Biostatistics and Epidemiology

Roadmap - Exactly 90 minutes...

• Generalizability

  • How applicable is a finding to the general population

• P-value

  • Probability of finding a value this extreme by random chance

• Confidence Interval

  • Interval over which population value is found with a specified probability (e.g. 95%)

• Efficacy

  • Performance of treatment under ideal circumstances

• Effectiveness

  • Performance of treatment under real world circumstances

• Assume:
  • There are two or more groups being compared, or
  • One group is being compared to zero, or
  • One group is being compared to expectation.

• For Step 1, probably safe to assume null is always rejected with \(p < 0.05\).
  • For ratios (e.g. Relative Risk, Odds Ratio), a 95% CI not overlapping 1 is significant.
  • For two sample tests, it is less straightforward how the CI relates to the p-value so don't worry about it.

• Once \(H_0\) is rejected, we accept the alternative hypothesis \(H_A\).

• Two sample: \(H_0\) = There is no difference between the disease and no disease groups

• Run the T-test (in this case, in R language)

  norm1 <- rnorm(5000, mean = 4.75, sd = 1.2)
  norm2 <- rnorm(5000, mean = 5.25, sd = 1.2)
  (t.test(norm1, norm2))$p.value
  

  ## [1] 4.687206e-88
  

  
  

  • Have we rejected the null hypothesis?

  • Yes, we have accepted \(H_A\). There is a difference between disease and no disease groups.

• Two common tests
  • Goodness-of-fit
  • Test of independence
• Goodness-of-fit
  • \(H_0\): The number of cases occuring in a subgroup is consistent with random expectation
  • \(H_A\): The number of cases occuring in a subgroup is not consistent with random expectation
• Test of independence
  • \(H_0\): Categorical variable A and categorical variable B are independent
  • \(H_A\): Categorical variable A and categorical variable B are not independent

Spearman correlation compares ranked values of two variables

• Primary - Prevention
  • An action taken to prevent development of disease in a person who is well
    
• Secondary - Screening
  • Identifying people in whom disease has begun but who do not have signs or symptoms
    
• Tertiary - Treatment
  • Preventing complications in those who have developed signs and symptoms and have been diagnosed
    
• Quaternary - Quit overtesting and overtreating
  • Recent effort to minimize excessive healthcare interventions in disease process

• Attack rate

  • Typically used during epidemics or pandemics
  • Number of people who get disease / Number of people at risk

• Incidence

  • Given a defined period of time
  • Number of people who get disease / Number of people at risk

• Prevalence

  • No time course (i.e. measured at a single point in time)
  • Number of people with disease / Number of people at risk
  • Simple diseases (e.g. SIR infections): Prevalence = Incidence x Average Disease Duration

• These are the defining characteristics of any clinical finding (e.g. history, physical, test, image).
  • They do not depend on anything... they are intrinsic to the exam/test

• If someone quotes the prositive or negative predictive value of a test, they are wrong.

• Therefore, if you do not know the sensitivity or specificity of a test, you are missing information
  • Without sensitivity and specificity, you cannot make a ROC curve
  • Never trust a paper, poster, or company presentation that does not include a ROC curve

• If the curve approximates the diagonal, it is a bad test
  • \(AUC = 0.5\) for a bad test
• If the curve goes up the y-axis and then turns right down x-axis, it is a perfect test
  • \(AUC = 1\) for a perfect test

• The value lies in the intuitive approach

• Frequentist: goal is to approximate objective truth through repeated trials
  • The important metric is the probability that our estimate does not match reality

• Bayesian: goal is to approximate objective truth by updating prior probability with new evidence
  • The important metric is the probability that our subjective experience matches reality

• Example: given a clinical test, which do you care more about?
  • If your patient has disease, there is a 2% chance of getting a test result this extreme by chance.
  • If your patient has a positive test, there is a 75% chance of having disease.

