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![Page 1: MDM Review 2009 12.14.09 Jason Sanders. Outline Measures of frequency Measures of association Study designs INTERMISSION Threats to study validity Defining.](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649de85503460f94ae2390/html5/thumbnails/1.jpg)
MDM Review 2009
12.14.09Jason Sanders
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Outline
• Measures of frequency• Measures of association• Study designs• INTERMISSION• Threats to study validity• Defining test and study utility• Descriptive statistics• Q and A
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Measures of disease frequency
• Incidence (risk, cumulative incidence, incidence proportion)
I = # new cases of disease during time period # subjects followed for time period
Important points: only new cases counted in numerator; time period must be specified
Benefits: easy to calculate and interpretDrawback: competing risks make I inaccurate over long time
periods
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Measures of disease frequency
• Incidence rate (rate)
R = # new cases of disease during time period total time experienced by followed subjects
Important points: only new cases counted in numerator; person time summed for each individual
Benefits: accounts for competing risksDrawback: not as easy to interpret
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Measures of disease frequency
• Prevalence (prevalence proportion)
P = # subjects with disease in the population # of people in the population
Important points: All people with active disease in numerator; can calculate “point” or “period” prevalence
Benefits: illustrates disease burdenDrawback: cross-sectional
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Disease frequency example
• You have a group of 100 people. At the start of the study, 10 have active disease. Over the course of 3 years, 18 new cases develop. You accrue 200 person-years of follow-up.
• Prevalence at start: 10/100 = 0.1 = 10%• Risk over 3 years: 18/(100-10) = 0.2 = 20%• Incidence rate: 18/200 = 0.09 cases per py
= 9 cases per 100 py
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Measures of disease frequencyProperty Incidence
(risk)Incidence rate (rate)
Prevalence
Smallest value 0 0 0Largest value 1 Infinity 1Dimensionality None 1/time NoneInterpretation Probability Rate; inverse
of waiting timeProportion
Attributable risk = Risk (E+) – Risk (E-) “Excess risk due to exposure”
Attributable risk % = [Risk (E+) – Risk (E-)] / Risk (E+) “% excess risk due to exposure”
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Questions on measures of disease frequency?
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Measures of association
RR = risk in E+ risk in E-
RR = rate in E+ rate in E-
OR = odds of E+ in cases odds of E+ in controls
Exposed Unexposed
# Cases NE NU
Total # or Total person-time
NTE or PTE NTU or PTU
E+ E-
Case A B
Controls C D
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Absolute vs. Relative measures of disease frequency
• Risk, rate, prevalence, AR are absolute measures– Used for describing disease burden, policy, etc.
• Relative risk, relative rate, prevalence proportion, odds ratio, AR% are relative measures– Used to describe etiology, association of disease with
exposure, etc.
RR can mean risk ratio or rate ratio
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Illustration of cohort study
Time
Risk E+
Risk E-
RR = Risk E+ Risk E-
“Exposed people are at X-fold greater risk to develop disease.”
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Illustration of case-control study
Time
Odds E+
Odds E+
OR = Odds E+ cases Odds E+ controls
“Cases have X-fold greater odds of being exposed.”
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• What if we could simultaneously achieve:– Prospective measurement of disease (i.e.
