**Basic BioStatistics concepts**

for Literature review

Juan M Maldonado, Pharm D, BCPS,BCCCP

Senior Clinical Research Scientist

Medical Division, Eli Lilly, P. R.

Clinical Assistant Professor -Ad-Honorem

School of Pharmacy-Trauma Hospital University of Puerto Rico

for Literature review

Juan M Maldonado, Pharm D, BCPS,BCCCP

Senior Clinical Research Scientist

Medical Division, Eli Lilly, P. R.

Clinical Assistant Professor -Ad-Honorem

School of Pharmacy-Trauma Hospital University of Puerto Rico

Measures of data spread and variability

Choosing a statistical Test

Discrete variables

: (Dichotomous/Categorical)

Nominal

: groups in an unordered manner

Ex. Sex (m/f); mortality (y/n); disease state (present/absent)

Ordinal

: ranked in a specific order but with no consistent level of magnitude of difference between

Ex. NYHA class I,II,III,IV ; Likert scale

Common error: use of means (SDs) with ordinal data

Continuous variables:

Interval

: ranked in a specific order with a consistent change in magnitude; zero is arbitrary.

Ex. Degrees Fahrenheit

Ratio scale

: like interval but with

absolute zero

Ex. Degrees Kelvin ; pulse, BP, time, distance

**Types of variables**

(NOC)

(NOC)

Bell Shape Curve

Descriptive statistics

Measures of Central Tendency

Mean

The sum of all values / total #values

Only for continuous and normally distributed data

Very sensitive to outliers

Most commonly use

Median

(50th percentile)

Midpoint of the values placed in order from highest to lowest.

Half above and below

Used with ordinal or continuos data

Insensitive to outliers

Mode

Most common value in a distribution

Used for nominal , ordinal, or continuous data

Data my be one mode, bimodal, trimodal, etc.

Describe meaningful distributions with a large range of values

Percentiles

Point in a distribution which a value is larger than some percentage of the other values

75th percentile: 75% of the values are smaller

Does not assume the population has a normal or any other distribution

IQR: percentile that describes the middle 50% , encompasses the 25th -75th percentile

Standard deviation

Range

Difference between smallest and largest

Applied to parametric and non parametric

Easy to compute

Size of range is very sensitive to outliers

Often reported as the actual value rather than the difference between the two extreme values

Survival Analysis

Studies the time between entry in a study and some event (death, MI, etc.) Subjects do not

enter the study at the same time

Kaplan-Meier

Uses survival times to estimate the proportion of people who would survive a length of time

Log-rank test

Compare the survival distributions of 2 or more groups

Cox proportional hazards model

Evaluate the impact of covariates on survival in 2 or more groups Allows calculation of HR and CIs.

Absolute Risk (AR) Patients Treated with PL or Drug for 1 yr

Placebo Drug

Number of Patients with MI (A) 75 25

Total number of pts (B) 500 500

Absolute risk (A/B) 0.15 0.05

Absolute Risk Reduction (ARR): Patients Treated with PL or Drug for 1 yr

ARR : Drug vs placebo

ARR = AR (placebo) - AR (Drug)

= 0.15 - 0.05

= 0.10 or 10%

If you treat 100 subjects with Drug

for 1 yr (as opposed to placebo) you would

prevent 10 subjects from developing a new event

Number Needed to Treat (NNT)

10 subjects need to be treated with Drug for 1 year to prevent a new cardiac event

Number Needed to Treat (NNT)

= 1 / 0.10 =10

Absolute Risk (AR) of events in Patients Treated with PL or Drug for 1 yr

Placebo Drug

Number of patients with event (A) 75 25

Total number of patients (B) 500 500

Absolute risk (A/B) 0.15 0.05

Relative Risk

= AR in Drug /AR placebo

= 0.05 / 0.15

= 0.33

Relative Risk Reduction

= 1 - RR

= 1 - 0.33

= 0.67 (RRR=67%)

95% Confidence Intervals for RR of

Drug vs Placebo

0.25 0.33 0.45

67% improvement

RR = 0.33

95% CI (0.25-0.45)

Confidence Interval Display for Relative Risk: Statistically Significant if CI Does Not Include 1

Confidence Interval Display for Absolute Risk Reduction: Statistically Significant if CI Does Not Include 0

Placebo

superior

Comparison of patients Treated with Placebo (N=544) and Drug (N=541)*

Odds Ratio: Placebo vs

Drug

Odds in Placebo

30 514

30/514 = 0.058

Not significant

significant

significant

Not significant

0.0 0.5 1.0 1.5 2.0 2.5

Treatment

superior

Placebo

superior

-10.0% - 5.0 % 0.0 5.0% 10.0%

Treatment

superior

Not significant

Significant

Significant

Not Significant

Odds in drug

14 527

14/527 = 0.027

Odds Ratio = Odds in placebo/

Odds in drug

= 0.058/

0.027

= 2.2

Parametric tests

Data near normal distributed

Continuous

Data have variances that are near equal

Paired test

: compares the mean difference of paired or matched samples. This is a related samples test.

