value

• If equation describes the

data well, residuals are

low

x

Y – f(x)

0

> 0

< 0

Example 4

Equation doesn’t describe the data well,

coefficient of determination is low, residuals are high.

Example 5

• Can we predict CRP concentrations if we know WBC count and MPV

values in a group of University Hospital „Sveti Duh” Emergency Department

patients with a suspicion of acute appendicitis?

Example 5

• Can we predict CRP concentrations if we know WBC count and MPV

values in a group of University Hospital „Sveti Duh” Emergency Department

patients with a suspicion of acute appendicitis?

Multiple regression

Example 5

Example 5






association


Example 5

There is no association between MPV and CRP in a group of

University Hospital „Sveti Duh” Emergency Department patients

with a suspicion of acute appendicitis.

MedCalc

Example 5

Independent variables

Dependent

variable

Example 6

Example 5

We wanted to predict an OUTCOME

Example 6



variable


(binomial)



• Cut-off value

Linear Logistic

Logistic regression

• We can analyze more than two groups of data

• Dependent variable is categorical and binomial (Y)

• Independent variables can be both, numerical and categorical (x1, x2, x3...)

Example 6

Dependent variable: OUTCOME (APPENDICITIS YES/NO)

Independent variables:

CLINICAL

(categorical)

LABORATORY

(numerical)

LABORATORY

(categorical)

Appetite CRP

Urine test strip

Vomiting WBC

Diarrhea RBC

Dysuria RDW

Rebound tenderness PLT

Pain migration MPV

Stepwise analysis

• Analyze all variables separately to

identify which are significantly

associated with the outcome

• Include significantly associated

variables

• Include other variables for

adjustment

1. Univariate analysis 2. Multivariate analysis

MedCalc

Example 6

Logistic regression

The goal of logistic regression is:

to find the best fitting model

(yet biologically reasonable)

to describe the relationship between the

dependent variable and the set of independent

(predictor or explanatory) variables.

https://www.biochemia-medica.com

correlation and regression - etusivu | …...correlation and regression vanja radišić biljak...

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