exposure came before disease)– Measurement of lots of confounders (for
adjustment)– Controls coming from same population as cases– Less recall bias– Less selection bias– Efficient, low cost study
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Nested case-control or case-cohort study
Time
You easily measure case/control status
But you know:1) E preceded D2) Other
confounders3) Controls
came from same group as cases
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Study design: observational studies (that count)Prospective cohort Retrospective
cohortCase-control
Study group E+ and E- groups E+ and E- groups Cases and controlsMeasures Rate ratio, risk
ratio, odds ratioRate ratio, risk ratio, odds ratio
Odds ratio
Temporal relationship
Possible to establish
Possible to establish Difficult to establish (except nested)
Time required Long follow-up Can be efficient Less time than othersCost Expensive Depends Relatively inexpensiveWhen to use? E is rare and/or D is
frequent among E+; investigate result of exposures
E is rare and/or D is frequent among E+; save time vs. prospective cohort
D is rare and E is frequent among D+; investigate causes of disease
Issues Selection of E-; loss to follow-up; change in E over time
Selection of E-; loss to follow-up; change in E over time
Selection of control group (selection bias); accurate E assessment (recall bias)
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Study design: experimental study (RCT)• Requirement: equipoise• Design:
– Randomize groups to new treatment or standard• Benefit: Balance frequency of KNOWN and UNKNOWN confounders in
groups (matching)• Drawback: Expensive; inefficient; doesn’t always work; can’t analyze
variables that are matched on
– Follow groups through time and assess endpoints (risk, survival, etc.)• Analysis:
– Intent-to-treat (on-treatment) • Benefit: Preserve randomization• Drawback: Subjects might not have followed treatment
– Efficacy• Benefit: Analyzes subjects who followed treatment for more accurate
assessment of treatment effects• Drawback: Breaks randomization; introduces more confounding
• Issues: loss to follow-up; time; cost; changing standard of care during study
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Measures in RCTs
Absolute risk reduction…attributable risk backwards:
ARR = Risk (Placebo) – Risk (Treatment) “Risk reduction attributable to treatment”
NNT = 1 / ARR “Number of patients you need to treat to prevent 1 case”
Relative risk reduction…attributable risk % backwards:
RRR = [Risk (Placebo) – Risk (Treatment)]/Risk (Placebo) “% Risk reduction attributable to treatment”
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What if we’re interested in the time to the event, and not just the event?
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Survival analysis, log rank, Cox proportional hazards
Bernier et al., NEJM. 2004.
HR=0.70, 95% CI 0.52-0.95
Proportional?
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Meta-analysis: steps
1) Formulate purpose2) Identify relevant studies3) Establish inclusion and exclusion criteria4) Abstract data5) Describe effect measure (OR, RR)6) Assess heterogeneity (Forrest plot, Q, I2)7) Perform sensitivity and secondary analyses8) Assess publication bias (Funnel plot)9) Disseminate results
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Can you group data: Forrest plot, Cochrane’s Q, I2
• Forrest plot – Illustrates size and precision of effect estimates for multiple studies.
• Cochrane’s Q – A hypothesis test of whether variation in effect estimates across studies is due to chance (H0) or not due to chance (H1).
• I2 – Percent of variation in effect estimates across studies that is due to heterogeneity rather than chance.
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Meta-analysis: heterogeneity and dealing with it
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Funnel plot: assessing publication bias
• Plot Sample size (y-axis) vs. Effect (x-axis)
Unskewed distribution: bias minimal Skewed distribution: bias present
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Questions on measures of association or study design?
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Break time?
• Scope and Scalpel 2004: Episode 1
• Scope and Scalpel 2004: Episode 2
• Mr. Pitt Med "Blue Steel" Ad
• MTV Cribs: Pitt Med
• Pitt Med Office: "New PBL Group Day"
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Bias, confounding, modification…a wine digression
Apricot wine Likability
Peach, Grape
Apricot wineLikabilityLikability
RoomIced
If differ by >10%, modification present
Confounding – mixing of effects; results in inaccurate estimate of exposure-outcome association; is never “controlled,” rather “adjusted for”
Effect modification – difference of effect depending on the presence or absence of a second factor; interesting phenomenon to investigate; detected with stratification or interaction term in model
Bias – systematic error (due to study) resulting in non-comparability; error that will remain in an infinitely large study; difficult to remove once there
Will a person who enjoys apricot like Bonny Doon if it comes from a bad barrel?
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Examining your new test: Sn, Sp, PPV, NPV
Sn = A / (A + C) “Of those with disease, how many did you identify?” Sp = D / (B + D) “Of those without disease, how many did you identify?” PPV = A / (A + B) “Of those you said had disease, how many truly did?” NPV = D / (C + D) “Of those you said did not have disease, how many truly did not?”
Gold standardPositive Negative
New
test
Positive A B
Negative C D
Prevalence alters PPV most
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Examining your new test: Likelihood ratios
LR is a ratio of two proportions: proportion of those with a particular result among the diseased compared to the proportion with that result among the non-diseased
LR(+) = A / (A + C) = Sn LR(-) = C / (A + C) = 1-Sn B / (B + D) 1-Sp D / (B + D) Sp “The likelihood of a test outcome (+ or -) if you have the disease is X-fold
higher than if don’t have the disease.”
