Chapter 14. Biostats

What is the formula for risk?

% unfavorable / % favorable

What is the formula for RR?

%treatment / %placebo

What is the formula for RRR?

(% control - %treatment) / (%control)

What is the formula for ARR?

%control - %treatment

What is the formula for NNT/NNH?

1 / ARR

NNT = round up

NNH = round down

What are the 2 types of data?

Continuous

Discrete (categorical)

What is continuous data?

Data is provided by some type of measurement which has unlimited options of continuous values

HR of 120 BPM is twice as fast as a HR of 60 BPM

What is ratio data?

Equal difference between values with a true, meaningful zero

(0 = NONE)

What is interval data?

Equal difference between values, but without a meaningful zero

(0 DOES NOT = NONE)

Age is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

a. Ratio data

Has a meaningful 0 (0 = not born yet)

Height is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

a. Ratio data

Also continuous and quantitative data

Weight is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

a. Ratio data

Time is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

a. Ratio data

00:00 = midnight

Blood pressure is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

a. Ratio data

BP of 0 = dead

Celsius and Fahrenheit are examples of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

b. Interval data

Does not have an meaningful 0

0 = still a measurement of temperature

What are the two subtypes of continuous data?

Interval data

Ratio data

Which subtype has no meaningful zero (zero does not equal none)?

Interval data

Which subtype has a meaningful zero (zero equals none)?

Ratio data

What are the two subtypes of discrete (categorical) data?

Nominal

Ordinal

What is Discrete (categorical) Data?

Data fits into a limited number of categories

What is Nominal Data?

Categories are in an arbitrary order

Order of categories does not matter

What is ordinal data?

Categories are ranked in a logical order, but the difference between categories is not equal

Order of categories matters

Gender is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

c. Nominal data

Limited # of categories (Male or female)

Ethnicity is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

c. Nominal data

Limited # of categories

Marital status is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

c. Nominal data

Limited # of categories

Mortality is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

c. Nominal data

Limited # of categories

NYHA Functional class score is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

d. Ordinal data

Limited # of categories and ranked

Pain score is an example of type of data?

a. Ratio data

b. Interval data

c. Nominal data

d. Ordinal data

d. Ordinal data

Limited # of categories and ranked

What is the definition of a p-value?

Probability of obtaining a value (NOT hypothesis) at least as extreme (away from the mean) as observed assuming null hypothesis is true

Which type of error is a true false positive?

Type I error

(Male that is told he is pregnant)

Which type of error is a true false negetive?

Type II error

(Telling a pregnant female they are not pregnant)

Which of the following describes a statistical significance between groups?

Rejecting the null

Which of the following describes no statistical significance between groups?

Failing to reject the null

Null hypothesis is also known as ...

Failing to reject the H0

Alternative hypothesis is also known as

Accepting the H0

This is what we want by testing the null hypothesis

"A study evaluated the effect of canagliflozin vs glipizide on reduction of ASCVD events"

Which is the dependent variable?

ASCVD events

Who sets the p-value?

The investigator

In terms of p-value, what is determined as statistical significant?

P-value < alpha

What does the p-value predict?

The probability that the result observed occurred by chance (type I error)

Remember: Chance of a type 1 error (false positive) is <5%

"A range of data from the sample that has a given probability of containing the "true" population value" is the definition of

Confidence interval

Which of the following are independent variables? (SATA)

a. Drugs

b. Drug doses

c. Placebos

d. Age

e. Gender

f. Comorbid conditions

g. HF progression

h. A1c

i. Blood pressure

j. cholesterol values

k. Mortality

a. Drugs

b. Drug doses

c. Placebos

d. Age

e. Gender

f. Comorbid conditions

Which of the following are dependent variables? (SATA)

a. Drugs

b. Drug doses

c. Placebos

d. Age

e. Gender

f. Comorbid conditions

g. HF progression

h. A1c

i. Blood pressure

j. cholesterol values

k. Mortality

g. HF progression

h. A1c

i. Blood pressure

j. cholesterol values

k. Mortality

What is known as a maximum permissible error margin?

Alpha

What is the most common alpha value set at?

5% (or 0.05)

2.5% on each side

What is the interpretation of an alpha value of 0.05?

