Samuel S. Kingsley Advocate Illinois Masonic Hospital Στατιςτιγς Samuel S. Kingsley Advocate Illinois Masonic Hospital

Basic Concepts Mean: The average value Median: The middle value Mode: The most common value

Probability Distribution Function PDF X-axis: possible values that variable may take Y-axis: probability of each value Integral of density: 1 (sum of all probabilities must be 1)

Expected Value (Mean): = Variance: Standard Error (of the mean):

ABSITE Question Types Type I, II error & power Hypothesis testing (which test should be employed) Study types (RCT, retrospective, case control, etc) Sensitivity & Specificity

Error Types

Error Types Type I error = false positive (rejecting null hypothesis when it it true) Type II error = false negative (accepting null hypothesis when it is false); inadequately powered

What type of error has been committed? Trial comparing pepcid with placebo wrt GI bleed for patients who are NPO finds no difference when one truly exists? Type II RTC finds that patients receiving activated protein c have lower mortality than those receiving placebo when truly no difference exists? Type I

What type of error has been committed? Trial comparing pepcid with placebo wrt GI bleed for patients who are NPO finds no difference when one truly exists? Type II RTC finds that patients receiving activated protein c have lower mortality than those receiving placebo when truly no difference exists? Type I

What type of error has been committed? Trial comparing pepcid with placebo wrt GI bleed for patients who are NPO finds no difference when one truly exists? Type II RTC finds that patients receiving activated protein c have lower mortality than those receiving placebo when truly no difference exists? Type I

Power = false negative rate False negatives + true positives = 1 1- = power = probability of rejecting the null hypothesis when null hypothesis is false

…what exactly is hypothesis testing?

…what exactly is hypothesis testing?

Student t-test Let’s say we want to compare two medications used for treating hypertension: We (ideally) would take a sample of hypertensive patients and randomize members to one of the treatments. Subsequently, blood pressure measurements are taken and compared. You would average the BP measurements of each group and would likely observe a difference. How do you know if that difference truly exists or is due to chance?

Distributions In order to determine whether the outcomes of two measures are different, you compare the data points from one intervention with the datapoints from another intervention

History Student t-test Claude Guiness of Guiness brewery in Ireland used to hire Oxford graduates to provide quality control. The QA personnel would collect samples from a batch for analysis but it was unclear what relavance each sample had to the entire batch. William Sealy Gosset was one such graduate and during his time there developed a means to compare a sample’s mean to the mean of the entire production. However, there was a company policy that prohibited publication of intellectual property so he published it under the name Student.

Things that make a true difference more likely: Larger difference between the means Smaller variances within each data set The student t-test takes the absolute difference and indexes it by the sample variances This gives you a number: the t-value The Student distribution represents the probability of each t-value. t=1.96 occurs less than 5% there for the odds of randomly having a t-value of >1.96 is less than 5%. 2.45 p<0.01, 3.18<0.01. If you are only interested in whether drug x is strictly better (or worse) than y, use a one tailed test; if you are interested if the two drugs are different, use a two tailed test.

Hypothesis Testing For purposes of the ABSITE, you will need to know the following 1. Type of variable 2. Paired or unpaired 3. 1, 2, or >2 groups

Variable Types Continuous: measurements existing along the real number line (age, weight, blood pressure) Discrete: variables whose values exist along a real line but only take certain values (number of siblings) Ordinal: Numbers represent states that can be ordered but ratios between categories do not exist (states of health, satisfaction, pain) Nominal: Numbering used only to signify categorize (ethnicity, language, zip code)

Continuous Variables

Continuous Variables Paired t-test: same population before and after treatment Rather than having a treatment + control group, treatment=control group More power What if I’m comparing more than two medications?

Continuous Variables Paired t-test: same population before and after treatment Rather than having a treatment + control group, treatment=control group More power What if I’m comparing more than two medications?

Continuous Variables ANOVA (analysis of variances) For comparing greater than two populations Example: comparing 4 antihypertensives

Continuous Variables Multivariate Analysis: variety of different empirical approaches; most pertinent to medicine: Linear regression

Ordinal Testing

Ordinal Variables Wilcoxian signed rank: differences between paired treatments Mann-Whitney: differences between two unpaired treatments Kruskal-Wallis AOV: differences in more than one treatment

Nominal Testing

Nominal Variable McNemar: compares paired treatments using nominal variables Chi-Squared: differences between treatments for unpaired nominal variables Logistic regression: gives the probability of 1 given independent variable values  

Sensitivty: Probability of a positive tests conditional on patient truly positive “How good is test at identifying a positive?” Specificty: Probability of a negative test conditional on patient truly negative “How good is test at identifying a negative?” PPV: How likely patient is to be positive conditional on positive test NPV: How Likely patient is to be positive conditional on negative test Accuracy: Overall score

Clinical Study Design Do not employ hypothesis testing – descriptive: Case report Case series Employ hypothesis testing: Case control: divide populations into two groups based on outcomes and look for risk factors (lung cancer vs. no lung cancer) Retrospective: divide popultions into groups based on risk factors and look for correlation with outcomes (tobacco vs no tobacco) Prospective: divide populations into groups based on risk factor prior to development of outcome Subject to bias… Hard to prove causation…

Clinical Study Types Employ hypothesis testing and remove bias: Randomized controlled trials (RCT) Double Blinded RCT Multicentered RCT Meta analyses Combine data from multiple RCT to increase power, look at secondary outcomes

Markov Chain Monte Carlo Many variables follow complex distributions without continuous or closed form descriptions Rather than trying to solve problems, model them quantitively

Bayesian Analysis Frequentist approach Based on logic of surprise (if my results were much different that the way I view the world, I should change my view of the world). Threshold for surprise varies (p = 0.05 vs 0.01, etc) Bayesian analysis Incorporates greater amount of information given same data Rather than declaring that the null is rejected and the alternate is true, it gives the probability that the derived estimate is true

Bayesian Approach A,B B B A

Null: P(S) = P(F) Data: SSFSSFSSSF

Questions?

Sensitivity Specificity NPV PPV Case series/case control/retrospective/prospective/rct