Statistics for Sports Medicine

Statistics for Sports Medicine Suzanne Hecht, MD University of Minnesota (suzanne.hecht@gmail.com) Fellow s Research Conference July 2012: Philadelphia

GOALS Try not to bore you to death!! Try to teach you something useful Introduce concepts Give you a stats reference guide Encourage sports med research

QUIZ What is the appropriate stats test to apply?. 50 soccer players wore head gear & 40 did not. Players were followed for diagnosis of concussion over one season. 1. Paired two tailed t-test 2. ANOVA 3. Chi-square analysis 4. McNemar test

MY TOP 10 STATS TIP LIST

OVERVIEW Introduction Variables Normal distribution Hypothesis testing Comparing means Measuring association Scatterplots & Correlation Regression

PURPOSE Stats is just a tool to analyze data you collect Learn the basics Add to your foundation over time Lots of names of tests, just like Sports Medicine!! You wouldn t talk about a Jobe s test during a knee exam Mt Stats

PURPOSE Infer something about a population based on information from a sample of that population Use probability concepts Describe how reliable the conclusions are ie: You have all this data & is it useful in someway?

Variables Discrete Examples Gender (m/f); Fracture (y/n) Nominal or Ordinal Nominal: Set of categories, no ordering ie: m/f Ordinal: Ordering, but no meaning to differences in scores ie Compare 1 st & 2 nd place finishers (ranking) without using actual times Continuous Examples Weight, race time Differences between values has meaning

USE FOR FUTURE REFERENCE Variable Summary Statistics Comparing 2 groups Measuring Association Nominal Mode Chi-square Contingency Coefficient Ordinal Median Chi-square Nonparametric Kappa Spearman r Kendall s tao Continuous Mean Median & SD t-test Nonparametric Spearman r Pearson r

SAMPLE SIZE & POWER Important to calculate Do this prior to the study Avoid expenses, time, resources, etc. Calculations available in stats software Let s you know that you have enough subjects to detect a meaningful change

HYPOTHESIS TESTING Null hypothesis (H 0 ) No difference between groups (groups are the same) Alternative hypothesis (H 1 ) There is a difference between groups Type I error Saying groups are different when they aren t Type II error Saying groups are the same when they are different

Normal Distribution Applies to continuous variables Mean=median=mode Many stats tests assume nl distr t-test; ANOVA; regression Ways to test to see if a nl distribution Use non-parametric tests or transform data (ie log) if not a nl distribution Methods that assume nl distr Robust to moderate departures of nl distr assumption if n is large enough!

Normal Distribution Symmetrical about the mean BLUE= 68.2% of values w/in 1 SD BLUE+ BROWN= 95.4% of values w/in 2 SD BLUE + BROWN + GREEN= 99.7% of values w/in 3 SD

P-Value = the probability of obtaining results by chance alone p=0.05 (5% chance) May not tell whole story Statistically significant Clinically significant Small or large n s Small n: Type II error Give both: p-value & CI

Comparing 2 groups or rxs Type of Outcome Continuous Binary (y/n) Nl Distribution Paired Unpaired Paired t-test Yes Parametric Unpaired t-test Sign test No Nonparametric Paired Sign rank test McNemar s test Unpaired Wilcoxon rank sum test Yes Large Sample Size Chi-Squared No Fischer s Exact Test

Comparing 3 or > groups Type of Outcome Continuous Binary (y/n) Nl Distribution Yes Parametric No Nonparametric Frequency Tables Chi-squared Methods ANOVA Kruskal- Wallis Test

Comparing 2 groups or rxs Type of Outcome Continuous Binary (y/n) Nl Distribution Yes No Parametric Nonparametric Paired Unpaired Paired Unpaired t-test t-test Sign test Sign rank test Wilcoxon rank sum test

Comparing Group Means t-test ANOVA Assumptions Data is continuous & nl distributed Methods 2 indep samples: 2 sample t-test Paired data: Paired t-test >2 indep samples: ANOVA Includes Confidence intervals Hypothesis testing

3 types 2 sample t-test Student s t-test t-tests Independent samples t-test Paired samples t-test Paired data: 2 measurements on same subject or test unit One sample t-test Compare to a known (norm) value

t-tests One-tailed vs two-tailed Almost always use two-tailed Results could be higher or lower not just one way

95% CI Confidence Intervals 95% confident that the true value falls in the interval. Wide CI suggests uncertainty about data Does the CI contain a value that implies no change or no effect? Mean: 0 Odds ratio: 1 Does the confidence interval lie partly or entirely within a range of clinical indifference?

