statistics in clinical research for residents

7/27/2019 Statistics in Clinical Research for Residents

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Statistical Methods

in Clinical Research


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Overview Data types

Summarizing data using descriptive statistics

Standard error

Confidence Intervals


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Overview P values

One vs two tailed tests

Alpha and Beta errors Sample size considerations and power

analysis

Statistics for comparing 2 or more groups

with continuous data Non-parametric tests


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Overview

Regression and Correlation

Risk Ratios and Odds Ratios

Survival Analysis

Cox Regression


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Types of Data Discrete Data-limited number of choices

Binary: two choices (yes/no) Dead or alive

Disease-free or not

Categorical: more than two choices, not ordered Race

Age group

Ordinal: more than two choices, ordered Stages of a cancer

Likert scale for response

E.G. strongly agree, agree, neither agree or disagree, etc.


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Types of data Continuous data

Theoretically infinite possible values (withinphysiologic limits) , including fractional values Height, age, weight

Can be interval Interval between measures has meaning.

Ratio of two interval data points has no meaning

Temperature in celsius, day of the year). Can be ratio

Ratio of the measures has meaning

Weight, height


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HistogramContinuous Data

No segmentation of data into groups


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Frequency Distribution

Segmentation of data into groups

Discrete or continuous data


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Box and Whiskers Plots


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Box and Whisker Plots

Popular in Epidemiologic Studies

Useful for presenting comparative data graphically


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Numeric Descriptive Statistics Measures of central tendency of data

Mean

Median

Mode

Measures of variability of data

Standard Deviation

Interquartile range


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Numeric Descriptive Statistics


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Sample Mean Most commonly used measure of central tendency

Best applied in normally distributed continuous data.

Not applicable in categorical data

Definition: Sum of all the values in a sample, divided by the number of

values.


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Sample Median Used to indicate the average in a skewed population

Often reported with the mean If the mean and the median are the same, sample is normally

distributed. It is the middle value from an ordered listing of the

values If an odd number of values, it is the middle value

If even number of values, it is the average of the two middle

values.

Mid-value in interquartile range


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Sample Mode Infrequently reported as a value in studies.

Is the most common value

More frequently used to describe the

distribution of data Uni-modal, bi-modal, etc.


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Interquartile range Is the range of data from the 25th percentile to

the 75th percentile

Common component of a box and whiskers

plot

It is the box, and the line across the box is the

median or middle value

Rarely, mean will also be displayed.


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Standard Error A fundamental goal of statistical analysis is to estimate

a parameter of a population based on a sample

The values of a specific variable from a sample are anestimate of the entire population of individuals whomight have been eligible for the study.

A measure of the precision of a sample in estimatingthe population parameter.


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Standard Error Standard error of the mean

Standard deviation / square root of (sample size)

(if sample greater than 60)

Standard error of the proportion Square root of (proportion X 1 - proportion) / n)

Important: dependent on sample size Larger the sample, the smaller the standard error.


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Clarification Standard Deviation measures the

variability or spread of the data in an

individual sample.

Standard error measures the precision

of the estimate of a populationparameter provided by the sample meanor proportion.


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Standard Error Significance:

Is the basis of confidence intervals

A 95% confidence interval is defined by Sample mean (or proportion) 1.96 X standard error

Since standard error is inversely related to the

sample size: The larger the study (sample size), the smaller the

confidence intervals and the greater the precision of theestimate.


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Confidence Intervals May be used to assess a single point

estimate such as mean or proportion.

Most commonly used in assessing the

estimate of the difference between two

groups.


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Commonly reported in studies to provide an estimate of the precision

of the mean.


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P Values The probability that any observation is due to chance

alone assuming that the null hypothesis is true

Typically, an estimate that has a p value of 0.05 or less is

considered to be statistically significant or unlikely to occurdue to chance alone.

The P value used is an arbitrary value

P value of 0.05 equals 1 in 20 chance

P value of 0.01 equals 1 in 100 chance

P value of 0.001 equals 1 in 1000 chance.


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P Values and Confidence Intervals P values provide less information than confidence

intervals. A P value provides only a probability that estimate is due to chance

A P value could be statistically significant but of limited clinicalsignificance.

A very large study might find that a difference of .1 on a VAS Scale of 0 to10 is statistically significant but it may be of no clinical significance

A large study might find many significant findings during multivariableanalyses.

a large study dooms you to statistical significance

Anonymous Statistician


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P Values and Confidence Intervals Confidence intervals provide a range of plausible values of the

population mean

For most tests, if the confidence interval includes 0, then it is notsignificant.

Ratios: if CI includes 1, then is not significant

The interval contains the true population value 95% of the time.

If a confidence interval range is very wide, then plausible value mightrange from very low to very high.

Example: A relative risk of 4 might have a confidence interval of 1.05 to9, suggesting that although the estimate is for a 400% increased risk, anincreased risk of 5% to 900% is plausible.


