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94 Cards in this Set

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What is a rate (as compared to a proportion or ratio)?
A change in disease status per unit of time or per disease event (these are the "dimensions")
Which measures of disease are proportions?
Cumulative Incidence and Prevalence
What measures of disease is a rate?
Incidence Density
Which measures of disease are ratios?
Odds, plus odds ratio, risk ratio and rate ratio.
Cross sectional studies can use what measures of disease?
Prevalence (point or period) or odds ratios.
Follow-up/ Propsective/Population-based studies can take which measures of disease?
Only *incident* cases are recorded in these studies: cumulative incidence and/or incidence density.
What is the formula for ID?
Incidence Density = (# new cases during time period)/(total person time at risk)
How is ID used?
To measure risk in populations and to test etiologic hypotheses.
What are the three ways PT (person time) is measured?
1) add it up.
2) in steady state pop, PT = N*delta t
3)otherwise PT = N at the halfway interval * delta t or can subract (number of incident cases and withdrawals * .5 * delta t) from that number
No information about steady state, steady state, changing population.
What are the two ways CI is used? Is it a rate?
To predict individual risk and to test etiologic hypotheses. It is defined over time, but IS NOT A RATE.
How is CI measured?
Simple, Actuarial or Density methods.
Formula for Simple CI
Incidence/N' at baseline = delta t year risk
Formula for Actuarial CI
Incidence/(N' at baseline - (W/2)) where W includes any removal from the study other than incidence (including death).
Formula for Actuarial CI over multiple years
1 - Π(1-Rj) where Rj is the CI at each year of the study
Formula for Density calculation of CI (assumes a closed cohort with no competing risks, age interval ID is constant)
1 - e^(-ID*Δt)
Formula for Density CI over multiple years
1 - e^(-Σ (IDj*Δt)) or 1 - Π(1-Rj) where Rj is the CI at each year of the study
Relationship between CI (density method) and ID?
They are roughly equal when:
time period is short
incidence is low (<10%)
rate is constant
population is fixed
Difference between hazard rate and incidence density?
Hazard is an instantaneous rate, ID is an average relative rate.
Formula for Infant Mortality Rate
Infant deaths in a calendar year/live births in sme calendar year - presented as per 1,000 or 100,000 live births
Formula for Neonatal Mortality Rate
Number of deaths during a calendar year of < 1 year/number of live births during same year, per 1,000 live births
Formula for Postneonatal Mortality Rate
same as NMR, but children aged 1 to 11 months
Formula for Maternal Mortality Rate
Number of deaths from puerperal causes in a year/number of live births per 100,000
Formula for Natality Rate
Live births during interval/total pop at mid interval, per 1,000
Formula for Fertility Rate
Live births during interval/# of women aged 15-44 y ears at mid interval, per 1,000
Formula for Crude Natural Increase
(Live births - number of deaths during interval)/population at mid-interval, per 1,000
Formula for Low Birth Weight Ratio
Live births < 2500 grams during interval/live births during same interval, per 100
Formula for Attack Rate
Incident cases/total pop at risk over restricted period of observation
Formula for Case Fatality Rate
Deaths due to THIS disease among incident cases/incident cases
Formula for Death to Case Ratio
Deaths attributed to THIS disease/new cases of THIS disease during same time period (a ratio, because some deaths may not be new cases in this interval)
Formula for Proportionate Mortality
Number of deaths due to THIS disease/number of all deaths (leading cause of death is..., while next biggest is...)
Formula for Proportionate Mortality Ratio
PM in one group/PM in another group
YPLL (Years of Potential Life Lost)
Sum of differences between mean age of death of pop Y (for instance) and actual age of death for those dying before mean fo a particular cause.
YPLL Rate
YPLL per 1,000 below mean age of death of pop Y (or 65y, or whatever cut point is)
Direct Age Adjustment
Compare 2 real populations against a third, standardized, population. Create age stratum death totals for new population with rates from A and B. Sum across each group and divide each by total standard population. This is Age Adjusted rates, and are comparable. Does not results in SMR.
Indirect Age Adjustment
Rates from standard population are applied to population A. Observed deaths (actual) in A/expected deaths from calculations = SMR. Do not compare one SMR to another.
Fixed (Closed) Cohort
No one can be added or removed, members are only lost to death or to disease of interest. N't = N'o*e^(-ID*Δt)
When do you begin measuring person time in an open cohort?
Begins when exposure begins, not at beginning of calendar year.