Example: Confidence Intervals Survey 19 millionaires Mean income donation=15% +/- 2 SD CI: +/- 2.4% Interpretation We are 95% confident that millionaires donate between 12.6-17.4 % of their income.

Comparing 2 groups or rxs Type of Outcome Continuous Binary (y/n) Nl Distribution Yes No Parametric Nonparametric Paired Unpaired Paired Unpaired t-test t-test Sign test Sign rank test Wilcoxon rank sum test

SIGN TEST Non-parametric test Not a nl distribution Alternative to paired t-test Good for small sample size Test the difference for matched pairs on before & after data Method: Calculate diffs Throw-out zero diff Test for # of + diff H 1 is true: median does not = 0

WILCOXON SIGN RANK TEST Same application as Sign Test Uses the ranks & the signs of diff More powerful test than Sign Test Method: Calculate differences in pairs Throw away zero differences Rank from smallest to largest difference w/out regard to +/- Test: sum of ranks of + diff

Wilcoxon Rank Sum Test Also known as: Mann-Whitney U test Comparing 2 independent samples Not nl distribution Good for detecting changes in medians Method: Combine data from 2 gps Rank smallest to largest Add ranks in the gp with smaller sample size Add ranks in gp with larger N Test: sum of ranks for smaller gp compared to larger gp

EXAMPLE: Rank-Sum Test Team Cheetah 5 team members Team Impala 7 team members Results TC: 3, 4, 7, 12, 13 (min) Results TI: 2, 5, 6, 8, 9, 10, 11 (min) Combine data & then rank: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Sum ranks of smaller gp 2 + 3 + 6 + 11 + 12 = 34 Test if sum ranks of smaller gp is the same or different from other group

Comparing 3 or > groups Type of Outcome Continuous Binary (y/n) Nl Distribution Yes Parametric No Nonparametric Frequency Tables Chi-squared Methods ANOVA Kruskal- Wallis Test

ANOVA Analysis of variance Comparing means of >2 groups Assumes Continuous Nl distrib Same variance w/in each group Benefits compared to t-tests Efficiency Avoids multiple testing problem Problem Sign F test tells you that at least 2 gps are different, but not which ones!

ANOVA-Problem Multiple Comparisons Procedures Used to tell which groups differ Stricter levels for accepting/rejecting that the means are the same 4 methods Bonferroni Tukey Neuman-Keuls Scheffe

Kruskal-Wallis Test Nonparametric test Use for comparing 3 or > independent groups Think of as a non-parametric ANOVA test Good for detecting changes in median

Comparing 2 groups or rxs Type of Outcome Continuous Binary (y/n) Paired Unpaired McNemar s test Yes Large Sample Size No Chi-Squared Fischer s Exact Test

Comparing Frequency Data Binary outcome (yes/no) Paired method McNemar s Test Non-paired methods Pearson s Chi-square Fisher s Exact Test

Assumes Pearson s Chi-square Random samples from 2 groups Compares expected with observed All samples sizes are large enough All frequencies must be > 5 2x2 table: Standard New Helmet Helmet Concussion No Concussion 18 6 7 13 TOTAL n 1 =25 n 2 =19 p 1 =18/25 =0.72 (72%) p 2 =6/19 =0.32 (32%)

Pearson s Chi-square OBSERVED Standard Helmet New Helmet TOTAL Concussion 18 6 24 No Concussion 7 13 TOTAL n 1 =25 n 2 =19 20 44 X 2 =7.1 (p=0.0077) EXPECTED (if not different) Concussion No Concussion Standard Helmet 24/44 x 25 =13.64 20/44 x 25 =11.36 New Helmet 24/44 x 19 =10.36 20/44 x 19 =8.64

Fisher s Exact Test Use this test when 1 or more of frequencies is < 5

McNemar s Test Use for paired binary data Same subject before & after rx Cross-over study

MY TOP 10 STATS TIP LIST http://statpages.org www.theresearchassistant.com www.ats.ucla.edu/stat/

RISK Risk difference Absolute difference in risk proportions Can be difficult to interpret Relative Risk (RR) Also known as Risk Ratio Risk in 1 gp/risk in other gps Odds Ratio (OR) Probability or Odds of an event OR= odds of exposed gp/odds of control gp OR=1 means no difference

