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Introduction to Multivariate analysis
This document discusses multivariate analysis and the relationship between smoking and lung cancer. It provides several key studies that established this relationship: - A 1950 case-control study that associated lung cancer with smoking. - A 1898 study finding elevated lung tumors in tobacco workers exposed to tobacco dust. - Later studies in the 1930s-1950s further strengthened the relationship by showing higher rates of lung cancer in heavy smokers.
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Overview of Multivariate Analysis as a statistical technique. Presented by Prof. Dr. Jamalludin Ab Rahman.
Studies linking smoking to lung cancer, including case-control studies and risk factors associated with heavy smoking.
Focus on analyzing the relationships between two or more variables.
Explanation of multivariate analysis, involving multiple independent and dependent variables.
Introduction to primary variables in analysis including outcome, exposure, effect modifiers, confounders, and mediators.
Discussion on the relationship between exercise intensity and fitness level, questioning differences between intensities.
Presentation of data showing the relationship between physical activity time and systolic blood pressure (SBP) with a regression line.
Discussion of how third variables can affect the relationship between two variables.
Identification of third variable types: confounder, mediator, and moderator.
Definition of a moderator variable that affects the strength of a relationship between two variables.
Study on the interaction of stress, coping mechanisms, and MS, presenting a statistical outcome.
Explanation of a mediator variable which plays a role within the pathway of the relationship.
Reasons for utilizing multivariate analysis, focusing on multiple factors and exploring associations.
Overview of regression as a common multivariate technique including types like linear and logistic regression.
Introduction to the structure of regression equations including dependent and independent variables.
Example illustrating how arterial blood pressure can be modeled using multiple variables.
Introduction to logistic regression, its equation, and its application in predicting events.
Interpretation of R-squared in relation to arterial blood pressure and its influencing factors.
Presentation of the main regression equation explaining arterial blood pressure.
Study example linking snoring to cardiovascular disease in women with multiple variables influencing risk.
Overview of assumptions necessary for validating linear regression including linearity and normality.
Definition and calculation of residuals in regression analysis.
Assessment of residuals to determine whether they follow a normal distribution.
Evaluation of residuals for heterogeneity or homogeneity in the regression model.
Explanation of influential data points and their potential effects on regression analysis.
Categorization of multivariate tests based on dependent and independent variables.
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Introduction to Multivariate analysis
- 1. Multivariate Analysis Prof. Dr.Jamalludin Ab Rahman MD MPH Department of Community Medicine Kulliyyah of Medicine
- 2. Smoking & lungcancer Good case-control study associating lung cancer to smoking (Wynder EL, Graham E. Tobacco smoking as a possible etiologic factor in bronchiogenic carcinoma: a study of 684 proven cases. JAMA 1950;143:329-36.) Tobacco dust (not smoke) might be causing the elevated incidence of lung tumours among German tobacco workers. (Hermann Rottmann in Würzburg 1898) Difference Causal Smoking might be related to lung cancer, but lung cancer is still rare (Adler I. Primary Malignant Growths of the Lungs and Bronchi. London: Longmans, 1912:22) 86 lung cancers patients were likely smoked (Müller FH. Tabakmissbrauch und Lungencarcinom. Zeitschrift für Krebsforschung 1939;49:57–85.) Smoking 35 sticks per day increase risk to 40 times (Doll R, Hill AB. The mortality of doctors in relation to their smoking habits. BMJ 1954;1:1451–5.) Animal study associating cigarette smoke tar with cancer (Wynder E, Graham EA, Croninger AB. Experimental production of carcinoma with cigarette tar. Cancer Res 1953;13:855–66) 8November2016(C)JamalludinAbRahman2015 2
- 3. It is aboutrelationship Analysis of the relationships between two or more variables. 8November2016(C)JamalludinAbRahman2015 3
- 4. Multivariate? Multivariate -general term – multiple IV May involved multiple DV DVIV IV DV DV IV IV 8November2016(C)JamalludinAbRahman2015 4
- 5. Outcome Exposure Exposure Exposure Exposure Exposure Effect modifieror Moderator Confounder Mediator 8November2016(C)JamalludinAbRahman2015 5
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- 8. Exercise & fitness LowModerate High Is there any difference % between Low & Moderate intensity? How big is the difference % between Low & Moderate? Is there any pattern now? What is your conclusion? Fitness level Exercise intensity 8November2016(C)JamalludinAbRahman2015 8