Prevalence = Incidence*mean duration of illness in population
If pop is steady state, and disease is rare (prevalence < 10%) and not chronic -> the number of people with the disease (prev) will roughly equal the number of people who get the disease * the lenght of the disease.
Measures of Disease
How much disease is in the population or group we're looking at?
Measures of Effect
What is the quantifiable effect of the exposure we're looking at?
What are the Ratio Measures of Effect?
IDR, CIR, OR, Hazard Ratio
What are the measures of RR in a cohort study (counts or person time), a case control study (counts) and a cross-sectional study (counts)?
Cohort Study with Counts: CIR
Cohort Study with PT: IDR
CC Study (Counts): OR
Cross Sectional (Counts): PR or OR
Formula for Incidence Density Ratio (a rate ratio)
(a/PTe)/(c/PTo)
the time dimension cancels out, leaving a rate ratio.
Formula for Cumulative Incidence Ratio (a risk ratio)
CIe/CIo or (a/(a+b))/(c/(c+d))
Odds Ratio - what's the difference between OR and EOR?
OR is odds of disease in ex/odds of disease in unexp, and is technically what you're measures in a cohort study. EOR is odds of exposure in diseased/odds of exposure in undiseased, and is technically what you're measure in a case control study. They are equivalent, though: ad/bc
OR and Risk Ratio
OR approximates the RR when disease is rare. Put another way, as the value of the RR approaches 1, the OR approaches the RR, until they can be the same at 1. As the RR gets farther from 1, the OR gets farther from the RR (more extreme).
Absolute Measures of Association (Difference Measures)
Risk Difference = Attributable Risk (RD is same as AR)
Pop Risk Difference = Pop Attributable Risk
Linear Regression
Ro, Re, Rt
Ro = risk or rate in unexposed
Re = risk or rate in exposed
Rt = risk or rate in total population
Pe
Prevalence of exposure in general population (may be estimated from noncase prevalence, or from subject matter experts)
Relative Risk or Relative Rate
Re/Ro is relative risk or rate of disease (depending on whether CIR or IDR is the underlying measure)
Risk Difference or Excess Risk
Re - Ro is difference in risk or rate in exposed vs. unexposed. This is the risk that would be prevented IN THE EXPOSED GROUP by eliminating the exposure.
Formula for AR in Case Control
(OR * Io)-(It/((OR*Pe)+Po))
Formula for Attributable Risk % in Any Study
((RR-1)/RR)*100
Formula for Attributable Risk in non-Case Control Studies
Ie-Io
Formula for Population Attributable Risk %
How much disease among the total population would be eliminated if exposure were eliminated?
((Pe*(RR-1))/(Pe*(RR-1)+1))*100
Formula for Population Attributable Risk (Population Risk Difference)
The excess risk or rate of disease in the total population associated with the exposure.
Ie - Io or AR*Pe
Population Attributable Risk %
((It - Io)/It) * 100 or
((Pe * (RR-1))/(Pe * (RR-1) + 1))*100
Type I (alpha) Error
Ho is true, but we reject it.
What is type II (beta) error?
Ha is true, but we fail to reject Ho. The power of a statistical tests is (1-beta) - this measures the ability of a test to correctly reject Ho when Ha is true.
What are the problems with p values?
Mixes the size of association and the precision of association (a big sample will usually produce a small p, even if the association is minor or missing).
It is easily misinterpreted: it is NOT a sign of causality, and it is NOT the probability that the Ho is true.
Confidence Interval Interpretation
If the study were repeated 100 times, 95 of the confidence intervals would contain the true measure of association.
Zα's
.1 (90%) = 1.64
.05 (95%) = 1.96
.01 (99%) = 2.576
Var for ln(CIR)
(b/(a*Ne))+(d/(c*No)
Var for ln(IDR)
(1/a)+(1/c)
Var for ln(OR)
1/a + 1/b + 1/c + 1/d
Formula for MH Statistic for Odds Ratios
(Σ(ai*di)/Ti)/(Σ(bi*ci)/Ti)
What is MH Χ^2? What is the null hypothesis?
Ho: RRmh = 1
Is there an association between exposure and disease? When p is low, there is.
Confounding is present when...
...the risk of disease in the unexposed group is not the same as that in the counterfactual unexposed group.
Exchangeability means...
...if the exposure was removed from the exposed group, the two groups would be identical. If you cannot assume this, you have confounding.