RELATIVE RISK Relative risk (RR) is the risk of an event relative to exposure. Risk of having a boy if mom took testosterone during pregnancy 75/100=75% Risk (probability) of having a boy= 51/100= 51% Risk Ratio=.75/.51=1.5 Easier to understand Risk ratio =0.5 =risk is half Risk ratio=2=risk is double

CALCULATING ODDS Odds of an event =# of events/# of nonevents 51 boys born for every 100 births Odds of any randomly chosen delivery being a boy=51/100-51=1.04 Odds>1: Event is more likely to happen than not Odds of certain event= Odds<1: Event is not likely to happen Odds of an impossible event=0

ODDS RATIO Testosterone example 75/100-75 51/100-51= 3/1.04= 2.9 The odds of having a boy is 2.9x higher in moms using testosterone vs mom s not using testosterone.

ODDS RATIO: Benefits No upper limit RR range varies depending on baseline prevalence When events are low (rare dz) OR approx RR OR ok to use with case control Don t use RR with case control

Calculating OR Cross Product Factor (Event) Group 1 Group 2 a b No Factor (No Event) c OR= a/c b/d d = a x d b x c Concussion No Concussion Standard New Helmet Helmet 18 6 7 13 18 x 13 = 5.57 6 x 7

SCATTERPLOT Can help answer the following Are variables X & Y related? Are X & Y linearly related? Are X & Y non-linearly related? Does the variation in Y change depending on X? Are there outliers? 1. Linear relationship 2. Small scatter (strong correlation) 3. + slope (+ correlation)

SCATTERPLOTS No relationship 1. Linear 2. Small scatter (strong correlation) 3. - slope (neg correlation)

SCATTERPLOTS Outlier Non-linear

CORRELATION: PEARSON Measures the strength of (linear) association between 2 variables Ranges from -1 to 1 1= -1= 0= Examples: r=0.8 r=0.3 r=-0.7 perfect + correlation perfect correlation no correlation strong + correlation weak + correlation moderate correlation

REGRESSION A straight line that describes the dependence of one variable on another is called a regression line Y=response variable ie finishing time X=explanatory variable ie body fat percentage Is finishing time predicted by body fat percentage?

Linear REGRESSION TYPES Data: Normal distribution Simple or Multiple Logistical Data: binary (y/n) Simple or Multiple Multiple Regression Models Allow estimation of the indep effect of each X after controlling for other variables in the model.

Simple LINEAR REGRESSION Use to predict Y given X Determine best fitting equation Test whether there is a relationship between X & Y

Linear Regression R 2 value =% of variance in Y explained by X If R 2 =1 then x can predict y 100% of the time F test for significance If p >0.05 then no significant relationship (slope of line =zero) exists between x & Y

Multiple Linear Regression Model that explains how a single dependent variable (Y) relates to several independent variables (x). Example: Test if age, gender, body fat %, prior triathlon competitions, & occupation predict finishing time.

Multiple Linear Regression How many variables to use? Recommend that you have 10-20x # of cases to variables tested. Test lots of variables Increase random chance of stat sign Model becomes unstable

Multiple Linear Regression Example cont: Model predicts 90% of variance in performance Now test for which variable or combinations of variables is most predictive Body fat %: 15% Age: 10% Gender: 30% Body fat & gender 35% Occupation 0% Prior triathlon 40%

QUIZ What is the appropriate stats test to apply?. 50 soccer players wore head gear & 40 did not. Players were followed for diagnosis of concussion over one season. 1. Paired two tailed t-test 2. ANOVA 3. Chi-square analysis 4. McNemar test

OTHER TIPS Stats support at Universities Usually charge per hour MS cheaper than PhD Authorship If stats person willing to: (International Committee of Medical Journal Editors (ICMJE) guidelines) Help design study Analyze data Format tables, graphs, etc Write a portion of article May be able to get small grant to cover $ of stats analysis On-line support

REFERENCES 1. Applied Biostatistics in Clinical Research Course Book; Case-Western Reserve General Clinical Research Center 2005 2. Biostatistics 100B Course Book; UCLA 1998 3. The Essentials of Clinical Investigation Course Book; UCLA Clinical Research Center 1999 4. Moore, McCabe, Craig (2009) Introduction to the Practice of Statistics, Sixth Edition. WH Freeman and Company, New York. ISBN-13: 978-1-4292-1622-7.