Biostats/Epi II Final

Linear Regression — outcome type

Continuous (Gaussian); uses identity link

Linear Risk — outcome type

Binomial; uses identity link

Log Risk — outcome type

Binomial; uses log link

Logistic Regression — outcome type

Binomial; uses logit link

Poisson Regression — outcome type

Count or rate; uses log link

β₀ — Linear Regression

Expected value of Y for the reference group (e.g., males, age 0, no high school education)

β₀ — Linear Risk

Risk (probability) of the outcome in the reference group

β₀ — Log Risk

Log risk of outcome in reference group; exponentiated = risk for reference group

β₀ — Logistic Regression

Log odds of outcome in reference group; exponentiated = odds for reference group

β₀ — Poisson Regression

Log incidence rate in reference group; exponentiated = incidence rate for reference group

β₀ — Cox Proportional Hazard

Log hazard rate for reference group; exponentiated = hazard rate for reference group

β₁ — Linear Regression

For every 1-unit increase in age, E(Y) changes by β₁, conditioning on other covariates

β₁ — Linear Risk

Risk difference: estimated change in risk for every 1-year increase in age, adjusting for other covariates

β₁ — Log Risk

For every 1-unit increase in age, the log risk increases by β₁, conditioning on other covariates

β₁ — Logistic Regression

For every 1-unit increase in age, the log odds ratio increases by β₁, conditioning on other covariates

β₁ — Poisson Regression

For every 1-unit increase in age, the incidence rate increases by a factor of β₁, conditioning on other covariates

β₁ — Cox Proportional Hazard

For every 1-unit increase in age, the hazard increases by a factor of β₁, conditioning on other covariates

β₂ — Linear Regression

Change in E(Y) when sex changes from referent (male) to non-referent (female), conditioning on age and education

β₂ — Linear Risk

Risk difference comparing female to male, adjusting for age and education

β₂ — Log Risk

Log risk increases/decreases by β₂ when sex changes from male (referent) to female, conditioning on age and education

β₂ — Logistic Regression

Log odds increases/decreases by β₂ comparing female to male (referent), conditioning on age and education

β₂ — Poisson Regression

Incidence rate increases/decreases by β₂ when sex changes from male (referent) to female, conditioning on age and education

β₂ — Cox Proportional Hazard

Hazard increases/decreases by β₂ when sex changes from male (referent) to female, conditioning on age and education

β₃ — Linear Regression

Change in E(Y) from no HS (referent) to HS or college grad, conditioning on age and sex

β₃ — Linear Risk

Risk difference comparing HS or college grad to no HS (referent), conditioning on sex and age

β₃ — Log Risk

Log risk increases/decreases by β₃ from no HS (referent) to HS or college grad, conditioning on age and sex

β₃ — Logistic Regression

Log odds increases/decreases by β₃ from no HS (referent) to HS or college grad, conditioning on age and sex

β₃ — Poisson Regression

Incidence rate increases/decreases by β₃ from no HS (referent) to HS or college grad, conditioning on age and sex

β₄ — Linear Regression (interaction)

Incremental change in the relationship between age and outcome associated with being female

β₄ — Linear Risk (interaction)

Incremental change in risk difference in the relationship between age and outcome associated with being female

β₄ — Log Risk (interaction)

Change in log risk in the relationship between age and outcome associated with being female

β₄ — Logistic Regression (interaction)

Change in log odds in the relationship between age and outcome associated with being female

β₄ — Poisson Regression (interaction)

Change in log rate in relationship between age and outcome associated with being female; exp(β₄) = incremental change in IRR for age associated with being female

β₁ with interaction term (age × sex)

Change in outcome per 1-unit increase in age when sex is in the referent group (male = 0)

Cohort + binary outcome → model

Log risk, linear risk, or logistic regression; can estimate risk, RR, and RD

Case-control + binary outcome → model

Logistic regression only; can estimate odds only

Cohort + count or rate outcome → model

Poisson regression; can estimate incidence rates and IRR

Cohort + binary rare events → model

Poisson regression; can estimate risk ratio (RR)

Case report

Detailed descriptive report on a single individual; focuses on new or unusual symptoms; used for hypothesis generation

Case series

Detailed descriptive report on a single group of individuals defined by a specific disease or outcome

Ecological study — unit of analysis

The GROUP (e.g., country, state); both exposure and outcome are measured at the group level, not the individual

Ecological study — metric

Measures prevalence and incidence; useful for rare diseases and hypothesis generation

Ecologic fallacy

Primary bias of ecological studies; associations observed at the group level do not necessarily hold true for individuals

Ecological study — strengths

Inexpensive; uses routinely collected data; excellent for hypothesis generation; useful for inherently group-level questions

Ecological study — limitations

Ecologic fallacy; limited ability to adjust for confounders; can mask individual-level relationships

Cross-sectional study

"Snapshot" study; individuals defined by exposure and disease status at a single point in time; measures prevalence

Cross-sectional study — metric

Exposure prevalence in relation to disease prevalence; can estimate risk via prevalence ratios

Cross-sectional study — strengths

Quick and inexpensive; high generalizability; temporal issues less concerning for long-term inalterable exposures (e.g., genetics)

Cross-sectional study — temporal sequence limitation

Cannot determine if exposure preceded the outcome (e.g., does inactivity cause CHD, or does CHD cause inactivity?)