95% probability (confidence) that the conclusion is correct; less than 5% it is not

95% CI for FEV1 is 18-58 mL. Is this statistically significant?

Yes, it does not include 0

Same applies to Relative risk, OR, HR

95% CI for FEV1 is -0.26-0.89 mL. Is this statistically significant?

No, it includes a 0

Same applies to Relative risk, OR, HR

What is the interpretation of the following sentence?

"

Which of the following is known as a false positive?

a. Type II error

b. Type I error

b. Type I error

Dr tells a man that he is pregnant. This is an example of what type of error?

a. Type I error

b. Type II error

a. Type I error

When a type I error is identified, what is the interpretation?

H0 is true and there is no difference between groups

H0 is rejected and alternative is accepted

Which of the following is known as a false negative?

a. Type II error

b. Type I error

a. Type II error

Dr tells a pregnant women that she is not pregnant. This is an example of what type of error?

a. Type I error

b. Type II error

b. Type II error

When a type II error is identified, what is the interpretation?

There is a significant difference in the groups

H0 fails to be rejected

Null is accepted

What is the formula for relative risk?

% Treatment / % Control

What is the formula for relative risk reduction?

1 - RR

Or

(% Control - % Treatment) / (% Control)

What is the formula for absolute risk reduction?

ARR = % Control - % Treatment

What is the formula for NNT/NNH?

1 / ARR

What is the interpretation of a NNH number of 47?

For every 47 patients treated with drug, the primary endpoint is PREVENTED in one patient

We want a low #

Which test is used when there are two groups and continuous data?

a. T-test

b. Chi-squared

c. Fisher's exact

d. ANOVA

a. T-test

Which test is used when there are two groups and categorical data?

a. T-test

b. Chi-squared

c. Fisher's exact

d. ANOVA

b. Chi-squared

Which test is used when there are two groups and categorical data with less than 5 subgroups?

a. T-test

b. Chi-squared

c. Fisher's exact

d. ANOVA

c. Fisher's exact

Which test is used when there are three groups and continuous data?

a. T-test

b. Chi-squared

c. Fisher's exact

d. ANOVA

d. ANOVA

"How well a test can CORRECTLY identify patients WITH the condition". This is the definition of which word?

a. Specificity

b. Sensitivity

b. Sensitivity

"How well a test can CORRECTLY identify patients WITHOUT the condition". This is the definition of which word?

a. Specificity

b. Sensitivity

a. Specificity

What does a high sensitivity tell us?

Increases likelihood of true positive and rule out false negatives (Type II error)

spIN (high specificity rules IN disease)

What does a low sensitivity tell us?

Increases likelihood of false negative (type II error)

What does a high specificity tell us?

True negative will most likely be true

snOUT (high specificity rules IN disease)

Which are types are the most reliable types of medical studies?

Systematic reviews & Meta analyses

Which type of study is usually a prospective study?

Cohort

But can be retrospective)

Which type of study starts with the exposure and looks forward to see if disease develops?

Cohort studies

Which type of study starts with the exposure and looks back to see how exposure develops?

Case-controlled studies

What is the formula for risk?

Risk = # in unfavorable event / total # subjects

What is the formula for relative risk?

RR = risk in treatment/risk in control

A placebo-controlled study was performed to evaluate whether metoprolol reduces disease progression in patients with HF. A total of 10,111 patients were enrolled and followed for 12 months. What is the relative risk of HF progression in the metoprolol-treated group vs the placebo group?

Metoprolol (n = 5,123)

HF progression = 823

Control (n=4,988)

HF progression = 1,397

RR = risk in treatment / risk in control

Risk = # in treatment / # total

Treatment

(823/5123)

Risk in treatment = 0.16

Control

(1397/4988)

Risk in control = 0.28

RR = 0.16/0.28

RR = 0.57 (57%)

A placebo-controlled study was performed to evaluate whether metoprolol reduces disease progression in patients with HF. A total of 10,111 patients were enrolled and followed for 12 months. What is the dependent variable?

Metoprolol (n = 5,123)

HF progression = 823

Control (n=4,988)

HF progression = 1,397

Heart failure

A placebo-controlled study was performed to evaluate whether metoprolol reduces disease progression in patients with HF. A total of 10,111 patients were enrolled and followed for 12 months. What is the independent variable?

