Biostats test 4

Question 1

What is binary logistic regression

Answer 1

prediction of a binary-valued DV on the basis of other variables, so response variable is not continuous, but binary-valued, as in:

yes/no, has/does not have, alive/dead, increased/decreased

Question 2

values of outcome variable

Answer 2

failure (coded 0) or success (coded 1)

success means “has the property”

Question 3

what do we try to predict with binary logistic regression

Answer 3

the probability of succes (DV = 1) on the outcome variable as a function of covariates: p(success) = f(cov1, cov2, …)

so probability of success is a function of covariates

Question 4

Assumptions of binary logistic

Answer 4

• categories must be mutually exclusive (no overlap) and collectively exhaustive (all cases can be assigned)
• if so, for all cases, success or failure can be coded in the data

Question 5

Link function

Question 6

Similarities of BLR with OLS

Answer 6

• model building and its issues (colinearity, order of entry, influential cases)

Question 7

Dissimilarities of BLR with OLS

Answer 7

• DV is binary (categorical), not continuous
• Interpretation of coefficients
• Assessment of model fit/quality of obtained model

Question 8

How do we ensure the [0,1] restircuted outcome range for the predicted values

Answer 8

• link function (logit) is used to relate the linear model part to the outcome variable
• it transforms the predicted values so that the outcomes are restrained to fall in the meaningful 0 to 1 range
• Regression techniques that make use of some kind of link function are called Generalized Linear Models (GLM)

Question 9

The logit function

Answer 9

• Natural logarithm of odds
• Logit = ln(odds) = ln(y hat/1-y hat)

Question 10

The logistic regression model when combined with the logit (link) function

Answer 10

ln(y hat/1-y hat) = b0 + b1X1 + b2X2 + …

So the difference with OLS model is on the dependent variable side of the model

Question 11

In OLS, rather than looking at the B coefficients themsleves, we look at

Answer 11

• ODDS RATIO = e to the bower of b, where e is the base of natural log ln
• change in the odds (of success) for a one-unit change in the predictor

Question 12

Wald test

Answer 12

Gives the p-value of the odds ratio

Question 13

Under H0, odds ration is

Answer 13

• Odds ratio = 1

Question 14

Multiplicative effect

Answer 14

The combined effect of predictors on the DV is a product of separate effects, so the effects of odds ratios multiply in binary logistic regression, while they add up in ordinary linear regression

Question 15

From probabilities to classification - what is classification of cases based on?

Answer 15

The predicted probabilities for success. The default setting for classification as ‘success’ is a predicted probability for success > .50.

Question 16

confusion matrix

Answer 16

the confusion matrix in your output gives predicted versus observed successes and failures, based on the cut-value

Question 17

Classification errors

Answer 17

false positives and false negatives

Question 18

The null model

Answer 18

starting point in the model building, a model without any actual predictors

if have to predict without knowing anything about predictors, the LARGEST CATEGORY WINS!

Question 19

How to decide which covariates to include

Answer 19

in the end, need to classify cases as success or fail cases - two groups

Question 20

Received operating characteristic

Answer 20

a plot that illustrates the performance of a binary classifier system for different discrimination methods

typically gives true positive rate against the false positive rate at various cut value settings

allows to see how diff cut value settings affect that classification results of your classifier

lenient threshold (low cut value): sensitivity is up!

strict threshold (high cut value): specificity is up!

Optimum typically: combination of high sensitivity and high specificiity

Question 21

ROC curve

Answer 21

area under curve is overall indicator of diagnostic accuracyw

Question 22

what does (P/1-P) in the logistic regression model represent

Answer 22

It represents the ODDS of the event happening

Question 23

what data does logistic regression model use to calculate probabilities, eg in the height and gender example and how does it do it

Answer 23

Data it uses:
- predictor variable (x)
- binary dependent vairble

How it uses it:

1. during training the model fits the data to the logit = B0 + B1X equation, and learns B0 and B1 by estimating
   how X changes with Y
2. uses predictor variables to calculate log odds (by inputting the predictor into the logistic regression equation), then converts them into probabilities using log transformations
3. uses the cutoff to classify the observation into one of the two outcomes

Question 24

odds ratios

Answer 24

change in the odds (of success) for a one-unit change in the predictor

Question 25

under H0, what is the odds ratio for logistic regression model

Answer 25

1

Question 26

survival analysis is about

Answer 26

analyzing time-to-event data

Question 27

examples of descriptive research questions that would warrant survivial data

Answer 27

median survival time in clinical studies

how does the probability for an event change over time?

Question 28

examples of inferential research questions that would warrant survivial data

Answer 28

• What variables explain the time to event best?
• Do they shorten or lengthen the expected time?
• By how much?

Question 29

mortality

Answer 29

refers to dropout in data

Question 30

censored data

Answer 30

when you have partial information: if a case drops out, you do not know when if ever, the endpoint was reached. survival analysis is developed to take censored data into account.

Question 31

right-censored

Answer 31

event not experienced at the end of the study - might or might not occur later, we don’t know

Question 32

left censored

Answer 32

event occufrs during study, but starting point lies before start of study, so exact time interval is not known

Question 33

interval censored

Answer 33

event occurs during study, but not exactly known when

Question 34

non-censored data

Answer 34

start time is known, end point of interest reached during study

Question 35

non-informative sensoring

Answer 35

censoring is not related to the likelihood of developing the event of interest

Question 36

hazard rate

Answer 36

the probability for event to occur in a next (small) time interval, assuming the event has not yet occured. like instantaneous risk

Question 37

survival rate

Answer 37

cumulative probability for non-event for a certain amount of time after some starting point