lecture 4

what type of graph does this describe? •Top of box at third quartile •Bottom of box at first quartile •Box shows the middle 50% of data; a.k.a. interquartile range •Median/midpoint depicted as a bar in the box middle •Whiskers at 1.5 X interquartile range above the 75th and below the 25th percentiles •Values outside the whiskers are outliers

Box Plot (A.k.a. Box and Whisker Plot)

what type of test is the only valid way of predicting a time-dependent outcome?

Cox Proportional Hazards Regression

Ad hoc analysis

Focuses on answering specific, one-off questions or addressing unforeseen problems that arise

what type of graph does this describe? •Line graphs •Created by connecting the midpoints of histogram columns

Frequency polygons

the preferred method for showing survival (Provides exact estimates of survival each time a patient dies)

Kaplan-Meier Curve

does correlation imply causation?

NO

One-way ANOVA vs two-way ANOVA

One-way ANOVA uses one independent variable two-way ANOVA uses two independent variables

what type of sampling is this? •Each member of the population has the same probability of being selected •Random number table/pseudo-random computer number generator. •Downside: can over-sample from one group of homogenous strata

Simple Random Sampling

intention to treat

aims to preserve the original randomization and to avoid potential bias due to exclusion of patients •Includes all patients enrolled in the study in the analysis •Patients who are enrolled are included in the analysis for the group they were randomized to even if they drop out/die

what does ANOVA analyze

analysis of variance •Looks for a difference between the means of the groups •If there is a difference, then need to make comparisons among pairs/combinations of groups

Censoring

analyzing survival for patients who are still living

research on two independent groups if nominal data (counts/frequencies)

chi-square

independent variable: nominal (qualitative) dependent variable: nominal which test is best?

chi-squared

what type of sampling is this? Create a sample by combining subgroups

cluster sampling

Descriptive statistics

collect and summarize data about a population

what type of sampling is this? •Availability sampling •Non-random •Commonly used in clinical studies •Geographical proximity •Availability at a given time •Randomly assign the members of the sample to treatment groups

convenience sampling

research on two independent groups if small sample size, small expected frequences

fisher's exact test

what type of graph does this describe? •Bars •X axis - measure of interest •Y axis - number of observations •Numbers or percentages •Area of each bar proportional to the number of observations

histogram

Pearson coefficient (r)

how close the data is to the line of best fit

Coefficient of determination (R^2)

how close the predicted values match the observed values (strength of a model)

independent variable: nominal dependent variable: numerical which test is best?

kaplan-meier

regression

linear relationship and outcome prediction

correlation

linear relationship between variables •Correlation coefficient (Pearson's) •Ranges from -1 to +1

correlation 0

no linear relationship

independent variable: >2 nominal variables dependent variable: numerical which test is best?

one-way ANOVA

correlation -1

perfect negative linear relationship

correlation +1

perfect positive linear relationship

independent variable: numerical dependent variable: numerical which test is best?

regression

what type of graph does this describe? •A.k.a. Bivariate Plot •Show relationship between two numerical characteristics •X - independent variable (cause) •Y - dependent variable (effect)

scatter plots

what type of plot does this describe? •Helps to show tally of observations •First step in creating a frequency table •Data observations is divided into subdivisions - classes/intervals •Stem is the first digit of each observation class Leaf is the second digit of each observation

stem and leaf plot

what type of sampling is this? •Population can be divided into homogenous strata •I.e., male/female gender •College grade levels •Prevents over sampling from one of the strata •Sample equal numbers from each strata •i.e., sample 100 college students, 25 from each of the four undergraduate grade levels Use simple random sampling within each strata

stratified sampling

what type of sampling is this? •Start with a random sample from the population •Choose a regular predetermined interval (every 10th person)

systematic sampling

independent variable: binary nominal dependent variable: numerical which test is best?

