statistics Flashcards
what is the null hypothesis?
Null hypothesis = the idea that there is no difference between 2 samples/groups and that any difference is the result of random variation
Risk difference (ARR)?
Relative risk (RRR)?
Odds ratio?
Number needed to treat?
Relative risk reduction?
Risk difference (absolute risk)(attributable risk) = A-C
= risk in experimental group -risk in control group
=2-10 = -8
Risk ratio (relative risk) = A/C
Proportion: risk in experimental/control group
= 2/10 = 0.2
> 1 implies the risk of disease is higher in the exposed group
Implies how much more likely something will occur, relative to the other group
Odds ratio = (A/B)/(C/D)
(2/60)/(10/50) = 0.166666
Compares the odds of something occurring in 1 group compared to the odds occurring in another group
E.g. Odds of contracting flu in the vaccine group was 16.66% of the odds in the placebo group
In rare outcomes the odds ratio approximates RR
For common outcomes the OR diverges from the risk ratio
Number needed to treat = 1/absolute risk reduction
NNT = 1/ARR
NNT = 1/control event rate – experimental event rate
Relative risk reduction = absolute risk reduction / control event rate
RRR = ARR/Control event rate
Sensitivity?
Specificity?
Sensitivity : SnOUT
Proportion of true positives (1-false negative rate)
Sensitivity – if high, rules things OUT – i.e. low false negative
Sensitivity = True positive / (True positive + false negative)
e.g. screening tests should have high sensitivity to not miss cases e.g. FOBT – other causes of blood in poo (low specifity) but hard to miss (sensitive)
Specificity : SpIN
Specificity – if high, rules things IN – i.e. low false positive
Specificity = True negative / (True negative + false positive)
Does sensitivity and specificity depend on prevalance?
Does positive predictice value or NPV depend on prevalance?
No
Yes
PREDICTIVE VALUES
Likelihood of a test result being the true result BUT impacted by prevalence.
Positive predictive value
PPV = A/A+C
= No. true positives/no. all positive calls
Negative predictive value
NPV = D/D+B
= No. true negatives/ no. negative calls
With high prevalence, the NPV drops as higher false negatives increases in the denominator
what happens to PPV when prevalance increases?
What happens to NPV as prevalance increases?
PPV: Prone to error related to PREVALENCE : High prevalence increases the PPV (as no. true positives increases but no. of false positives stays the same)
NPV: With high prevalence, the NPV drops as higher false negatives increases in the denominator
What is a likelihood ratio?
Likelihood ratios determine the likelihood of having / not having disease. They are INDEPENDENT of prevalence.
e.g. positive likelihood ratio = likelihood of having the disease with a positive result
negative likelihood ratio = likelihood of not having the disease with a negative result
how do you calculate positive likelihood ratio?
Negative likelihood ratio?
Positive likelihood ratio
PLR = Sensitivity / 1-Specificity
PLR = likelihood that a disease is present in the setting of a positive test result
E.g. PLR of 6 = likelihood of having the disease has increased 6 fold by having a positive test
Negative likelihood ratio
NLR = 1-Sensitivity / Specificity
No. test –ve with disease/ no. test –ve without disease
LR>10 or < 0.1 generate large changes from pre to post test probability
what is a type 1 error?
Type I error = False positive
(type 1= false positive because +ve before -ve)
= incorrect rejection of the null hypothesis when it is true
AKA alpha error
The lower the p value, the less likely it is to be a false positive
May be due to ; bias, confounding, chance.
Ways to minimize : blinding, intention to treat analysis, risk factor stratification
What is a Type II Error?
Type II error = False negative
(type 2 = false negative because –ve after +ve)
= failing to reject the null hypothesis when it is false
AKA beta error
May be due to; insufficient sample size
Minimise : improve power of the study, i.e. increase sample size
What does error mean?
incorrect rejection or acceptance of the null hypothesis
