Nemours Biomedical Research Statistics Course. Li Xie Nemours Biostatistics Core October 14, 2014

Transcription

1 Nemours Biomedical Research Statistics Course Li Xie Nemours Biostatistics Core October 14, 2014

2 Outline Recap Introduction to Logistic Regression

3 Recap Descriptive statistics Variable type Example of graphical displays Example of summary statistics Categorical variable (C) Quantitative variable (Q) Table Barplot Pie chart Density plot Stem and leaf plot Histogram * Count Relative proportion Marginal proportion Mean (with standard deviation (SD)) Median (with interquartile range (IQR)) Minimum, maximum

4 Recap Univariate analysis technique Examples (1 outcome, 1 covariate) Scenario Graphical technique Descriptive technique Inferential technique Q=βC+ε Boxplot Group mean (SD) Group median (IQR) Paired t-test Wilcoxon signed rank test Unpaired t-test Mann-Whitney U test ANOVA Kruskal-Wallis H test Simple linear regression Q=βQ+ε Scatterplot covariance Pearson correlation Spearman s correlation Kendall s tau Simple linear regression C=βC+ε Mosaic plot Count Relative proportion Chi-squared test Fisher s exact test Relative risk Odds ratio Agreement/concordance Simple logistic regression

5 Recap Multivariable analysis technique Examples (1 outcome, >1 covariates) Scenario Q=βC+βQ+ +ε C=βC+βQ+ +ε Inferential technique Multivariable/multiple linear regression Multivariable/multiple logistic regression In addition to those discussed in this course, there are other statistical analysis techniques that may at times be more suitable than others for specific purposes. ALL technique are based on assumptions and have strength and weaknesses. Know the techniques before use them. Calculate exhaustively descriptive statistics before beginning inferential statistics.

6 Logistic regression Logistic regression is used to analyze relationships between a dichotomous outcome variable (eg: yes/no recovery, yes/no survival, yes/no female, yes/not high risk ) and categorical & quantitative covariates (eg: yes/no comorbidity, age at diagnosis, BMI, yes/not smoker ) Logistic regression uses the covariates VARIABILITY to estimate the probability that a particular event of the outcome will occur if can estimate the probability of event in a dichotomous situation, automatically know the probability of non-event

7 Assumptions Unlike linear regression, logistic regression does not make any assumptions about linearity between outcome and covariate(s), and normality or homogeneity of variance of ε

8 Binary Logistic Regression In linear regression, the outcome is modeled as-is i.e.: height = age + ε In logistic regression, the probability of yes/no event happening is transformed into the log odds of yes/no event happening, and this log odds is modeled as a linear combination of the covariates i.e.: Probability of being taller than 5 ft Probability of being as tall as 5 ft = age + ε During interpretation, the log odds of yes/no event happen is transformed back into the probability of yes/no event happening

9 Recap: Statistical Model General form of a statistical model: g( y) f ( x) Simple linear regression Logistic regression y Pr( event ) ln( ) 1 Pr( event ) x x 1

10 Binary Logistic Regression A researcher is interested in the association between demographic factors and gun ownership. He has observed the following (informally) Men are more likely to own guns than women The older persons are, the more likely they are to own guns Caucasians are more likely to own guns than those of other races The more educated persons are, the less likely they are to own guns He retrieved survey results from the 2002 General Social Survey and would like to test these concepts in these data Is this study: prospective retrospective Is this study: cohort study case-control study randomized controlled trial Is this study: longitudinal cross-sectional

11 Binary Logistic Regression Variables are measured as such: Outcome: Havegun: no gun = 0, own gun(s) = 1 Covariate: 1. Sex: men = 0, women = 1 2. Age: entered as number of years 3. White: all other races = 0, white =1 4. Education: entered as number of years 1. What is the variable type of each covariate? 2. What summary statistics would you use to describe each covariate? 3. What graphic technique would you use to visually inspect age? 4. If you are to examine whether men who answered the survey are more highly educated than women who answered the survey, what would you do? 4. If you are to examine whether older men constituent a larger portion of survey responder than other age-sex groups, what would you do?

12 Binary Logistic Regression SPSS: Analyze Regression Binary Logistic Interpreting Coefficients ln[p/(1-p)] = β 0 + β 1 X 1 + β 2 X 2 + β 3 X 3 + β 4 X 4 e β X 1 X 2 X 3 X 4 1 β 1 β 2 β 3 β 4 β 0 What are the characteristics of an average (typical) gun owner? How well does education relate to gun ownership? What are the assumptions on which the inference is based?