Bias and Confounding

Question 1

Overarching categories of bias

Answer 1

Information bias

Selection bias

Question 2

Selection bias is especially common in ___.

Answer 2

Selection bias is especially common in case-control studies.

Question 3

Social desirability bias

Answer 3

People tend to systematically overreport things that make them look good, and underreport or underestimate things that make them look bad.

Question 4

Rule of thumb for confounding

Answer 4

If the effect estimate changes by at least 10% when accounting for the potential confounding variable, it can be assumed that the variable is indeed confounding.

Question 5

Ways to account for confounding in study design

Answer 5

1. Restriction (restrict to only one stratum, eliminating the confounding variable entirely)
2. Matching (design a paired study and do paired t tests)
3. Randomization of exposure

Question 6

Effect modification

Answer 6

There is a different level of relationship between the exposure and outcome due to the presence of the effect modifier.

Question 7

Can something be both an effect modifier and confounder?

Answer 7

Yes!

In this case, the stratum specific OR or RR are different from one another, AND different from the OR and RR overall, in the same direction.

Question 8

Simple vs complex regression

Answer 8

Simple = 1 independent variable

Complex = 2 or more independent variables

Question 9

Logistic regression

Answer 9

Used for binary dependent variables. Essentially, you convert the raw data into a percentage likelihood of binary variable x given an independent variable.

Question 10

The correlation coefficient

Answer 10

r

Ranges from -1 to 1. Absolute value determines strength of the relationship, sign determines direction.

Question 11

Interpretation of thresholds of r magnitude

Answer 11

r > | 0.6 | implies a strong correlation

r > | 0.8 | implies a very strong correlation

Question 12

Format of an equation derived from linear regression

Answer 12

y = β₀ + β_{<span>1</span>} x + e

β₀ = intercept

β₁ = slope

e = error term / residuals

Question 13

“Goodness of fit” measure

Answer 13

r²

Question 14

When testing whether or not a relationship determined by linear regression is statistically significant, the null hypothesis is. . .

Answer 14

. . . that the predicted value of y should be the average value of y for all sample datapoints regardless of the value of x.

Question 15

A simple linear regression model for a binary independent variable is effectively the same as . . .

Answer 15

. . . a two sample t test.

Question 16

Nondifferential bias

Answer 16

The frequency of errors is approximately the same in the groups being compared.

In general, nondifferential misclassification tends to result in estimates of effect that are closer to “null” than the true effect.

Question 17

hazard ratio

Answer 17

Expression of relative risk which quantifies the probability of an event (e.g. dying) during a particular time interval, given that a subject has survived until that time

Question 18

Multivariate linear regression

Answer 18

y = intercept + b1 x1 + b2x2 + residual error

Question 19

Multivariate logistic regression

Answer 19

ln(p/1-p) = intercept + b1 x1 + b2x2 + residual error

where p/1-p is the odds ratio of condition y.

Question 20

Multivariable models are useful for identifying . . .

Answer 20

Multivariable models are useful for identifying both confounding and effect modification

Question 21

A correlation coefficient and an effect estimate from a simple linear model (i.e., beta) can both give information about . . .

Answer 21

A correlation coefficient and an effect estimate from a simple linear model (i.e., beta) can both give information about the strength and direction of a relationship between two continuous variables.

Question 22

Preterm birth

Answer 22

When a baby is born before 37 completed weeks of gestation

1/10 infants in the US. Racial and ethnic differences are substantial.

Question 23

A cofounder should meet these three criteria

Answer 23

• It is associated with the exposure under study
• It is a cause or correlate of the outcome under study, independent of the exposure
• It is not a natural intermediate step between an exposure and outcome, nor is it naturally upstream of the exposure or downstream of the outcome.

Question 24

If stratum-specific RRs/ORs are equal to each other AND equal to the crude RR/OR, . . .

Answer 24

If stratum-specific RRs/ORs are equal to each other AND equal to the crude RR/OR, then the suspect variable is neither a confounder nor an effect modifier

Question 25

f stratum-specific RRs/ORs are equal to each other but are different from crude RR/OR, . . .

Answer 25

If stratum-specific RRs/ORs are equal to each other but are different from crude RR/OR, then the third variable is a confounder.

Question 26

If stratum-specific RRs/ORs are different from each other, . . .

Answer 26

If stratum-specific RRs/ORs are different from each other, then effect modification is present

Question 27

Methods of correcting for confounding

Answer 27

• In the design stage:
  
  • Stratification
  • Restriction
  • Randomization
• In the analysis stage:
  
  • Stratification
  • Statistical adjustment

Question 28

The intent of a model can be primarily ___ or ___

Answer 28

The intent of a model can be primarily explanatory or predictive

Question 29

As in all statistical tests, we are making ___.