Gold standardPositive Negative
New
test
Positive A B
Negative C D
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Examining various tests: ROC curves
Sn
1-Sp
Picking the best test depends on:1) Optimizing Sn and
Sp (highest AUC)2) Real world
conditions
HIV: We want highest Sp and sacrifice Sn
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Parametric biostats: T-test, ANOVA, χ2, Pearson• T-test: if you want to test the difference in means of 2 groups (continuous)
– Assumptions and how to verify them: • Independence (are subjects related?)• Random sampling (assumed)• Normal distribution of variable (histograms, formal test)• Equal variance of variable in each group (F-test)
• ANOVA: if you want to test the difference in means between ≥2 groups (continuous)– Assumptions and how to verify them:
• Same as T-test• χ2: if you want to test the difference in frequencies among ≥2 groups (categorical)
– Assumptions and how to verify them: • Cell sizes in table (>5, formal test Use Fisher’s exact test if unfulfilled)
• Pearson r: if you want to test the degree of linear relationship between two continuous variables; does not imply causal association or a mathematical association other than linear– Assumptions and how to verify them:
• Linear relationship (look at it)• Independence, random sampling (as above)• At least 1 variable must be normally distributed
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Nonparametrics: Rank sum, Kruskal-Wallis, Spearman• Mann-Whitney rank sum: if you want to test the difference in means of 2 groups
(continuous)– Assumptions and how to verify them:
• Independence (are subjects related?)• Random sampling (assumed)• Variable follows same distribution in both groups, whatever the distribution may
be• Kruskal-Wallis: if you want to test the difference in means between ≥2 groups (continuous)
– Assumptions and how to verify them: • Same as rank sum
• Spearman r: if you want to test the degree of linear relationship between two continuous variables; does not imply causal association or a mathematical association other than linear– Assumptions and how to verify them:
• Linear relationship (look at it)• Independence, random sampling (as above)
• Nonparametrics do have assumptions!• Great alternative if assumptions met, but can lack power and don’t give a good idea of
how the data are different (rely on significance)
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P-values and confidence intervals
• P-value– “Is the data consistent with the null hypothesis? If not,
then there is a “statistically significant” difference.”– Depends upon sample size and magnitude of effect;
doesn’t illustrate real values A POOR MEASURE
• Confidence interval– “What is the range of possible values for the difference
observed?”– Provides information on precision of data and possible
range of values A BETTER MEASURE
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Extra slides
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Odds and probability
Odds = Chance of something = p Chance of not something 1-p
If p=50%, odds are 0.5/(1-0.5) = 0.5 / 0.5 = 1. Hence, 50% chance means that it is equally likely that “something” and “not something” will happen.
If p=33%, odds are 0.33/(1-0.33) = 0.33/0.67 = ½. Hence, 33% chance means that it is ½ as likely that “something” will happen compared to “not something” happening. Alternatively, it is twice as likely that “not something” will happen compared to “something” happening.
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Standard Deviation vs. Standard Error• The SD is a measure of the variability in the measurements you took.
Variability can come from biologic variability, measurement variability, or both. If you believe the tool you use to measure has zero error, then the variability is solely due to biologic variability. If you want to emphasize the biologic variability (i.e. scatter) in your sample, then the SD is the appropriate statistic.
• The SEM is a measure of how well you approximated the true population mean with your sample. Again, error can come from biologic variability, measurement variability, or both. If you assume there is no biologic variability, then the only error comes from the tool you use to measure. With larger sampling sizes from the population, the measurement error becomes less and less because you are more likely to determine the true population mean with sample sizes that become closer to the true population. If you want to emphasize how precisely you determined the true population mean, then the SEM is the appropriate statistic
• The SEM is used to calculate Confidence Intervals.
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Extra study design: observational studiesCase report/series Cross-sectional Ecological
Study group Patient(s) Defined pop; measure E and O simultaneously in each person
Select groups (country, county); measure E and O in population
Measures None Prevalence Correlation coefficientTemporal relationship
Unable to establish Unable to establish
Time required Little Very littleCost Intermediate InexpensiveWhen to use? Interesting/new
case(s)E and O are common Aggregate data
available; establish hypotheses
Issues Not population-based
No temporality; prevalence bias
Ecological fallacy; difficult to adjust for confounding