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Statistics

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Juan Maldonado

on 19 February 2016

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Transcript of Statistics

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


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)

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.

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)

Definitions:
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