- 9. Physical activity &blood pressure Time SBP 30 140 40 145 85 130 90 143 100 130 110 120 110 110 120 120 130 110 130 109 140 98 150 100 140 110 135 120 160 100 160 96 170 100 200 89 200 100 240 80 y = -0.3287x + 155.89 R² = 0.8508 0 20 40 60 80 100 120 140 160 0 50 100 150 200 250 300 SBP(mmHg) Time (minutes/week) 8November2016(C)JamalludinAbRahman2015 9
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- 11. The 3rd factorscan be a... 1. Confounder 2. Mediator or intervening factor 3. Moderator or effect modifier (interaction) 8November2016(C)JamalludinAbRahman2015 11
- 12. The 3rd variable Outcome Exposure Exposure Confounder Confounder influencea relationship (between two variables) but it is not a part of the pathway 8November2016(C)JamalludinAbRahman2015 12
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- 14. The 3rd variable Outcome Exposure Exposure Moderator Whenan exposure has different effects on disease at different values of a variable (interaction) 8November2016(C)JamalludinAbRahman2015 14
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- 16. Stress vs. MSvs. Coping mechanism Multiple sclerosis new lesions Coping Mech. Stress Mohr, D. C., Goodkin, D. E., Nelson, S., Cox, D., & Weiner, M. (2002). Moderating Effects of Coping on the Relationship Between Stress and the Development of New Brain Lesions in Multiple Sclerosis. Psychosom Med, 64(5), 803-809. OR = 1.62, p = 0.009 Distraction (OR=0.69, p=0.009), instrumental (OR=0.77, p=0.081), emotional preoccupation (OR=1.46, p=0.088) & palliative (NS) 8November2016(C)JamalludinAbRahman2015 16
- 17. The 3rd variable Outcome Exposure Exposure Mediator Mediator influencea relationship (between two variables) and it is also a part of the pathway 8November2016(C)JamalludinAbRahman2015 17
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- 20. Why multivariate? Multi-factorial– which are the significant factors? Multiple outcomes Multiple unit of measurements Exploration of associations 8November2016(C)JamalludinAbRahman2015 20
- 21. Regression Most commonmultivariate technique Best line to fit the data - OLS Many types: Linear regression Logistic regression & many others!! 8November2016(C)JamalludinAbRahman2015 21 x y 𝑦 = 𝛽0 + 𝛽1 𝑥 𝛽0
- 22. Regression equation e.g.Linear regression 8November2016(C)JamalludinAbRahman2015 22 Dependent Var Intercept Coefficient for Var x1 Explanatory Var x1 Error/Residual 𝑌 = 𝛽𝑜 + 𝛽1 𝑥1 + 𝛽2 𝑥2 + ⋯ 𝛽 𝑛 𝑥 𝑛 + 𝜀
- 23. Example #1 Arterial BP= Constant + Age + Body weight + Pulse rate + Stress + Residual 𝑌 = 𝛽𝑜 + 𝛽1 𝑥1 + 𝛽2 𝑥2 + ⋯ 𝛽 𝑛 𝑥 𝑛 + 𝜀 8November2016(C)JamalludinAbRahman2015 23
- 24. Logistic regression 𝐿𝑛 𝑃 1−𝑃 =𝛽𝑜 + 𝛽1 𝑥1 + ⋯ + 𝛽 𝑛 𝑥 𝑛 P = Probability that Y=1 i.e. Event occurs 1-P = Event not occur 𝐿𝑛 𝑃 1−𝑃 = Ln of OR = Logit 8November2016(C)JamalludinAbRahman2015 24
- 25. R2 = 0.986,meaning 99% of variation in ABP is explained by Age, Body Weight, Pulse Rate & Stress (F(4,15)=291.948), P<0.001) 8November2016(C)JamalludinAbRahman2015 25
- 26. Main Result Arterial BP= 17.3 + 0.6(Age) + 0.9(Body weight) + 0.09(Pulse rate) + 0.01(Stress) 8November2016(C)JamalludinAbRahman2015 26
- 27. Example #2 Snoringand risk of cardiovascular disease in women . Hu 2000. From The Nurses’ Health Study. Cohort. Baseline, N=71,779 women 40 to 65 years old and without diagnosed CVD or cancer in 1986. Till 31st May 1994. CVD = Snoring + Age +Smoking + BMI + Alcohol + Physical Activity + Menopausal status + Family history of MI + DM + Cholesterol + Hours sleeping + Sleeping position 8November2016(C)JamalludinAbRahman2015 27
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- 30. Testing assumptions forlinear regression 1. Linearity between DV & IVs – Scatter plot residuals vs. predicted 2. Normality – Histogram of residuals 3. No outliers – Casewise diagnostics (within +/- 2SD), Cook’s D (for influential points, <1), leverage point (< 4/n) 4. Homogeneity – Scatter plot 5. Independence (no autocorrelation) – Durbin Watson 1.5-2.5 (or some says 0-4) 6. No multicollinearity – Tolerance > 0.1, VIF <10 8November2016(C)JamalludinAbRahman2015 30
- 31. Residuals x y Residual = Observed- Predicted 𝑦 = 𝛽0 + 𝛽1 𝑥 𝛽0 8November2016(C)JamalludinAbRahman2015 31
- 32. Residual statistics -Linearity Predicted Residuals Residuals Linear Non linear 8November2016(C)JamalludinAbRahman2015 32
- 33. Residual statistics -Normality Predicted Residuals Residuals Normal distribution Not Normal 8November2016(C)JamalludinAbRahman2015 33
- 34. Residual statistics -Heterogeneity Predicted Residuals Residuals Homogenous Heterogenous 8November2016(C)JamalludinAbRahman2015 34
- 35. Influential data x y AB C A = Outlier, still within the range of x, large residual value B & C = Leverage points B = Good leverage, it won’t impact the regression line C = Bad leverage. It will change the regression line 8November2016(C)JamalludinAbRahman2015 35
- 36. Type of multivariatetests Dependent Variables Independent Variables Test 1 – Cont ≥ 2 – All Cont Linear Regression 1 – Cont ≥ 2 – All Cat ANOVA 1 – Cont ≥ 2 – Cont + Cat ANCOVA > 1 – Cont All Cat MANOVA > 1 – Cont Cat + Cont MANCOVA 1 – Dichotomous ≥ 2 – Cont + Cat Binary Logistic Regression 8November2016(C)JamalludinAbRahman2015 36