Stats Flashcards
How to relate prevalence and incidence
Prevalence = incidence x duration
Prevalence- diseased / everyone
Incidence- new cases over certain time period
Formula for incidence vs. prevalence
Incidence = new cases over a specific time frame
Prevalence = rate of disease / all population
ex] sick / (sick plus well)
When does mortality start to equal incidence
Mortality approaches incidence if high case rate mortality and short duration of illness
Formula for sensitivity
Sensitivity= (SnOut)- chance of positive test if you have disease
- probability test will be positive when disease is present
Sensitivity = True Pos / (True pos plus false neg)
SN = a / (a + c)
Formula for specificity
Sensitivity = SpOut- chance of not having disease given a negative test
- probability test result negative when disease not present
Specificity = (true neg) / (true neg plus false pos)
SP = d / b + d
How to change the
(a) Sensitivity/specificity
(b) PPV/ NPV
(a) Changing the cutoff of positive or negative value
-otherwise is fixed!
(b) While PPV/NPV will change based on prevalence of disease in a population
Formula for positive predictive value
PPV = chance disease is present when test is positive
PPV = true pos / (true pos plus false pos)
PPV = a/ a + b
Formula for negative predictive value
NPV = chance disease not present when test is negative
NPV = true neg / (true neg plus false neg)
Increased prevalence would increase or decrease
(a) PPV of a test
(b) NPV
(c) Sensitivity
(d) Specificity
Increase prevalence (amount of ppl with illness)
(a) Increases positive predictive value = chance of having disease if test is positive
(b) Decreases NPV (chance of not having disease is test is negative
(c, d) does not change sens/spec b/c those are specific to the test
What is a positive likelihood ratio?
(a) Formula with respect to true pos/neg
(b) Formula with respect to Sn/Sp
PLR = ratio of positive test result given presence vs. absence of disease
PLR = (true pos rate) / (false pos rate) = sensitivity / (1- specificity)
What is a negative likelihood ratio?
(a) Formula with respect to true pos/neg
(b) Formula with respect to Sn/Sp
NLR = chance of negative test with presence vs. absence of disease
NLR = (false neg rate) / (true neg rate) = (1- sensitivity) / specificity
Differentiate lead-time and length-time bias
Biases with screening tests
Lead-time bias: survival (time from diagnosis to death) prolonged only because you diagnosed earlier, not b/c you delayed death
-lead time due to earlier Diagnosis, no real delay in survival
Length time bias- overestimation of survival (ppl who survive / ppl with disease) b/c detecting more earlier/slowly progressive cases (increasing the denominator)
-ex: more ppl with breast CA survive if you include DCIS cases that you detect early, but they weren’t going to die from the DCIS anyway
Gold standard for types of trials
(a) Observational
(b) Experimental
Gold standard for the two types of trials: experimental when the researcher alters the exposure
(a) Observational- no intervention, just see what happens based on different exposures- cohort study (prospective, take group exposed and those not then look forward to see outcome) preferred over case-control (retrospective, collect outcome and controls then look backwards at who was exposed to risk factor)
(b) Experimental- you change something about their exposure- RCTs (duh)
Differentiate case-control and cohort studies
Cohort (gold standard of observational): take ppl with and without exposure and see who gets disease prospectively
ex] take some patients given them statins, others not, follow with time and see who gets ASCVD
ex] fellows who used and didn’t use ultrasound, compare CVL complication rate
Case-control study: see ppl who do and don’t have disease, then look back (retrospectively) and see who was exposed
ex] lung CA and non-lung CA, look back to see who was exposed to agent orange
Compare cross-sectional study to case-control study
Cross-sectional: exposure and outcome measured at same time
ex: sample of nonsmoking vets asked if they had exposure to burn pits and if have been diagnosed with lung CA
Case-control: retrospective observational, certain disease (cases) and controls (w/o disease) then look back to see if exposed to risk factor
ex: vets with lung CA, look back to see if exposed to agent orange f
Differentiate relative risk and odds ratio
Relative risk- (risk in exposed/treated) / (risk in unexposed/untreated)
-used in cohort study (
ex: RR over 1- higher chance of disease if exposed
ex: RR less than one- lower chance of disease in exposed (ex: rate of ASCVD in ppl who exercise frequently)
- derived from prospective case-control, not from retrospective cohort studies
vs.
odds ratio- odds of disease in exposed vs. unexposed
-used for both cohort and case-control studies
Odds ratio approaches relative risk if the sampled population is representative of the general population
How are the following observational studies’ results reported
(a) Case-control
(b) Cohort study
(a) Case control reported in odds ratio
-ratio of odds of disease in exposed group: odds of disease in nonexposed group
(b) Cohort (gold standard) can be reported in either relative risk or odds ratio (RR or OR)
Explain relative risk in something protective, ex: relative risk of heart disease in ppl who exercise daily
Relative risk (risk in treated / risk in control) under 1 (ex: 0.8) in something protective
Describe what the following mean
(a) RR over 1
(b) RR under 1
(a) RR over 1: positive association
-risk in exposed greater than risk in nonexposed
ex: lung cancer higher in smokers than nonsmokers
(b) RR under 1: risk in exposed less than nonexposed
ex: ASCVD lower in pts who exercise
ex] type II error is 10%
(a) Explain what this means
(b) What is the power of the study
(c) How to increase power
ex] type II error (false negative rate) is 10%
(a) means .1 chance of accepting null hypothesis even though null hypothesis is false
-10% chance of not finding an association when one in fact exists
(b) power = 1 - beta = 90% (probability of finding an association if one exists, are rejecting an association when one doesn’t exist = probability of being right!)
