statistical methods in clinical research james b. spies m.d., mph professor of radiology georgetown...

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Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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Page 1: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Statistical Methods in Clinical Research

James B. Spies M.D., MPHProfessor of Radiology

Georgetown University School of Medicine

Washington, DC

Page 2: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Overview Data types

Summarizing data using descriptive statistics

Standard error

Confidence Intervals

Page 3: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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

Page 4: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Overview Regression and Correlation

Risk Ratios and Odds Ratios

Survival Analysis

Cox Regression

Page 5: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Further Study Medical Statistics Made Easy

M. Harris and G. Taylor Informa Healthcare UK

Distributed in US by:Taylor and Francis

6000 Broken Sound Parkway, NW Suite 300

Boca Raton, FL 33487

1-800-272-7737

Page 6: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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.

Page 7: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Types of data Continuous data

Theoretically infinite possible values (within physiologic 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

Page 8: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Types of Data Why important? The type of data defines:

The summary measures used Mean, Standard deviation for continuous data Proportions for discrete data

Statistics used for analysis: Examples:

T-test for normally distributed continuous Wilcoxon Rank Sum for non-normally distributed

continuous

Page 9: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Descriptive Statistics Characterize data set

Graphical presentation Histograms Frequency distribution Box and whiskers plot

Numeric description Mean, median, SD, interquartile range

Page 10: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

HistogramContinuous Data

No segmentation of data into groups

Page 11: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Frequency Distribution

Segmentation of data into groupsDiscrete or continuous data

Page 12: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Box and Whiskers Plots

Page 13: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Box and Whisker Plots

Popular in Epidemiologic StudiesUseful for presenting comparative data graphically

Page 14: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Numeric Descriptive Statistics Measures of central tendency of data

Mean Median Mode

Measures of variability of data Standard Deviation Interquartile range

Page 15: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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.

Page 16: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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

Page 17: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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.

Page 18: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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.

Page 19: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 an estimate of the entire population of individuals who might have been eligible for the study.

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

Page 20: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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.

Page 21: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 population parameter provided by the sample mean or proportion.

Page 22: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 the estimate.

Page 23: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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.

Page 24: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Confidence Intervals

Commonly reported in studies to provide an estimate of the precisionof the mean.

Page 25: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Confidence Intervals

Page 26: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 occur due 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.

Page 27: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 clinical

significance. A very large study might find that a difference of .1 on a VAS Scale of 0

to 10 is statistically significant but it may be of no clinical significance A large study might find many “significant” findings during

multivariable analyses.

“a large study dooms you to statistical significance”

Anonymous Statistician

Page 28: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 not

significant. 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

might range from very low to very high. Example: A relative risk of 4 might have a confidence interval of 1.05 to

9, suggesting that although the estimate is for a 400% increased risk, an increased risk of 5% to 900% is plausible.

Page 29: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 different populations but they may not.

Also called the error. Typically 0.05 is used

Page 30: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 can’t be detected without a proper power analysis

Page 31: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Errors

Null Hypothesis

H0

Alternative Hypothesis

H1

Null Hypothesis

H0

No Error Type I

Alternative Hypothesis

H1

Type II

No Error

Test Result

Truth

Page 32: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Sample Size Calculation Also called “power analysis”. When designing a study, one needs to determine

how large 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 to detect 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.

Page 33: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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.

Page 34: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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

sided test. When comparing two samples, we usually

cannot be sure which is going to be be better.

You never know which directions study results will go.

For routine medical research, use only two-sided tests.

Page 35: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Sample size for proportions

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

Page 36: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Sample Size for Continuous Data

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

Page 37: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Statistical Tests Parametric tests

Continuous data normally distributed

Non-parametric tests Continuous data not normally distributed Categorical or Ordinal data

Page 38: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Comparison of 2 Sample Means Student’s T test

Assumes normally distributed continuous data.

T value = difference between means standard error of difference

T value then looked up in Table to determine significance

Page 39: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Paired T Tests Uses the change before

and after intervention in a single individual

Reduces the degree of variability between the groups

Given the same number of patients, has greater power to detect a difference between groups

Page 40: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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, can’t tell which sample is different. Would need to do pair-wise tests.

Page 41: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Non-parametric Tests Testing proportions

(Pearson’s) Chi-Squared (2) Test Fisher’s Exact Test

Testing ordinal variables Mann Whiney “U” Test Kruskal-Wallis One-way ANOVA

Testing Ordinal Paired Variables Sign Test Wilcoxon Rank Sum Test

Page 42: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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

ranks or other non- value related methods Interpretation:

Is the P value significant?

Page 43: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

(Pearson’s) 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

Page 44: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Chi-Squared (2) Test Chi-Squared (2) Formula

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

Fisher’s exact test

Page 45: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Correlation Assesses the linear relationship between two variables

Example: height and weight Strength of the association is described by a correlation

coefficient- 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 Pearson’s, Spearman correlation coefficient Tells nothing about causation

Page 46: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Correlation

Source: Harris and Taylor. Medical Statistics Made Easy

Page 47: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Correlation

Perfect Correlation

Source: Altman. Practical Statistics for Medical Research

Page 48: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Correlation

Source: Altman. Practical Statistics for Medical Research

Correlation Coefficient 0 Correlation Coefficient .3

Page 49: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Correlation

Source: Altman. Practical Statistics for Medical Research

Correlation Coefficient -.5 Correlation Coefficient .7

Page 50: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 variable’s value based on the

value of an independent variable. Very helpful- In analysis of height and weight, for a known

height, one can predict weight. Much more useful than correlation

Allows prediction of values of Y rather than just whether there is a relationship between two variable.

Page 51: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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- survival

analysis.

Page 52: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 (and all other factors)

Page 53: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Multiple Regression Models In published papers, the multivariable models are

more powerful than univariable models and take precedence.

Therefore we discount the univariable model as it does not control 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.

Page 54: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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 those

unexposed.

Page 55: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Risk Ratios Typically used in cohort studies

Prospective observational studies comparing groups with various exposures.

Allows exploration of the probability that certain factors are associated with outcomes of interest For example: association of smoking with lung

cancer Usually require large and long-term studies

to determine risks and risk ratios.

Page 56: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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, thus

would not be statistically significant.

Page 57: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Odds Ratios Odds of an event occurring divided by

the odds of the event not occurring. Odds are calculated by the number of

times an event happens by the number of times it does not happen.

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

Page 58: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Odds Ratios Are calculated from case control studies

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

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

Instead we can calculate the odds for each group.

Page 59: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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

Page 60: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Risk reduction Absolute risk reduction: amount that the risk is

reduced. 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%

Page 61: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Survivial 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.

Page 62: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Survival Analysis

Source: Altman. Practical Statistics for Medical Research

Page 63: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Kaplan-Meier Curve

Source: Wikipedia

Page 64: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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.

Page 65: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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

Page 66: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

Cox Regression Model Common use in long-term studies

where various factors might predispose to an event. Example: after uterine embolization, which

factors (age, race, uterine size, etc) might make recurrence more likely.

Page 67: Statistical Methods in Clinical Research James B. Spies M.D., MPH Professor of Radiology Georgetown University School of Medicine Washington, DC

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