Ex. Group 1

Measure 1 vs. measure 2

Common error: use multiple t-test to compare more than two groups

ANOVA

One way ( single factor) ANOVA

Compares the mean of 3 >/ groups

Independent samples test

Ex. Young--group 1--group 2--group 3

Two way (two factor) ANOVA

Additional factor added

Ex. Young--group 1--group 2--group 3

Elderly--group 1--group 2--group 3

Repeated measures ANOVA

Related samples test, extension of paired t- test

Ex. Related measurements

Young--measurement 1--- measurement 2-- measurement 3

(group 1)

Non Parametric tests

Tests for independent samples

Wilcoxon rank sum and Mann-Whitney U-test

Compares 2 independent samples ( independent samples t-test)

Kruskal-Wallis one way ANOVA

Compares 3 or more independent groups ( one way ANOVA)

Post hoc test

Test for related or paired samples

Sign test and Wilcoxon signed rank test

Compares 2 matched or paired samples ( paired t- test) Friedman ANOVA by ranks

Compares 3 or more groups matched or paired groups

{Nominal data}

Chi-square test

: compares expected and observed proportions between 2 or more groups

Test of independence

Test of goodness of fit

Fisher exact test

: use of chi- square test for small groups ( cells) containing less than 5 observations

McNemar

: paired samples

Mantel-Haenszel

: controls for the influence of confounders

One sample Student's t- test

Compares the mean of the study sample with population mean

Ex. Group 1 vs. known population mean

Two samples, independent samples, or unpaired test

Compares the means of two independent samples

Ex. Group 1 vs. group 2

Equal variance test. Rule of thumb: ratio larger to smaller variance is greater than 2.

Formal test : F test

Adjustments can be made for cases of unequal variance

Unequal variance test

Correction employed to account for variances

Parametric tests

Data are not normally distributed

Data do not meet other criteria (discrete data) Test for ordinal or continuous data

Non-Parametric Tests

Measures the variability about the mean

Applied to continuous data that are normally distributed

68 % within 1 SD, 95% within 2 SD; and 99% within 3SD Coefficient of variation (CV) relates the mean to the SD: (SD/mean x 100%) Variance =[SD]2

Standard error of the mean SEM

Quantify the uncertainty in the estimate of the mean, NOT the variability in the sample.

Application: 95% CI is approx. mean +- 2 x SEM

Parametric Tests

1. Clinical Pharmacis's Guide to Biostatistics and Literature Evaluation. Di Cenzo,R. 2014

2. Pharmacotherapy 2010; 30: 1117-1126.

3. JAMA 2007;298:1010-1022.

4. Pharmacist's Letter / Prescriber's letter, June 2005. Volume 21:Number 210610

5. NEJM.2007;357:2001-15

6. Statistical Concepts in Clinical Trials. 2002. Sides, G.D.,DMitrienko,A.A.

1. Clinical Pharmacis's Guide to Biostatistics and Literature Evaluation. Di Cenzo,R. 2014

2. Pharmacotherapy 2010; 30: 1117-1126.

3. JAMA 2007;298:1010-1022.

4. Pharmacist's Letter / Prescriber's letter, June 2005. Volume 21:Number 210610

5. NEJM.2007;357:2001-15

6. Statistical Concepts in Clinical Trials. 2002. Sides, G.D.,DMitrienko,A.A.

**References**

**Try to help to understand how to interpret the basic biostatistic concepts in the medical literature**

**Objectives**

Aspirin efficacy and safety

Odds ratio= Odds in drug/odds in placebo

= 0.027/0.058 = 0.46

Comparison of patients treated with placebo (N=544) and drug (N=541) Odds ratio: Drug vs Placebo

Ex. 40 +65+68+71+73

= 63.4 yrs

Ex. 40+65+68+71+73

= 68

Ex. (4,6,3,6,9,7) = 9-3 = 6

Ex. 25 tests scores , put in order (small to high), then if you want to know the 90th percentile, multiply: (0.9 x 25) = 22.5 round to the nearest (23) of the 25 values

Definition:

P value

is associated with a test statistic. It is "the probability, if the test statistic really were distributed as it would be under the null hypothesis.

A

p-value of .05

or less rejects the null hypothesis "at the 5% level" that is, the statistical assumptions used imply that only 5% of the time would the supposed statistical process produce a finding this extreme if the null hypothesis were true.

http://economics.about.com/od/termsbeginningwithp/g/pvaluedef.htm

Finally out ....of the jungle !!!

No questions ???, please...

**Correlation**

Ex. 40+65+65+68+71+73

= 65

Simple Regression

**Pearson or Spearman Rank (r)**

Examines the strength of the association between two variables

Ability of one variable to predict another variable

**Relative risk vs Odd ratio**

Continuous Data

Continuous Data

Ordinal Data

Statistics:

science that use the math to fascilitate decision making in situations where uncertainty is present

Biostatistics:

application of statistics to a wide range of topics in biology.(6)

Statistics:

science that use the math to fascilitate decision making in situations where uncertainty is present

Biostatistics:

application of statistics to a wide range of topics in biology.(6)

**Definitions:**