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Regression Research Presentation
- 2. REGRESSION Melinda Avery, Jessica Blake, Jenny Boyd, Kaitlyn Glass, Sheena Gopal, Rachael Sottile, Claire Valentine, Diana Wilbur
- 3. Objectives 1. Discuss relevant concepts relating to Regression Analyses 2. Understand the methods of the study 3. Adequately interpret study results 4. Understand the findings of the study 5. Understand the clinical implications of the findings 6. Apply concepts through completion of a quiz!
- 4. Regression - What is It? ❖ Predictive modeling technique between variables ➢ Is the value of the dependent variable affected by the independent variable? ❖ Line of Best Fit: y=ax+b → good predictor for future data points ❖ Correlation does not imply causation!
- 5. Main Regression Analysis Techniques: Linear vs. Logistic ❖ Forms of Predictive Analysis: ➢ Linear ➢ Logistic ❖ When do you use Linear vs. Logistic? ➢ Depends on the type of variables you have
- 6. Linear Regression ❖ Used when… ➢ Dependent variable is continuous ➢ Independent variable may be continuous or discrete ❖ Based upon the type of dependent variable
- 7. Logistic Regression ❖ Used when… ➢ Dependent variable is dichotomous ➢ Independent variable may be continuous or discrete ❖ Based upon the type of dependent variable
- 8. Other Types of Regression Analysis Techniques ❖ Simple Regression ❖ Multiple Regression ❖ Multivariate Regression
- 9. Regression Analysis Techniques: Simple Regression ❖ Used when… ➢ 1 independent variable and 1 dependent variable ❖ Can be linear or logistic ❖ Based upon the number of independent and type of dependent variables
- 10. Regression Analysis Techniques: Multiple Regression ❖ Used when… ➢ 2 or more independent variables and 1 dependent variable ❖ Can be linear or logistic ❖ Based upon the number of independent and type of dependent variables
- 11. Regression Analysis Techniques: Multivariate Regression ❖ Used when… ➢ 1 independent variable and 2 or more dependent variables ❖ Can be linear or logistic ❖ Based upon the number and type of dependent variables
- 12. R2 = Coefficient of Determination ❖ Measure of how closely data falls on the line of best fit ❖ Always between 0 and 1.0 (0-100%) ➢ The higher the number = the better the predictive equation explains your data’s variance ❖ However… a low R2 is not always bad, and a high R2 is not always good! http://blog.minitab.com/blog/adventures-in-statistics-2/regression-analysis-how-do-i-interpret-r-squared-and-assess-the-goodness-of-fit
- 13. R2 Example ❖ Strength vs ER ROM ❖ Appears that strength is a much better predictor of pitch speed than ER ROM So, if a pitcher has a lot of strength, but is lacking ER ROM, would you draft him?
- 14. Regression Example: What Kind Is It? Independent: Strength of external rotator muscles Dependent: Pitch speed Question: How well does strength of external rotator muscles predict pitch speed?
- 15. Regression Example: What Kind Is It? Independent: Strength of external rotator muscles Dependent: Any change in pitch speed Question: Does strength of the external rotators predict a change in pitch speed (yes or no)?
- 16. Regression Example: What Kind Is It? Independent: Strength of external rotators AND ROM of external rotators Dependent: Pitch speed Question: How well do strength and range of motion of external rotators predict pitch speed?
- 17. Regression Example: What Kind Is It? Independent: Strength of external rotators AND ROM of external rotators Dependent: Any change in pitch speed Question: Do strength and range of motion of external rotators predict a change in pitch speed (yes or no)?
- 18. Regression Example: What Kind Is It? Independent: Strength of external rotator muscles Dependent: Pitch speed AND pitch accuracy Question: How well does strength of external rotators predict pitch speed and pitch accuracy?
- 19. Regression Example: What Kind Is It? Independent: Strength of external rotator muscles Dependent: Change in pitch speed AND change in accuracy Question: Does strength of the external rotators predict a change in both pitch speed and accuracy (yes or no)?
- 20. METHODS
- 21. Clinical Question Does the number of single-leg heel raises predict plantar flexion strength measured by a hand-held dynamometer? =
- 22. Hypothesis Null: Number of heel raises will fail to predict with reasonable accuracy hand-held dynamometry results for ankle plantar flexor strength. Alternative: Number of heel-raises will predict with reasonable accuracy hand-held dynamometry results for ankle plantarflexor strength.