t test

research on two independent groups if outcome is measured numerically (assumes normal distribution & equal SD)

t test

research on one group - questions about means

t test - if normal distributions

Inferential statistics

take a sample of the population; make inferences about the entire population

research on one group if non-normal distributions

use a transformation (linear, non-linear: logs, nonparametric)

Multiple regression

used with two or more independent variables

research on two independent groups if skewed distributions or different standard deviations

wilcoxon rank sum

research on one group - questions about proportions

z distribution - if normal distribution

Propensity Scoring

•Alternative to multiple regression and analysis of covariance •Used to control for a group of confounding variables •Experimental studies the probability of being exposed (or unexposed) is 0.5 - its random

t test

•Answer research questions about one group of subjects measured on one or two occasions. •Very commonly used statistical test in medical research •Answer questions about means •Critical value is calculated using the α and sample size (degrees of freedom) •Test statistic is calculate using the sample mean and standard deviation, as well as the population mean and the number of samples

types of graphs/plots to use for nominal (qualitative) data - counts/frequency of occurrences

•Contingency Table •Bar Chart •Pie Chart Pictograph

Linear Regression

•Correlation describes a relationship, and regression describes both a relationship and predicts an outcome •Regression involves predicting the value of one characteristic from knowledge of another

frequency tables

•Display the frequency of observations (E.g., number of patients, percentages) •Created after data is divided for stem and leaf plot •Data divided into classes as in stem and leaf

Pre-specified Analyses

•More "respected" •Identify good prior reasons for anticipating that the proportional effects of treatment might be very different in different circumstances •Pre-specify a particular subgroup analysis in the study protocol •Include a prediction of the direction of the proposed interaction

number needed to harm

•Number of people who need to be treated to cause harm to one more person •1/ARI •ARI is the difference in the incidence of harm in people treated and the incidence of harm in the people not treated.

number needed to treat

•Number of people who need to be treated to prevent one event •1/ARR •If small ARR, larger number of people need to be treated to prevent one case

Comparing Two Frequency Distributions

•Percentage polygon •Like a frequency polygon •But converted to percentages

Chi Square

•Qualitative (nominal) variables •Tests for independence between the variables •Compares the observed frequencies in each group to the expected frequencies *Avoid when expected frequency is 2 or less

Fisher's Exact Test

•Replacement for Chi Square for nominal variables when there are small sample sizes and frequency expected events is 2 or less, and using a 2 x 2 table •Determines the probability of the observed frequencies

Post hoc - "after this"

•Statistical analyses that were specified after the data were seen •Used to uncover specific differences between three or more group means when an analysis of variance (ANOVA) test is significant •Sometimes called data dredging •Statistical associations that it finds are often spurious •Motivated by a desire to produce positive results or see a project as successful

types of graphs/plots to use for numerical (quantitative) data - numbers

•Stem and Leaf Plots •Histogram •Box Plots •Frequency Polygon

Hypothesis Testing Steps

•Step 1: State the Hypotheses - null hypothesis (which is what we test) and the research hypothesis (which is what we expect) •Step 2: Find the Critical Values: α (how much of the area under the curve composes our rejection region) and the directionality of the test •Step 3: Compute the Test Statistic - collect data and calculate our test statistic •Different tests are used for different data, and are calculated in different ways, •Step 4: Make the Decision - compare the test statistic to the critical value •Decide whether to reject/fail to reject the null hypothesis

Subgroup analysis

•Tx effect on the outcome of interest differs according to the presence/absence of a baseline/demo-graphic factor •Statistical analysis of the influence of a baseline factor on the effect •Often used in clinical trials •Goal is to learn how to use the treatment most effectively

Cox Proportional Hazards Regression

•Used in studies that look at the impact of multiple variables on survival •Numerical and nominal variables •Independent variables can vary with time •Results used to determine relative risk/odds ratio associated with each variable

per protocol

•aims to identify a treatment effect which would occur under optimal conditions •Includes only those patients who completed the treatment originally allocated •If done alone, it leads to bias