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

2. Overview Data types Summarizing data using descriptive statistics
Standard error
Confidence Intervals

3. 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

4. Overview Regression and Correlation Risk Ratios and Odds Ratios
Survival Analysis
Cox Regression

5. 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

6. 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.

7. 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

8. 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

9. Descriptive Statistics
Characterize data set
Graphical presentation
Histograms
Frequency distribution
Box and whiskers plot
Numeric description
Mean, median, SD, interquartile range

10. Histogram Continuous Data
No segmentation of data into groups

11. Frequency Distribution
Segmentation of data into groups
Discrete or continuous data

12. Box and Whiskers Plots

13. Box and Whisker Plots Popular in Epidemiologic Studies
Useful for presenting comparative data graphically

14. Numeric Descriptive Statistics
Measures of central tendency of data
Mean
Median
Mode
Measures of variability of data
Standard Deviation
Interquartile range

15. 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.

16. 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

17. 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.

18. 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.

19. 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.

20. 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.

21. 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.

22. 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.

23. 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.

24. Confidence Intervals
Commonly reported in studies to provide an estimate of the precision
of the mean.

25. Confidence Intervals

26. 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 equals 1 in 1000 chance.

27. 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

28. 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.

29. 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

30. 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

31. Alternative Hypothesis
Errors
Test Result
Null Hypothesis H0
Alternative Hypothesis H1
No Error
Type I 
Type II 
Truth

32. 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.

33. 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.

34. 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.

35. Sample size for proportions
Stata input: Mean 1 = .2, mean 2 = .3,  = .05, power (1-) =.8.

36. Sample Size for Continuous Data
Stata input: Mean 1 = 20, mean 2 = 30,  = .05, power (1-) =.8, std. dev. 10.

37. Statistical Tests Parametric tests Non-parametric tests
Continuous data normally distributed
Non-parametric tests
Continuous data not normally distributed
Categorical or Ordinal data

38. 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

39. 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

40. 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.

41. Non-parametric Tests Testing proportions Testing ordinal variables
(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

42. 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?

43. (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

44. 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

45. Correlation Assesses the linear relationship between two variables
Example: height and weight
Strength of the association is described by a correlation coefficient- r
r = low, probably meaningless
r = low, possible importance
r = moderate correlation
r = high correlation
r = very high correlation
Can be positive or negative
Pearson’s, Spearman correlation coefficient
Tells nothing about causation

46. Correlation
Source: Harris and Taylor. Medical Statistics Made Easy

47. Correlation Perfect Correlation
Source: Altman. Practical Statistics for Medical Research

48. Correlation Correlation Coefficient .3 Correlation Coefficient 0
Source: Altman. Practical Statistics for Medical Research

49. Correlation Correlation Coefficient -.5 Correlation Coefficient .7
Source: Altman. Practical Statistics for Medical Research

50. 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.

51. 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.

52. 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)

53. 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.

54. 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.

55. 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.

56. 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 ) includes 1, thus would not be statistically significant.

57. 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.

58. 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.

59. 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
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

60. 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%

61. 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.

62. Survival Analysis
Source: Altman. Practical Statistics for Medical Research

63. Kaplan-Meier Curve
Source: Wikipedia

64. 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.

65. 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

66. 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.

67. 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