(c) increase sample size
Difference btwn type I and type II error
Type I error (alpha) = false positive rate- reject the null hypothesis when null hypothesis is true
-say there’s an association (reject null hypothesis) when outcome is actually just due to chance, generally ~5% is acceptable
Type II error (beta) = false negative rate- accept the null hypothesis when null hypothesis is false
-say the outcome is due to chance when there actually is an association
Efficacy vs. effectiveness
Efficacy- benefit under ideal circumstances (ex: in RCT)
Effectiveness- benefit under real life/clinical circumstances
Formula for absolute risk reduction
Absolute risk reduction = control event rate - experimental event rate
Relate absolute risk reduction to number needed to treat
NNT is the inverse of the absolute risk reduction
NNT = 1 / ARR
Ex: 50% of pts taking ICS alone had exacerbation, while 40% taking ICS/LABA had exacerbation
NNT to prevent an exacerbation?
NNT = 1 / ARR
Absolute risk reduction = control event rate - experimental event rate
ex: ARR = .5-.4 = .1
NNT = 1/.1 = 10
Describe what the following mean
(a) RR over 1
(b) RR under 1
(a) OR over 1: exposure or disease positively related with outcome
ex: exposure and disease are positively related
(b) RR over 1: positive association, risk in exposed is greater than risk in nonexposed
ex: smoke
Compare cross-sectional study to case-control study
Cross-sectional: exposure and outcome measured at same time
ex: sample of nonsmoking vets asked if they had exposure to burn pits and if have been diagnosed with lung CA
Case-control: retrospective observational, certain disease (cases) and controls (w/o disease) then look back to see if exposed to risk factor
ex: vets with lung CA, look back to see if exposed to agent orange f
Confidence interval better at guessing for heterogeneous or homogeneous population
More heterogeneous the population- less likely that the sampled population represents the entire population appropriately
=> sampling bias produces a more flawed confidence interval in a heterogeneous population
What does the confidence interval tell you?
95% sure that the true value of the entire population falls within the interval
-using the study sample to make an inference
about the entire population
-larger study sample more representative of the entire population => can narrow the confidence interval
ARDSNet NEJM 2000 mortality for low TV 30% vs. high TV 40%
(a) What is the relative risk reduction?
(b) What is the absolute risk reduction?
(a) Relative risk reduction: (40-30) / 40 = 25%
-proportional reduction in rates of bad events in experimental vs. control group
(b) 40-30 = 10% absolute risk reduction
-absolute difference in event rates
Differentiate relative and absolute risk reduction
(a) Which typically makes a drug effect sound better
Relative- proportional reduction in rates of bad events vs. absolute arithmetic difference
(a) Relative risk reduction typically larger number and makes reduction seem more impressive
Calculate the number needed to harm with thrombolytics if chance of major bleed is 9% w/ thrombolytics vs. 3% without
NNT = (1 - ARR)
while NNH = (1 - absolute harm added)
ex: risk of major bleed is 6% higher with thrombolytics, so 1 / 0.06 = 16
so need to give 16 ppl thrombolytics to cause one major bleed
Which statistical variable describes:
(a) Chance of having the disease if you have a positive test result
(b) Chance test comes positive if have the disease
(c) Ratio probability of positive test if have disease vs. positive test if don’t have disease
(a) Positive predictive value = chance of having the disease if there is a positive test result
(b) Sensitivity = chance of positive test if disease is present
(c) Positive likelihood ratio = probability of positive test with disease vs. probability of positive test without disease
Differentiate PLR and NLR
PLR- chance of positive test with disease / chance of positive test without disease
-increases with increased prevalence of disease
NLR = chance of negative test with disease / chance of negative test without disease
-decreases with increase in prevalence of disease
Clinically how do we use likelihood ratios?
Use likelihood ratio to guide our pre and post-test probability of disease
+LR: increase between pre and post-test probability (aka more likely pt has disease if est is positive)
4x4 table
(a) Formula for sensitivity
(b) Formula for PPV
(a) Sensitivity = chance pt has a positive test if disease is present
= a / a + c
(b) PPV- given a positive result, how likely disease is present
= a / a + b
4x4 table
(a) Formula for specificity
(b) Formula for negative predictive value
(a) Specificity- chance test comes back negative if disease absent
= d / b + d
(a) NPV- how likely disease absent if test negative
= d / c + d
Differentiate null and alternative hypothesis
H0 (null hypothesis) = sample observation is due purely to chance
Ha (alternate hypothesis) = observation due to a non-random cause (aka some correlation)
Differentiate power and confidence level
(a) Rejects the null hypothesis when it’s false
(b) Accepts the null hypothesis when it’s true
(a) Power = rejects null hypothesis when it’s false- study says this is not due to chance when there is in fact an association
(b) Confidence level = accept null hypothesis (that sample observation results purely from chance) when null hypothesis is true (no association exists)
Differentiate type I and II error
(a) Rejects null hypothesis when it’s true
(b) Accepts the null hypothesis when its false
(a) Type I error- rejects null hypothesis when it’s true
think there’s a correlation when it’s actually just due to chance
(b) Type II error- accepts null hypothesis when it’s false
think it’s just chance when there is actually an association
Mounier-Kuhn syndrome
Congenital form of tracheobronchomegaly- enlargement of central airways (trachea and main bronchi)
can allow for airway diverticula => retained secretions => bronchiectasis