- 23. Participants ❖ 37 healthy student PTs from GWU DPT Program ❖ Exclusion Criteria: any history of... ➢ Cardiovascular disease ➢ DM ➢ Renal disease ➢ Neurological problems ➢ Injury of selected LE within past 2 wks ➢ Surgical history in selected LE ➢ Cancer ➢ < 20 y/o or > 45 y/o
- 24. Procedure ❖ 8 total investigators ❖ Method creation for data collection ❖ Performance of data collection ➢ Groups of 4 taken to testing room ➢ Randomized → start at heel raise station OR dynamometry station ➢ Self-selected testing leg ❖ Analysis of collected data to determine linear regression of variables ❖ Determination of clinical relevance of results
- 25. Dynamometry ❖ One rater recording intake data ❖ One rater performing dynamometry testing ➢ Microfet2 by Hoggan ➢ Pt in supine, shoes off, ball of foot against dynamometer ➢ Dynamometer held against wall ➢ No HHA allowed ➢ 3 trials → recorded best of 3 ➢ Participants blinded to results
- 26. Heel Raises ❖ Two separate MMT stations ➢ One rater & one recorder per station ➢ Pt performed single-leg heel raises to failure on selected leg with shoes off ➢ Allowed 2 fingers on chair for balance
- 27. Data Analysis ❖ We decided simple linear regression was appropriate for the data we collected and for answering our clinical question Independent variable: heel raises (discrete) Dependent variable: dynamometer (continuous) ❖ 1 discrete independent variable and 1 continuous dependent variable = simple linear regression
- 28. RESULTS
- 32. Discussion: Heel Raises vs Dynamometer ❖ Plantar flexion MMT is not a great indicator of dynamometer strength readings ❖ There was a better relationship between the two when dynamometer was followed by heel raises ➢ MMT for plantar flexion is generally considered more of an endurance test than a strength test ➢ Doing MMT first could have fatigued the muscles, thus lowering dynamometer readings
- 33. Discussion: Males vs Females Male Overall Average: Dynamometer Score = 79.4 lbs Female Overall Average: Dynamometer Score = 63.4 lbs
- 34. MMT first? Dynamometer first? Heel Raises before Dynamometer = 67.1 lbs avg. dynamometer score Dynamometer before Heel Raises = 70.5 lbs avg. ❖ Those who performed the dynamometer before the heel raises had higher scores ➢ Why?
- 35. Clinical Implications ❖ Deciding between the use of MMT or the use of dynamometer could depend upon why you are testing the plantar flexors ➢ If you are looking to test pure strength of plantar flexors, dynamometer may be best ➢ If you are looking to test endurance of plantar flexors, MMT may be best ❖ Plantar flexors are important for walking, running, and other endurance activities so testing them with MMT may be more clinically and functionally relevant than using dynamometer
- 36. Limitations of Study ❖ Limited sample size ❖ Homogenous sample ❖ Sliding on the table during dynamometer reading ❖ Knee position: flexed or extended during MMT ❖ PT and patient positioning variability ❖ If patient had recently exercised and was already fatigued
- 37. Summary Regression is a predictive modeling technique between variables - Different types of regression used based on types of variables Heel raise count and ankle plantarflexion dynamometry are both reliable measures of PF strength (required for everyday activities) But the number of single leg heel raises performed is not a strong predictor of hand-held dynamometry score for healthy PT students Heel raises more for endurance vs. Dynamometry score more for strength
- 38. References 1. Harris-Love, MO., Shrader, JA., Davenport, TE., Joe, G., Rakocevic, G., McElroy, B., Dalakas M. Are repeated single-limb heel raises and manual muscle testing associated with peak plantar-flexor force in people with inclusion body myositis? Phys Ther. 2014; 94(4): 543-552. 2. Marmon, A., Pozzi, F., Alnahdi, A., Zeni, J. The validity of plantarflexor strength measures obtained through hand-held dynamometry measurements of force. International Journal of Sports Physical Therapy. 2013;8(6): 820-827. 3. Mattacola, C., Downar, S. Isometric muscle-force measurements obtained by handheld dynamometry. Athletic Therapy Today. 2003;8(4): 38-40. 4. Mentiplay, B., Perraton, L., Bower, K., Adair, B., Pua, Y., Williams, G., McGaw, R., Clark, R. Assessment of lower limb muscle strength and power using hand-held and fixed dynamometry: A reliability and validity study. PLoS ONE. 2015; 10(10): 1-18. 5. Stark, T., Walker, B., Phillips, JK., Fejer, R., Beck, R. Hand-held dynamometry correlation with the gold standard isokinetic dynamometry: A systematic review. American Academy of Physical Medicine and Rehabilitation. 2011;3: 472-479. 6. Hislop H, Avers D, Brown M. Testing the muscles of the lower extremity. In: Hislop H, Avers D, Brown M. 9th ed. Saint Louis, MO: Elsevier Saunders. 2014.