Survivorship bias (cross-sectional)

Only captures those who survived long enough to be in the study; ignores those who died or left due to the outcome

Cohort study — definition

Individuals defined by exposure status and followed forward in time to see if they develop the outcome; must NOT have outcome at enrollment

Cohort study — metrics

Estimates incidence, risk ratios (RR), and risk differences (RD)

Cohort study — strengths

Excellent for establishing temporal sequence; can calculate true risk; best observational design

Cohort study — limitations

Expensive; requires large samples and long follow-up; loss to follow-up can undermine validity; inefficient for rare diseases

Case-control study — definition

Individuals defined by outcome status (cases have disease, controls do not); past exposures are then compared between groups

Case-control study — metric

Can ONLY calculate odds ratios (OR); cannot calculate absolute risk or incidence

Case-control study — strengths

Efficient for rare diseases or long latency; useful when exposure data is expensive or difficult to obtain

Case-control study — limitations

Highly susceptible to recall bias and selection bias; limited to one outcome; inefficient for rare exposures

Experimental study (clinical trial) — definition

Investigators actively assign individuals to groups (e.g., treatment vs. placebo) and follow them to measure outcome incidence

Experimental study — strengths

Gold standard for evidence; randomization ensures group similarity at baseline and balances measured and unmeasured confounders

Experimental study — limitations

Expensive and resource-heavy; requires long follow-up; ethical concerns if risks/benefits not yet well understood

Causal (directed) path — DAG

All arrows point away from exposure toward outcome (e.g., E→M→D); represents the effect you are trying to estimate

Non-causal (backdoor) path — DAG

Contains at least one arrow pointing "the wrong way" (e.g., E←C→D); represents potential confounding/bias

Open path — DAG

Association can flow between variables; open non-causal paths represent bias that must be controlled

Closed (blocked) path — DAG

Association cannot flow through the path; naturally blocked by a collider

Collider — definition

A variable that is a common "child" of two variables on the same path; arrows from two different variables collide at this node (e.g., E→C←Z)

Collider — rule

Do NOT adjust for colliders; adjusting opens a previously closed path and creates a spurious association between its parent variables

Blocking an open path — DAG

Adjust for (condition on) a non-collider variable along that path

Minimally sufficient adjustment set

The smallest set of variables you must condition on to block all open non-causal paths while keeping causal paths open

Mediator — DAG adjustment rule

Generally do NOT adjust for mediators (E→M→D) unless estimating the direct effect rather than the total effect

Why use multivariable regression?

To control for confounding, identify independent associations, or evaluate interaction (effect measure modification)

Interaction term — when to use

When the effect of the main exposure differs across levels of another variable (e.g., effect of smoking on death differs by sex)

Interpreting main effect when interaction is present

Do not say "adjusting for"; interpret as the effect of the exposure "when the other variable = 0" (the referent group)

Poisson regression — when to use

Counts (e.g., number of clinic visits) or rates (e.g., mortality rates)

Poisson regression — offset term

log(person-time); adjusts for unequal follow-up time across individuals, standardizing results into a rate

Poisson regression — coefficient interpretation

Incidence rate ratio; "for every 1-unit increase in [predictor], the incidence rate changes by a factor of X"

Poisson regression — assumptions

Mean equals variance; independence

Survival analysis — key distinction

Considers WHEN an event happens, not just IF it happens

Kaplan-Meier

Non-parametric method that re-estimates survival probability at every event time

Median survival time

The time point on a KM curve where survival probability = 0.50 (50%)

Cox proportional hazards model

Estimates the hazard — instantaneous risk of the event occurring at time t given survival up to that point

Hazard ratio (HR)

Represents the relative risk of the event occurring at any given moment between two groups

Proportional hazard assumption

The hazard ratio between groups must remain constant over the entire follow-up period; underlying hazards can vary but their ratio stays the same

Right censoring

Most common type; participant exits before the outcome occurs (lost to follow-up or administrative censoring at study end)

Left censoring

The event occurred before the observation period began

Informative censoring

Reason for dropping out is related to the outcome (e.g., too sick to continue); introduces bias; ideally want non-informative censoring

Why use KM/Cox over logistic regression?

Survival methods account for timing of events and use data from censored individuals rather than discarding it

Loss to follow-up bias

Type of selection bias; participants who leave the study differ systematically from those who remain, distorting results

Non-response bias

Type of selection bias; those who do not respond to a survey/study differ from those who do

Healthy worker effect

Type of selection bias; workers are healthier than the general non-working population, making occupational exposures appear less harmful

Berkson's bias

Hospital patient bias; individuals in the hospital differ from the general population, distorting case-control studies using hospital controls

Recall bias

Type of information bias; cases remember past exposures differently than controls, distorting exposure estimates

Interviewer bias

Type of information bias; interviewer probes cases and controls unequally, influencing reported exposures

Confounding

A third variable distorts the exposure-disease relationship; it is associated with both the exposure and the outcome and is not on the causal pathway

Which of the following are common purposes of multivariate analyses?

Control confounding; Estimate associations adjusted for multiple covariates/predictors; Identify associations that are independent of other variables

In practice, how can the status of a path be changed from open to closed?

Restriction, stratification, multivariate regression, matching

Hair loss predicts disease A. Hair loss is a marker for high hormone levels, which are causally related to disease A. If you look at a sample all with the same hormone level, what would you expect to see?

Hair loss is not a predictor of disease A in the sample

A cohort study investigates smoking (4 categories: non-smokers; <1 pack/week; 2 packs/week; >2 packs/week) and colon cancer. Which statement about estimating strength of association is TRUE?

The most logical approach would be to calculate the relative risk of each of the smoking groups using non-smokers as a reference group

In order to estimate the excess risk caused by a risk factor, which measure of association should be calculated?

Risk difference

Case control studies are most useful in the following scenarios EXCEPT:

When the disease is rare

When the exposure is rare

When the disease has a long latency period

When little is known about the disease

When it is difficult or expensive to obtain exposure data

None of the above

When the exposure is rare