Metoprolol (n = 5,123)

HF progression = 823

Control (n=4,988)

HF progression = 1,397

Metoprolol

A placebo-controlled study was performed to evaluate whether metoprolol reduces disease progression in patients with HF. A total of 10,111 patients were enrolled and followed for 12 months. What is the interpretation of the relative risk?

Metoprolol (n = 5,123)

HF progression = 823

Control (n=4,988)

HF progression = 1,397

Patients treated with metoprolol were 57% AS LIKELY to have progression of disease as placebo-treated patients

What does a RR of 0 indicate?

No difference in risk between the groups

What does a RR >1 indicate?

Greater risk of the outcome in the treatment group

What does a RR of <1 indicate?

Lower risk of the outcome in the treatment group

What does relative risk reduction determine?

How much risk is reduced in the treatment group vs control

What is the formula for relative risk reduction?

RRR = (% risk in control - % risk in treatment) / % risk in control

or

1 - RR

Using the risk previously calculated, metoprolol 16% and placebo 28%, calculate the RRR of HF progression

RRR = (% in control - % in treatment) / % control

RRR = (28% - 16%) / 28%

RRR = 43%

or

RRR = 1 - ARR

RRR = 1 - 57%

RRR = 43%

What is the interpretation of a RRR of 43%?

Patients were 43% LESS LIKELY to have the disease than placebo-treated patients

What is the formula for absolute risk reduction?

ARR = (% in treatment - % in control)

Using the previously calculated risks, calculate the ARR

Metoprolol risk

(823/5,123) = 0.16

Control risk

(1,397/4,988) = 0.28

ARR = (0.16 - 0.28)

ARR = 0.12 (12%)

What is the interpretation of an ARR of 12%?

Every 12 out of every 100 patients benefit from the treatment

or

For every 100 patients treated with metoprolol, 12 fewer patients will have HF progression

What is NNT?

# of patients who need to be treated for a certain period of time in order for one patient to benefit

What is the formula for number needed to treat?

NNT = 1 / (risk in control - risk in treatment)

or

1/ARR

The ARR in the metoprolol study was 12%. The duration of the study period was one year. Calculate the number of patients that need to be treated with metoprolol for one year in order to prevent one case of HF progression.

NNT = 1/ARR

NNT = 1/12

NNT = 8.3

Remember to round UP with NNT.

NNT = 9

What is the interpretation of NNT of 9?

For every 9 patients who receive metoprolol for one year, HF progression is prevented in one patient

What is number needed to harm?

# of patients who need to be treated for a certain amount of time in order for one patient to experience harm

A study evaluated the efficacy of clopidogrel vs placebo, both given in addition to aspirin, in reducing the risk of CV death, MI, and stroke. The study reported a 3.9% risk of major bleeding in the treatment group and a 2.8% risk of major bleeding in the control group. What is the ARR and what is the interpretation?

ARR = 3.9 - 2.8

ARR = 1.1

There is a 1.1% higher risk of major bleeding in the treatment group

A study evaluated the efficacy of clopidogrel vs placebo, both given in addition to aspirin, in reducing the risk of CV death, MI, and stroke. The study reported a 3.9% risk of major bleeding in the treatment group and a 2.8% risk of major bleeding in the control group. What is the NNH?

ARR = 3.9 - 2.8

ARR = 1.1

NNH = 1 / 1.1

NNH = 0.9 = 90

What is the interpretation of a NNH of 90?

One additional case of major bleeding is expected to occur for every 90 patients taking clopidogrel instead of placebo

What type of study is the odds ratio used to estimate the risk of unfavorable events associated with a treatment or intervention?

Case-controlled

What is the formula for OR?

Exposure--Outcome Present--Absent

Present--A----B

Absent--C----D

OR = AD / BC

A case-control study was conducted to assess the risk of falls with fracture (outcome) associated with serotonergic antidepressant (AD) use (exposure) among a cohort of Chinese females > 65 YO. Cases were matched with 33,000 controls (1:4 by age, sex, and cohort entry date). What is the OR?

4,991 | 18,270

3,259 | 14,730

OR = [ (4991 x 14730) / (18270 x 3259)]

OR = 73,517,430 / 59,541,930

OR = 1.23

What is the interpretation of an OR of 1.23?

Favorable outcome is associated with a 23% increased risk of falls with fracture