What are the steps for identifying backdoor pathways in DAGs?
0.Identify confounder
1.No variables in C should be descendants of E
2.Delete all non-ancestors of {E, D, C}
3.Delete all arrows emanating from E
4.Connect any two parents with a common child
5.Strip arrowheads from all edges
6.Delete C
7.Test: If E is disconnected from D in the remaining graph, then adjustment for C is sufficient to remove confounding
Should you control for things in the exposure-outcome causal pathway of DAGs?
No. If you control for "tar" in a study of smoking and lung cancer, you have controlled for your exposure by removing a link in the causal pathway. Your analysis of E and O becomes worthless. So, is your variable something in the pathway, or is it a confounder (or does it have nothing to do with E and O)?
On controlling indirect confounders
After you do the steps to determine if you have a backdoor pathway, you have to break the pathway by removing one additional variable. Even if it's not a direct confounder of the E->D relationship, that pathway will SHOW an association until you break the path.
Identifying Confounder in DAGs
1.Remove all edges showing direct effects of exposure of interest (including to outcome).
2.Do exposure and outcome share an ancestor (a common cause), now? Only forward point arrows (C causes E and O) count. If "yes" - there is confounding with that ancestor.
Three ways to reduce confounding in design phase
Restriction
Randomization
Matching
Ways to Reduce Confounding in Analysis Phase
Stratifed analysis
Multivariate analysis
Effect Modification
1.Finding to be reported and not eliminated/adjusted for.
2.Details the true relationship between an exposure and outcome.
3.Natural phenomenon that exists independently of the study design.
4.Presence and interpretation depends on the effect measure (ratio vs. difference)
Three features of effect modifiers
Change relationship between exposure and outcome
Biological interaction DOES NOT EQUAL statistical interaction
Are scale dependent
Effect Modification Additive vs. Multiplicative
Additive variation is in the RD across groups.
Multiplicative variation is in the RR across groups (rel. risk).
Steps to Check for EMM or Confounding
1.Stratify and estimate RR for each strata.
2.Determine whether EMM is present - use test of homogeneity, if there is a possibility.
3.If yes, report stratum specific RR estimates and CIs.
4.If no, is confounding present? Test RRmh vs. RRunadj.
5.If yes, report RRmh with CI, and look for evidence of effect.
If no, Report RRunadj with CI.
Test of Homogeneity: Ho
The RRs from different strata do not differ from an estimate of the RR for the combined groups. (If rejected, there IS EMM)
Test of Homogeneity Steps
1.Calculate CIRmh
2.Calculate var ln(CIR) for strata
3.Calculate chi^2
4.Determine df
5.Accept or reject Ho
6.Conclude
A priori Confounding Criteria
C must be independently associated with E
C must be an independent risk factor for D
C must not be on the causal pathway
Χ^2 Mantel Haenszel Test Ho
There is no association between E and O, when confounder is held constant (RRmh)
Logistic Regression
A linear model of the log odds of a binary outcome
ln(p/(1-p))=B0+B1X1+B2X2...
Logistic Regression: OR for one Exposure
e^Bof interest
Collapsibility in RR and ER/AR
If RRpooled = RRstrata and C and D are not associated in both the exposed and the unexposed and C and E are not associated, the strata are collapsible.
Collapsibility in OR
If ORpooled = ORstrata and C and D are not associated in both the exposed and the unexposed and C and E are not associated in both the diseased and the undiseased, the strata are collapsible. If disease is rare, OR approximates RR, so special conditions are not a problem.
What is Collapsibility?
A statistical means of identifying potential counfounders. If the RRpooled = RRstrata and other conditions are met, confounding is not present. If not, counfounding may be present, and needs further investigation.
Cohort Study Frequency Measure: Acute Disease
Fixed (or dynamic treated as fixed) population, cumulative incidence is measure.
What is the cohort study frequency measure given chronic disease or death as outcome (something you can't recover from)?
A dynamic population is assumed, incidence density is measure (or mortality density).
Cross-Sectional Studies: Extended Risk Period (Diabetes) Frequency Measure
Incidence density
Cross-Sectional Studies: Restricted Risk Period (Birth Defects) Frequency Measure
Cumulative incidence (relative risk)
What are measures of Relative Risk or Risk Ratio?
Odds Ratio, Prevalence Ratio, or Cumulative Incidence Ratio
Rate Ratio
Incidence Density Ratio (or any ratio of two risks identified as rates by author)