Editor's Notes
- Does the number of heel raises predict the strength when measured by dynamometer?
- Polynomial, step-wise, ridge, lasso, elsticnet: TONS of regression techniques we can utilize http://www.restore.ac.uk/srme/www/fac/soc/wie/research-new/srme/modules/mod4/quizb/Logistic_versus_linear.jpg
- Continuous: infinite amount of possibilities (e.g. dynamometer because you can have 50.75lbs) Discrete: finite number (e.g. heel raises because you can’t have 20.32 heel raises)
- Continuous: infinite amount of possibilities (e.g. dynamometer because you can have 50.75lbs) Discrete: finite number (e.g. heel raises because you can’t have 20.32 heel raises) Dichotomous: yes or no
- Correlation: just shows a linear relationship. As one value goes up, so does the second value, but you can’t use that to predict other values. Regression: uses a line of best fit to predict that linear relationship. The line gives an equation of best fit that we can then use to predict future values of this relationship.
- Left: 38.7% Right: 87.4% Regression model on right accounts for 87.4% of variance in data, while left is only 38.7 THe higher the number, the more variance in the data is explained by the line of best fit Shows a stronger relationship between dependent and independent variable If R2 = 1.0, then the equation line would explain all variance.All of the points would fit onto the line of best fit and equation would predict all future data points. However, not all good/bad… Some predictors will usually give low predictive quality, such as human behavior, but still be statistically significant. Higher results could indicate too much bias and actually not be a good representation of the population
- R2 for strength and pitch speed linear regression is .98, meaning that 98% of the variance in the data is explained by strength and suggesting that the equation will be a good predictor for future pitchers’ speed However, this could indicate bias → are there other variables influencing the results that were not accounted for? Have to R2 for ROM and pitch speed is pretty low, indicating there is not a good predictive relationship between ROM and pitch speed and that there are probably many other variables that are influencing the pitch speed. Now, how many of you are feeling some regression aggression and are as confused as we were? Jessica is going to try to help make things a little less confusing with some examples.
- Simple Linear Regression 1 Independent variable, dependent variable is continuous Application: for a recruitment tool for baseball teams
- Simple Logistic Regression - the dependent variable is dichotomous (yes or no, it either does or it doesn’t) 1 independent variable
- Multiple Linear Regression - because there are now two independent variables and the dependent variable is continuous
- Multiple Logistic Regression - because there are now TWO independent variables and the dependent variable is dichotomous
- Multivariate Linear Regression - because there are now two dependent variables that are continuous
- Multivariate Logistic Regression - 1 independent and 2 dependent variables
- Diana
- Discuss Independent vs dependent Independent is heel raises Dependent is dynamometer
- Questionnaire was provided to ensure the participants met inclusion/exclusion criteria prior to the study
- KG
- Independent: Heel raises (discrete) Dependent: Dynamometer (continuous) The type of data we have indicates the need for linear regression Because there is 1 dependent variable it is also considered univariate
- Rachael
- R2 is 0.1607 which is pretty low for a whole class prediction, when determining if heel raises can predict dynamometer strength. Higher the r2 the better the linear regression line explains your data (more predictive relationship between dependent and independent variable) 84% other extraneous variables affecting our data
- R is 0.4659 which is not great, but it is okay - This group started with Dynamometer station first and moved to MMT station second. Orange dots are the data points that fit onto the regression line Blue are data points that do not fit onto the regression line
- R squared is 0.1273 which is not very good. This group started with heel raises first and moved to dynamometer second. This could suggest that other variables, such as fatigue, were influencing the data prediction equation. Rachael
- Ask the class WHY? Likely was fatigued after the heel raises
- Our results do not suggest that either test is “bad”, per se, it just suggests that these two tests are not great predictors of each other in our test setting. However, we will probably still want to use both types of measurement in the clinic depending on what we are testing. If you want to test strength, probably the dynamometer is the best choice, while the heel raise MMT is a better choice for endurance of the plantar flexor muscles. There are potentially still clinicians who do not understand this though. For example, a patient comes in and is complaining that they are fatiguing after climbing stairs to their apartment on the 15th floor of a building, and the PT uses a dynamometer once to test their PF strength. This reading suggests above average PF strength, so the PT ignores the fatigue factor of the gastroc. Ideally, the PT should have used a heel raise test because that tests endurance which is what is needed to climb that many stairs, whereas the dynamometer only tested the one rep max strength of the muscle.
- Homogenous sample may not transfer to other populations