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Errors Type I error

Claiming a difference between two samples

when in fact there is none. Remember there is variability among samples-

they might seem to come from differentpopulations but they may not.

Also called the error. Typically 0.05 is used


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Errors Type II error

Claiming there is no difference between two

samples when in fact there is.Also called a error. The probability of not making a Type II error

is 1 - , which is called the power of the

test. Hidden error because cant be detected

without a proper power analysis


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Errors

Null Hypothesis

H0

Alternative

Hypothesis

H1

Null Hypothesis

H0 No Error Type I

AlternativeHypothesis

H1

Type II

No Error

Test Result

Truth


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Sample Size CalculationAlso called power analysis.

When designing a study, one needs to determine howlarge a study is needed.

Power is the ability of a study to avoid a Type II error. Sample size calculation yields the number of study

subjects needed, given a certain desired power todetect a difference and a certain level of P value that

will be considered significant. Many studies are completed without proper estimate of

appropriate study size.

This may lead to a negative study outcome in error.


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Sample Size Calculation Depends on:

Level of Type I error: 0.05 typical

Level of Type II error: 0.20 typical

One sided vs two sided: nearly always two

Inherent variability of population

Usually estimated from preliminary data

The difference that would be meaningful

between the two assessment arms.


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One-sided vs. Two-sided Most tests should be framed as a two-

sided test.

When comparing two samples, we usuallycannot be sure which is going to be bebetter. You never know which directions study results

will go. For routine medical research, use only two-

sided tests.


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Sample size for proportions

Stata input: Mean 1 = .2, mean 2 = .3, = .05, power (1-) =.8.


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Sample Size for Continuous Data

Stata input: Mean 1 = 20, mean 2 = 30, = .05, power (1-) =.8, std. dev. 10.


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Statistical Tests Parametric tests

Continuous data normally distributed

Non-parametric tests

Continuous data not normally distributed

Categorical or Ordinal data

Ch i t t f i th f 2


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Choosing a test for comparing the averages of 2 or moresamples of scores of experiments with one treatment factor

Data Between subjects

(independent samples)

Within subjects

(related samples)2 samples

Interval Independent t-test Paired t-test

Ordinal Wilcoxon-Mann-Whitney

test

Wilcoxon signed ranks

test, Sign test

Nominal Chi-square test Mc Nemar test

> 2 samples

Interval One way ANOVA Repeated measuredANOVA

Ordinal Kruskal-Wallis test Friedman test

Nominal Chi-square test Cochrans Q test

(dichotomous data only)


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Scheme for choosing one-sample test

Nominal 2 categories >2 categoriesBinomial test Chi-square

testOrdinal Randomness Distribution

Runs test Kolmogorov-Smirnov test

Interval Mean Distribution

t-test Kolmogorov-Smirnov test


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Comparison of 2 Sample Means Students T test

Assumes normally distributed continuous

data.

T value = difference between meansstandard error of difference

T value then looked up in Table todetermine significance


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Paired T Tests Uses the change before

and after intervention in asingle individual

Reduces the degree ofvariability between thegroups

Given the same number ofpatients, has greaterpower to detect adifference between groups


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Analysis of Variance Used to determine if two or more samples are

from the same population- the null hypothesis.

If two samples, is the same as the T test. Usually used for 3 or more samples.

If it appears they are not from same

population, cant tell which sample is different.

Would need to do pair-wise tests.


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Non-parametric Tests Testing proportions

(Pearsons) Chi-Squared ( 2) Test Fishers Exact Test

Testing ordinal variables Mann Whiney U Test

Kruskal-Wallis One-way ANOVA

Testing Ordinal Paired Variables Sign Test

Wilcoxon Rank Sum Test


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Use of non-parametric tests Use for categorical, ordinal or non-normally

distributed continuous data

May check both parametric and non-parametric tests to check for congruity

Most non-parametric tests are based on ranksor other non- value related methods

Interpretation: Is the P value significant?


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(Pearsons) Chi-Squared (

2) Test Used to compare observed proportions of an

event compared to expected.

Used with nominal data (better/ worse;dead/alive)

If there is a substantial difference between

observed and expected, then it is likely that

the null hypothesis is rejected.

Often presented graphically as a 2 X 2 Table


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Chi-Squared (

2) Test Chi-Squared ( 2) Formula

Not applicable in small samples If fewer than 5 observations per cell, use

Fishers exact test


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CorrelationAssesses the linear relationship between two variables

Example: height and weight

Strength of the association is described by a correlationcoefficient- r

r= 0 - .2 low, probably meaningless

r = .2 - .4 low, possible importance

r = .4 - .6 moderate correlation

r = .6 - .8 high correlation

r = .8 - 1 very high correlation

Can be positive or negative

Pearsons, Spearman correlation coefficient

Tells nothing about causation


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Correlation

Source: Harris and Taylor. Medical Statistics Made Easy


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Correlation

Perfect Correlation

Source: Altman. Practical Statistics for Medical Research


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Correlation


Correlation Coefficient 0 Correlation Coefficient .3


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Correlation


Correlation Coefficient -.5 Correlation Coefficient .7


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Regression

Based on fitting a line to data Provides a regression coefficient, which is the slope of the line

Y = ax + b

Use to predict a dependent variables value based on thevalue of an independent variable.