Answer 29

As in all statistical tests, we are making inferences from a sample

Question 30

Generally, when designing a multivariable model, we want to choose variables that. . .

Answer 30

1. we know from other research to be important
2. add to the ability of the model to explain or predict the outcome
3. whose inclusion changes the parameter estimates of the main predictor(s) of interest substantially (a common rule of thumb is more than 10%), since this suggests that the additional variable is a confounder of the exposure-outcome relationship.

Question 31

Effect modification won’t be apparent from a regression model unless . . .

Answer 31

Effect modification won’t be apparent from a regression model unless you look for it.

The simplest way is to stratify data and re-analyze.

Question 32

With logistic regression and proportional hazards regression, the coefficients have a special meaning:

Answer 32

The antilogarithm of the coefficient equals the odds ratio (for logistic regression) and the relative hazard (for proportional hazards regression).

Question 33

The underlying assumption of multiple linear regression is that . . .

Answer 33

as the independent variables increase (or decrease), the mean value of the outcome increases (or decreases) in a linear fashion.

Question 34

The underlying assumption of multivariable logistic regression is that. . .

Answer 34

each one-unit increase in a predictor multiplies the odds of the outcome by a certain factor (the odds ratio of the predictor) and that the effect of several variables is the multiplicative product of their individual effects.

Question 35

The underlying assumption of proportional hazards models is that. . .

Answer 35

the ratio of the hazard functions for persons with and without a given risk factor is the same over the entire study period

This one has a special name, the proportionality assumption

Question 36

If the hazard of death were higher with surgery at the beginning of the study (as is often the case with surgical interventions because of perioperative mortality) but lower with surgery later in the study (because persons who survived after surgery had a longer life expectancy as a result of the beneficial effects of carotid endarterectomy), this would . . .

Answer 36

. . . violate the proportionality assumption.

Question 37

When the data do not support the proportionality assumption, proportional hazards analysis can still be performed by using . . .

Answer 37

When the data do not support the proportionality assumption, proportional hazards analysis can still be performed by using time-varying covariates.

Question 38

Time-varying covariates

Answer 38

Independent variables whose values change over time. With time-varying covariates, the proportional hazards model can correctly account for hazard ratios that vary over the course of the study

Question 39

A major study design advantage of proportional hazards analysis is that. . .

Answer 39

A major study design advantage of proportional hazards analysis is that it includes persons with varying lengths of follow-up.

Question 40

Censored

Answer 40

A person who does not experience the outcome of interest by the end of the study is considered censored

Question 41

Residual analysis

Answer 41

Method for determining goodness-of-fit. Residuals are the differences between the observed and the estimated values

Unfortunately, journals rarely print residual plots; readers must assume that the investigators reviewed them.

Question 42

Automatic variable selection algorithms

Answer 42

Computer programs which systematically test the contribution of variables in different ways in order to eliminate irrelevant variables or variables of questionable relevancy and arrive at a simplified equation.

Question 43

Hosmer–Lemeshow goodness-of-fit test

Answer 43

Works for logistic regression models. Compares the estimated-to-observed likelihood of outcome for groups of persons. In a well-fitting model, the estimated likelihood will be similar to the observed likelihood.

Question 44

The reliability of a model depends on . . .

Answer 44

The reliability of a model depends on its purpose

If the model is explanatory, reliability means that a different set of data would probably yield a model with the same variables and similar coefficients.

A reliable predictive model predicts outcomes equally well for settings or for data other than those for which it was developed

Question 45

As a rule of thumb, to have confidence in the results, there should be at least . . .

Answer 45

As a rule of thumb, to have confidence in the results, there should be at least 20 persons for each independent variable eligible to be included in a linear regression model and at least 10 outcomes for each independent variable eligible to be included in a logistic regression or proportional hazards model

Question 46

Even if a study has a large enough number of events per independent variable, the estimates of the association between a risk factor and an outcome may still be inaccurate if ___.

Answer 46

Even if a study has a large enough number of events per independent variable, the estimates of the association between a risk factor and an outcome may still be inaccurate if the risk factor is rare

Question 47

Non-differential misclassification tends to bias relative risk estimates . . .

Answer 47

. . . towards 1

Question 48

If you match on a characteristic, you can no longer . . .

Answer 48

If you match on a characteristic, you can no longer examine the association of this characteristic with the outcome.