Overview of Biostatistical Methods

Randomized

Clinical Trials (RCT)

X

Treatment population Control

population

0

Overview of Biostatistical Methods

Randomized

Clinical Trials (RCT)

Examples: Drug vs. Placebo, Drugs vs. Surgery, New Tx vs. Standard Tx Let X = decrease (–) in cholesterol level (mg/dL);

Patients satisfying inclusion criteria

RANDOMIZE

Treatment Arm

Control Arm

RANDOM SAMPLES

End of Study

T-test F-test

(ANOVA)

Experiment

~ GOLD STANDARD ~Designed to compare two or more treatment groups for a statistically significant difference between them – i.e., beyond random chance – often measured via a “p-value” (e.g., p < .05).

significant?

1 2

0 1 2:H

possible expected distributions:

S(t) = P(T > t)

0

1

T

Overview of Biostatistical Methods

Randomized

Clinical Trials (RCT)

Examples: Drug vs. Placebo, Drugs vs. Surgery, New Tx vs. Standard Tx

~ GOLD STANDARD ~Designed to compare two or more treatment groups for a statistically significant difference between them – i.e., beyond random chance – often measured via a “p-value” (e.g., p < .05).

Let T = Survival time (months);

End of Study

Log-Rank Test,Cox Proportional Hazards Model

Kaplan-Meier estimates

population survival curves:

significant?

S2(t)Control

S1(t)Treatment

AUC difference

0 1 2: ( ) ( )H S t S t

survival probability

Overview of Biostatistical Methods

Case-Control studies

Case-Control studies

Cohort studiesCohort studies

E+ vs. E–

Overview of Biostatistical Methods

Observational study designs that test for a statistically significant association between a disease D and exposure E to a potential risk (or protective) factor, measured via “odds ratio,” “relative risk,” etc. Lung cancer / Smoking

PRESENT

E+ vs. E– ? D+ vs. D– ?

Case-Control studies

Case-Control studies

Cohort studiesCohort studies

Both types of study yield a 22 “contingency table” of data:

D+ D–

E+ a b a + b

E– c d c + d

a + c b + d n

relatively easy and inexpensive subject to faulty records, “recall bias”

D+ vs. D–

FUTUREPAST

measures direct effect of E on D expensive, extremely lengthy…

Example: Framingham, MA study

where a, b, c, d are the numbers of individuals in each cell.

cases controls reference group

End of Study

Chi-squared Test

McNemar TestH0: No association between D and E.

–1 0 +1

Overview of Biostatistical Methods

As seen, testing for association between categorical variables – such as disease D and exposure E – can generally be done via a Chi-squared Test.

But what if the two variables – say, X and Y – are numerical measurements?

Furthermore, if sample data does suggest that one exists, what is the nature of that association, and how can it be quantified, or modeled via Y = f (X)?

JAMA. 2003;290:1486-1493 Correlation Coefficient

measures the strength of linear association

between X and Y

X

Y

Scatterplot

r

positive linear correlation

negative linear correlation

–1 0 +1

Overview of Biostatistical Methods

As seen, testing for association between categorical variables – such as disease D and exposure E – can generally be done via a Chi-squared Test.

Furthermore, if sample data does suggest that one exists, what is the nature of that association, and how can it be quantified, or modeled via Y = f (X)?

JAMA. 2003;290:1486-1493 Correlation Coefficient

measures the strength of linear association

between X and Y

X

Y

Scatterplot

r

positive linear correlation

negative linear correlation

But what if the two variables – say, X and Y – are numerical measurements?

–1 0 +1

Overview of Biostatistical Methods

As seen, testing for association between categorical variables – such as disease D and exposure E – can generally be done via a Chi-squared Test.

Furthermore, if sample data does suggest that one exists, what is the nature of that association, and how can it be quantified, or modeled via Y = f (X)?

JAMA. 2003;290:1486-1493 Correlation Coefficient

measures the strength of linear association

between X and Y

X

Y

Scatterplot

r

positive linear correlation

negative linear correlation

But what if the two variables – say, X and Y – are numerical measurements?

Overview of Biostatistical Methods

As seen, testing for association between categorical variables – such as disease D and exposure E – can generally be done via a Chi-squared Test.

Furthermore, if sample data does suggest that one exists, what is the nature of that association, and how can it be quantified, or modeled via Y = f (X)?

Correlation Coefficient

measures the strength of linear association

between X and Y

But what if the two variables – say, X and Y – are numerical measurements?

For this example, r = –0.387(weak, negative linear correl)

For this example, r = –0.387(weak, negative linear correl)

residuals

Overview of Biostatistical Methods

As seen, testing for association between categorical variables – such as disease D and exposure E – can generally be done via a Chi-squared Test.

Furthermore, if sample data does suggest that one exists, what is the nature of that association, and how can it be quantified, or modeled via Y = f (X)?

But what if the two variables – say, X and Y – are numerical measurements?

Want the unique line that minimizes the sum of the squared residuals.

Simple Linear Regression gives the “best” line

that fits the data.

Regression Methods

?

For this example, r = –0.387(weak, negative linear correl) For this example, r = –0.387(weak, negative linear correl)

Y = 8.790 – 4.733 X (p = .0055)

residuals

Overview of Biostatistical Methods

As seen, testing for association between categorical variables – such as disease D and exposure E – can generally be done via a Chi-squared Test.

Furthermore, if sample data does suggest that one exists, what is the nature of that association, and how can it be quantified, or modeled via Y = f (X)?

Regression Methods

But what if the two variables – say, X and Y – are numerical measurements?

Want the unique line that minimizes the sum of the squared residuals.

Simple Linear Regression gives the “least squares”

regression line.

Furthermore however, the proportion of total variability in the data that is accounted for by the line is only r 2 = (–0.387)2 = 0.1497 (15%).

Overview of Biostatistical Methods

Extensions of Simple Linear Regression

• Polynomial Regression – predictors X, X2, X3,…

• Multilinear Regression – independent predictors X1, X2,

…

w/o or w/ interaction (e.g., X5 X8)

• Logistic Regression – binary response Y (= 0 or 1)

• Transformations of data, e.g., semi-log, log-log,…

• Generalized Linear Models

• Nonlinear Models

• many more…

Overview of Biostatistical Methods

Sincere thanks to

• Judith Payne

• Heidi Miller

• Rebecca Mataya

• Troy Lawrence

• YOU!