Very helpful- In analysis of height and weight, for a knownheight, one can predict weight.

Much more useful than correlationAllows prediction of values of Y rather than just whether there

is a relationship between two variable.


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Regression

Types of regression

Linear- uses continuous data to predict continuous

data outcome

Logistic- uses continuous data to predict probability

of a dichotomous outcome

Poisson regression- time between rare events.

Cox proportional hazards regression- survivalanalysis.


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Multiple Regression Models

Determining the association between two

variables while controlling for the values of

others. Example: Uterine Fibroids

Both age and race impact the incidence of fibroids.

Multiple regression allows one to test the impact of

age on the incidence while controlling for race (andall other factors)


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Multiple Regression Models

In published papers, the multivariable models aremore powerful than univariable models and takeprecedence.

Therefore we discount the univariable model as it does notcontrol for confounding variables.

Eg: Coronary disease is potentially affected by age, HTN,smoking status, gender and many other factors.

If assessing whether height is a factor:

If it is significant on univariable analysis, but not on multivariable

analysis, these other factors confounded the analysis.


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Risk Ratios

Risk is the probability that an event will happen. Number of events divided by the number of people at risk.

Risks are compared by creating a ratio Example: risk of colon cancer in those exposed to a factor vs

those unexposed

Risk of colon cancer in exposed divided by the risk in thoseunexposed.


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Risk Ratios

Typically used in cohort studies Prospective observational studies comparing

groups with various exposures.

Allows exploration of the probability thatcertain factors are associated with outcomesof interest For example: association of smoking with lung

cancer Usually require large and long-term studies to

determine risks and risk ratios.


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Interpreting Risk Ratios

A risk ratio of 1 equals no increased risk

A risk ratio of greater than 1 indicates increased risk

A risk ratio of less than 1 indicates decreased risk

95% confidence intervals are usually presented Must not include 1 for the estimate to be statistically significant.

Example: Risk ratio of 3.1 (95% CI 0.97- 9.41) includes 1, thuswould not be statistically significant.


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Odds Ratios

Odds of an event occurring divided by

the odds of the event not occurring.

Odds are calculated by the number of timesan event happens by the number of times it

does not happen.

Odds of heads vs the odds of tails is 1:1 or 1.


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Odds Ratios

Are calculated from case control studies

Case control: patients with a condition (often rare) are comparedto a group of selected controls for exposure to one or morepotential etiologic factors.

Cannot calculate risk from these studies as that requires theobservation of the natural occurrence of an event over time inexposed and unexposed patients (prospective cohort study).

Instead we can calculate the odds for each group.


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Comparing Risk and Odds Ratios

For rare events, ratios very similar

If 5 of 100 people have a complication: The odds are 5/95 or .0526.

The risk is 5/100 or .05.

If more common events, ratios begin to differ

If 30 of 100 people have a complication: The odds are 30/70 or .43

The risk is 30/100 or .30

Very common events, ratios very different

Male versus female births The odds are .5/.5 or 1

The risk is .5/1 or .5


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Risk reduction

Absolute risk reduction: amount that the risk isreduced.

Relative risk reduction: proportion or percentage

reduction. Example:

Death rate without treatment: 10 per 1000

Death rate with treatment: 5 per 1000

ARR = 5 per 1000

RRR = 50%


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Survival Analysis

Evaluation of time to an event (death,recurrence, recover).

Provides means of handling censored data Patients who do not reach the event by the end of

the study or who are lost to follow-up

Most common type is Kaplan-Meier analysis Curves presented as stepwise change from

baseline There are no fixed intervals of follow-up- survival

proportion recalculated after each event.


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Survival Analysis



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Kaplan-Meier Curve

Source: Wikipedia


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Kaplan-Meier Analysis

Provides a graphical means of comparing the

outcomes of two groups that vary by intervention or

other factor.

Survival rates can be measured directly from curve.

Difference between curves can be tested for statistical

significance.


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Cox Regression Model

AKA: Proportional Hazards Survival Model.

Used to investigate relationship between an event

(death, recurrence) occurring over time and possible

explanatory factors.

Reported result: Hazard ratio (HR).

Ratio of the hazard in one group divided the hazard in

another.

Interpreted same as risk ratios and odds ratios HR 1 = no effect

HR > 1 increased risk

HR < 1 decreased risk


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Maksud lu??


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Summary

Understanding basic statistical concepts is central to

understanding the medical literature.

Not important to understand the basis of the tests or

the underlying math.

Need to know when a test should be used and how to

interpret its results


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statistics in clinical research for residents

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