• Start with pre-test probability
  • This data is available all over the place (e.g. any prevalence data)
  • Example: Region 6 prevalence of influenza right now is \(\approx 4\%\)

• Do something (e.g. rapid flu test)
  • Absolute best Rapid Flu test: \(Sensitivity \approx 70\%\) and \(Specificity \approx 95\%\)
  • If positive, use likelihood ratio positive (a.k.a. bayes factor positive)
  • \(LR+ = \frac{sensitivity}{1 - specificity} = \frac{0.7}{1 - 0.95} = 14\)
  • If negative, use likelihood ratio negative (a.k.a. bayes factor negative)
  • \(LR- = \frac{1 - sensitivity}{specificity} = \frac{1 - 0.7}{0.95} = 0.32\)

• Pre-test Probability \(\rightarrow\) Pre-test Odds \(\rightarrow\) Pre-test Odds x LR \(\rightarrow\) Post-test Odds \(\rightarrow\) Post-test Probability

• Probability \(\rightarrow\) Odds: \(O = \frac{P}{1 - P}\)
• Odds \(\rightarrow\) Probability: \(P = \frac{O}{1 + O}\)

• Positive test: \(0.04 \rightarrow 0.04/0.96 = 0.042 \rightarrow 0.042 * 14 = 0.583 \rightarrow 0.583/1.583 = 0.37\)
  • Post-test probability following positive test: \(37\%\)

• Negative test: \(0.04 \rightarrow 0.04/0.96 = 0.042 \rightarrow 0.042 * 0.32 = 0.0134 \rightarrow 0.0134/1.0134 = 0.0132\)
  • Post-test probability following negative test: \(1.32\%\)
  • So this time of year a negative test is basically useless

• Selection bias
  • Non-random partitioning of individuals into groups
• Observer-expectancy
  • Observer is unblinded and expects a particular outcome
• Effect modification bias
  • Magnitude of effect varies by third variable
  • Can be eliminated by stratification
• Confounding
  • Unseen third variable is an underlying cause for correlation of two other variables
  • Cannot be eliminated by stratification

• Recall bias
  • Subjects with disease can recall exposures better than healthy subjects

• Procedure bias
  • Experimenters vary systematically in the way they do work
  • e.g. Experimenters don't follow the specified procedure

• Instrument bias
  • Instrument is broken
  • Instruments can also be things like surveys or clerkship evaluations
  • Just means instrument is not reliable

• Lead-time bias
  • New test detects disease earlier
  • Survival appears improved with new test

• Attrition bias
  • Subjects systematically withdraw
  • Could be things like side effects or lack of improvement

• Loss-to-follow up
  • Subjects randomly do not report for scheduled followup

• This is widely considered the gold standard for clinical evidence

• Question: Primary purpose of randomization?
• Answer: To eliminate selection bias
  • Selection bias is eliminated if randomization is technically correct

• Question: Secondary goal of randomization?
• Answer: To control confounders
  • Confounders are not necessarily eliminated even with perfect technical execution

• Can use relative risk because investigator knows prevalence of disease and prior exposures

• This post hoc analysis is overly simplified for real life

• This understanding is sufficient for step 1

• Confounders reduced because a patient can serve as their own control

• Can use relative risk because investigator knows prevalence of exposure and disease
• Subjects vary by exposure status
• Can calculate incidence

• Selection bias is the biggest problem
  • Investigator has infinite control over inclusion
• Other biases
  • Attrition, loss-to-follow up, confounding, Hawthorne

• Retrospective
  • Information bias

• Must use odds ratio because investigator does not know prevalence of disease
• Subjects grouped by cases and controls
  • Measure odds of exposure in case and control groups
• Significantly improved power and decreased resource requirements compared to cohorts
  • Due to cases being selected at out set
• Selection and Recall biases are the biggest problem
  • Selecting appropriate controls is highly non-trivial
  • Sick people remember exposures (e.g. Melanoma patients stew about their sunburns)
• Also common
  • Information biases
• Cannot calculate incidence or prevalence

• Quick, cheap, and easy
  • Typically this is a starting point
• Can establish prevalence of disease
• Must use chi-squared or correlation for statistical test
• Subjects can be grouped by exposure and diease in to the 2x2 contingency

• Cannot establish causation
• Cannot calculate risk metrics