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(Outcome (Continous (Independent observation (2 groups/ time points…

- - - - 2 groups/ time points
        
        2-sample t-test
        
        Mechanics
        
        Difference in means : T- distribution
        (Z distribution for larger samples)
        
        SE of the difference in means (pooled)
        
        More precise estimate of SE
        
        T-distribution has more df
        
        Required Homogeneity of variances
        
        SE of the difference in means (unpooled)
      - 2
        
        F test
        
        Difference in means of the groups more than background noise (=variability within groups) ?
        
        F = (Variability btw groups/ Variability within groups)
        
        Hypothesis : two variances are equal (F statistic =1)
        
        Global test
        
        Total sum of square (TSS)
        
        Sum of Squares within (SSW) or Sum of Squares Error (SSE)
        
        Sum of Squares Between (SSB) or Sum of Squares Regressgion (SSR)
        
        TSS = SSW + SSB
        
        Coefficient of Determination
        
        The amount of variation in the outcome variable (dependent variable) that is explained by the predictor (independent variable).
        
        Corection for multiple comparisons post-hoc
        
        Bonferroni correction
        
        Holm/Hochberg
        
        Tukey (adjusts p)
        
        Scheffe (adjusts p)
        
        Pairwise t-tests?
        
        Type I error (5% each test)
        
        1 - (0.95)3 = 14%
      - Continous variable
        
        Linear correlation (Pearson): 2 variables treated equals
        
        Covariance
        
        cov(x,y)=0 : X and Y independent
        
        cov(x,y)>0 : X and Y positively correlated
        
        cov(x,y)<0 : X and Y inversely correlated
        
        Var(x) = Cov(x,x)
        
        Correlation coefficient
        
        Strength of linear relationship
        
        0: no correlation (independent)
        
        -1 : perfect inverse correlation
        
        +1: perfect positive correlation
        
        Unitless
        
        PEARSON's Correlation Coefficient
        
        R2 (R-squared)
        
        Proportion of variability explained by the predictors
        
        Measure of model fit
        
        Distribution
        
        Normal for larger n
        
        T-distribution for smaller n (n<100)
        
        Linear regression: Predictor ~ Outcome
        
        Simple linear regression
        
        Y = bx+ a
        
        Intercept
        
        Slope (beta coefficient)
        
        Distribution of beta coefficient
        
        T distribution
        
        Multiple linear regression
        
        Each regression coefficient is the amount of change in the outcome variable that would be expected per one-unit change of the predictor, if all other variables in the model were held constant
        
        Functions
        
        Control for confounders
        
        10% change in adjusted beta
        
        Do not judge confounders by their effect on p-values
        
        Improve predictions
        
        Test of interactions btw predictors (Effect modification)
        
        Categorical predictors?
        
        Binary: Treat as numbers (0 and 1)
        
        Categorical : Dummy coding!
        
        Residual analysis
        
        Residual = Observed - Predicted
        
        Residual analysis for normality
        
        Residual analysis for homogeneity of variances
        
        Residual plots
        
        WATCH OUT
        
        Over fitting
        
        Missing data
        
        Variable transformation
        
        NOT normaly distributed (n<100)
        
        NON-homogenous variances
        
        Predictor and Outcome do not have a linear relationship
    - - 2 groups/ time points
        
        Paired t-test
      - 2
        
        Repeated-measures ANOVA
        
        Question
        
        Are there significant differences across time periods? (Time factor)
        
        Are there significant differences between groups (=your categorical predictor)? (Group factor)
        
        Are there significant differences between groups in their changes over time? (Group x Time) factor
        
        Serial paired t-test : type I error
    - - Normally distributed outcome
      - Homogeneity of variances
        
        Models are robust against this assumption
        
        NOT required for 2 sample t-test if using unpooled variance
      - Violated?
        
        Wilcoxon rank-sum test ~ Mann-Whitney U test ("t-test" )
        
        Wilcoxon sign-rank test ("paired t-test")
        
        Kruskall-Wallis test ("ANOVA")
        
        Spearman rank correlation coefficient ("Pearson's correlation coefficient")
  - - - Risk difference/ Relative risk (2x2 table)
        
        Z-distribution
        
        Risk ratio
        
        Odds ratio from logistic regression
      - Chi-square test (RxC table)
        
        P(A)*P(B)= P(A&B) !Independence
        
        Expected cell count =P(A)P(B)N
        
        Chi-square distribution
      - Logistic regression (multivariate regression technique)
    - - McNemar's chi-square test (2x2 table)
      - Conditional logistic regression (multivariate regression technique)
      - GEE modeling (multivariate regression technique)
    - - McNemar's exact test ("McNemar's chi-square test")
      - Fisher's exact test ("Chi-square")
  - - - Rate ratio (2 groups)
      - Kaplan-Meier statistics (2 or more groups)
        
        Non-parametric estimate of the survival function
        
        Empirical probability of surviving
        
        Taking into account of censoring
        
        Compare different group by log-rank test (a type of chi-square test)
      - Cox regression (multivariate regression technique)
    - - Frailty model (multivariate regression technique)