Statistics Flashcards
Powering a study
a) Usual power thresholds
b) If study has inadequate power for an outcome but a p-value <0.05, what does this mean?
c) “90% power to detect a 15% difference between treatment group A and group B” - explain
d) Factors affecting the power of a study
e) Defining the power of a study
a) >80%
If a safety outcome, 90% is preferred
b) It may have arisen due to chance
c) There is a 90% chance of detecting a real benefit of 15% between treatment A and treatment B (if it exists)
d) - Effect size: Larger effects are more easily detected
- Measurement error: Systematic and random errors in recorded data reduce power.
- Sample size: Larger samples reduce sampling error and increase power.
- Significance level: Increasing the significance level (p-value considered significant) increases power.
e) The probability of correctly rejecting a false null hypothesis
Adverse events
a) Best way of detecting a suspected link between a drug and a particular ADR
a) Meta-analysis of existing data
Further RCTs unlikely to be ethical/practical
Type 1 and type 2 error
a) Explain each
b) How is the risk of each reduced
Type 1 error:
- False positive rate
- Equal to P value
- The chance of falsely rejecting the null hypothesis (accepting a treatment that doesn’t work)
- Risk reduced by setting lower P-value significance threshold (but this increases risk of a type 2 error)
Type 2 error:
- False negative rate
- Inverse of the statistical power
- The chance of falsely accepting the null hypothesis (rejecting a treatment that works)
- Risk reduced by increasing power of study (but this increases the risk of a type 1 error)
P value 0.05
5% of the time you would see a result as extreme or more so if the null hypothesis were true
95% confidence intervals
You are 95% confident that the “true” mean value of the measured outcome lies between the lower and upper limits of the confidence interval for the “measured” mean
Screening
a) Length- and lead-time bias
Lead-time bias: Overestimation of survival duration due to earlier detection by screening than clinical presentation.
Length-time bias: Overestimation of survival duration due to the relative excess of cases detected that are slowly progressing.
Intention to treat vs. per-protocol
a) Describe each
b) Pros and cons of each
c) Which is more fair and applicable to clinical practice?
ITT:
- includes all patients randomised, including dropouts or those who did not comply with the protocol
- maintains randomisation, preserves sample size and reduces bias
- provides an answer to the question “What is the effect of assigning a drug to a group of patients?” (more applicable to clinical practice)
PP:
- includes only those patients who followed the protocol of the trial properly
- The groups for analysis may not be well-balanced as they were at randomisation, so there is a bias
- may be overly optimistic, as likely excludes patients who did not tolerate or derive benefit from the drug
- Answers the question: “What is the effect of receiving a drug in a group of patients?”
Intention to treat vs. per-protocol analysis
a) Explain each
b) Pros and cons
c) Which is more applicable to real life practice?e
ITT
- All study participants included in the analysis, including dropouts and those who did not comply with the protocol
- Maintains between-group balance in terms of randomisation, sample size, reduces bias
- Answers the question “What is the effect of assigning a drug to a group of patients?”
- More applicable to real life
PP:
- Only those who adhered to the protocol are included in the analysis
- As those with worse side effects/reduced benefit excluded, this analysis may overestimate the effectiveness of a treatment
- Answers the question: “What is the effect of receiving a drug in a group of patients?”
Case-control studies
a) Biases
a) Recall bias:
- People cannot recall exactly what they had for dinner last Thursday, etc.
Ascertainment bias:
- where there are differences in the rate of ascertainment of the exposure in the case vs control groups
- E.g. comparing rates of carotid bruit in patients with and without TIA - patients with TIA symptoms more likely to have carotids auscultated - hence it will seem as though a much higher proportion of TIA vs control patients have a bruit than the actual numbers
Referral bias:
- Where the case and control populations are different due to a relationship to the outcome being assessed
- E.g. Comparing rates of mortality from pneumonia between hospital A and hospital B. Hospital A has an ITU whereas Hospital B does not. Therefore Hospital A likely to get sicker patients than Hospital B and so a higher mortality rate. This is due to a “referral bias” to hospital A
Admission rate bias (Berkson bias):
- The fact that patients with 2 or more conditions are more likely to be hospitalised than patients with just 1 condition
- E.g. Studying rates of cancer in patients with stroke versus those without stroke in hospital. Rates of cancer in stroke patients will be found to be higher than the true number since having both cancer and stroke increases the likelihood of being admitted to hospital (hence this group are over-represented, compared with those with just cancer or just stroke)
Variance vs standard deviation
SD is the square root of the variance
Effect of prevalence of PPV and NPV
imagine what would happen to each if prevalence were 0% or 100%
As prevalence decreases, the PPV decreases because:
- There will be more false positives for every true positive.
- This is because you’re hunting for a “needle in a haystack”
- If prevalence were 0%, every positive test result would be a false positive (hence PPV would be 0%)
- If prevalence were 100%, every positive test result would be a positive case (hence PPV would be 100%)
As prevalence decreases, the NPV increases because:
- There will be more true negatives for every false negative.
- This is because a false negative would mean that a person actually has the disease, which is unlikely because the disease is rare (low prevalence)
- If prevalence were 100%, every negative test result would be a false negative (hence NPV would be 0%)
- If prevalence were 0%, every negative test result would be a true negative case (hence NPV would be 100%)
Sensitivity and specificity are not affected by prevalence
D-dimer
a) Sensitivity, specificity, PPV and NPV
b) Explain its use in conjunction with pre-test probability (Wells score)
High sensitivity –> picks up high proportion of those who have a DVT
Low specificity –> not SPECIFIC to DVT. Can be raised for lots of reasons
High NPV –> if negative result, high chance of negative DVT
Low PPV –> if positive result, lots of possible causes other than DVT
b) Due to poor specificity (and low PPV), it is not a useful diagnostic test, so positive result should be interpreted in context of pre-test probability of DVT
Screening occurs in a population of 1,000 people.
New bowel cancer screening test has 99.9% specificity.
a) What is the chance of someone with a positive test result having bowel cancer, where bowel cancer prevalence is 1%?
b) What is the chance of someone with a positive test result having bowel cancer, where bowel cancer prevalence is 0.1%?
Specificity = 99.9% –> False positive rate = 0.1% (0.001)
0.1% of 1,000 = 1 person (False positives)
Prevalence is 1%.
1% of 1,000 = 10 people (True positives)
Hence, you would expect to have 11 positive test results in this population sample: the 10 TPs and 1 FP.
= Therefore, the risk of having bowel cancer if you have a positive result is 10/11 (90%)
b) Prevalence is 0.1%
0. 1% of 1,000 = 1 person (True positives)
Hence, you would expect to have 2 positive test results in this population sample: 1 TP and 1 FP
= Therefore, the risk of having bowel cancer if you have a positive result is 1/2 (50%)
Relative risk reduction
RRR = ARD/RR in control group
To detect side effects occurring in 1/1000 people, how many trial participants are needed?
3,000
