Biostatistics
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Casecontrol study
 Observational, retrospective
 Design:
 compares a group of people with disease to a group without disease
 Looks for prior exposure or risk factor ("what happened?")
 Measures/examples:
 Odds ratio (OR)
 "patients with COPD had higher odds of a history of smoking than those without COPD had"

Cohort study
Observational, prospective or retrospective
 Design:
 Compares a group with a given exposure or risk factor to a group without such exposure
 Looks to see if exposure ↑ the likelihood of disease
 Prospective (who will develop disease?)
 Retrospective (who developed the disease?)
 Measures/examples:
 Relative Risk (RR)
 "smokers had a higher risk of developing COPD than nonsmokers had"

Crosssectional study
Observational
 Design:
 Collects data from a group of people to assess frequency of disease (and related risk factors) at a particular point in time
 "What is happening?"
 Measures/examples:
 Disease prevalence
 Can show risk factors associated with disease, but does not establish causality

Twin concordance study
 Design:
 Compares the frequency with which both monozygotic twins or both dizygotic twins develop same disease
 Measures/example:
 Measures heritability

Adoption study
 Design:
 Compares siblings raised by biological vs. adoptive parents
 Measures/examples:
 Measures heritability and influence of environmental factors

Clinical trial
Compares therapeutic benefits of 2 or more treatments, or of treatment and placebo
 Study quality improves with:
 Randomization
 Controlled
 Doubleblinded (neither pt nor doctor knows patient's group)
 Tripleblinded: additional blinding of the researchers analyzing the data

Clinical trial
Phases, sample size, purpose
 Phase I: small number of healthy volunteers → Assesses safety, toxicity, pharmacokinetics
 Phase II: small number of patients with disease of interest → Assesses treatment efficacy, optimal dosing, adverse effects
 Phase III: Large number of pts, randomly assigned to investigational treatment group/best available treatment, or placebo → compares the new treatment to standard of care
 Phase IV: Postmarketing surveillance of trial of patients after approval → Defects rare or longterm adverse reactions

Evaluation of diagnostic tests
2× 2 table
 Compares test results with actual presence of disease
 TP/TN = true positive/true negative
 FP/FN = false positive/false negative

Sensitivity/specificity vs positive/negative predictive value
 Sensitivity and specificity are fixed properties of test
 PPV and NPV vary with prevalence or pretest probability

Sensitivity (truepositive rate)
  Proportion of all people with disease who test positive, or the probability that a test detects disease when disease is present
 
  Sensitivity = 1  falsenegative rate
 Value approaching 100% is desirable for ruling out disease → low falsenegative rate
 Used for screening in diseases with low prevalence

Specificity (truenegative rate)
 Proportion of all people without disease who test negative, or the probability that a test indicates nondisease when disease is absent
 Sensitivity = TN/(TN+FP) = 1  falsepositive rate
 Value approaching 100% is desirable for ruling in disease → low falsepositive rate
 Used as a confirmatory test after a positive screening test

Positive predictive value (PPV)
 Proportion of positive test results that are true positive
 PPV = TP /(TP+FP)
 Probability that person actually has the disease given a positive test result
 *PPV varies directly with prevalence or pretest probability: high pretest probability → high PPV

Negative predictive value (NPV)
 Proportion of negative test results that are true negative
 NPV = TN/(FN + TN)
 Probability that person actually is disease free given a negative test result
 *NPV varies inversely with prevalence or pretest probability: high pretest probability → low NPV

 A = 100% sensitivity
 B = practical compromise between specificity and sensitivity
 C = 100% specificity

Incidence
 Incidence looks at new incidents
 Incidence rate = (# of new cases in a specific time period)/(population at risk during same time period)

Prevalence
 Prevalence looks at all current cases
 Prevalence = (# of existing cases)/(Population at risk)
 Prevalence ≃ incidence rate × average disease
 Prevalence > incidence for chronic diseases (e.g., diabetes)


Odds ratio (OR)
 Uses: casecontrol studies
 Odds that the group with disease (cases) was exposed to a risk factor (a/c) divided by the odds that the group without the disease (controls) was exposed (b/d)

Relative risk (RR)
 Uses: cohort studies
 Risk of developing disease in the exposed group divided by risk in the unexposed group
 If prevalence is low, RR = OR
 (e.g., if 21% of smokers develop lung cancer vs 1% of nonsmokers, RR = 21/1 = 21)

Attributable risk
 The difference in risk between exposed and unexposed groups, or the proportion of disease occurrences that are attributable to the exposure
 (e.g., if risk of lung cancer in smokers is 21% and risk in nonsmokers is 1%, then 20% of the 21% risk of lung cancer in smokers is attributable to smoking)

Absolute risk reduction (ARR)
 Absolute reduction in risk associated with a treatment as compared to a control
 (e.g., if 8% of people who receive a placebo vaccine develop flu vs. 2% of people who receive a flu vaccine, then ARR = 8%  2% = 6%)

Number needed to treat
 Number of patients who need to be treated for 1 patient to benefit
 Calculated as 1/absolute risk reduction
 Number needed to treat = 1/ARR

Number needed to harm
 Number of patients who need to be exposed to a risk factor for 1 patient to be harmed
 Calculated as 1/attributable risk

Precision
 The consistency and reproducibility of a test (reliability)
 Random error: reduces precision in a test
 ↑ precision → ↓ standard deviation

Accuracy
 The trueness of test measurements (validity)
 The absence of systematic error or bias in a test
 Systematic error: reduces accuracy in a test

Bias
ways to reduce
 Occurs when there is systematic error or favor in a particular direction
 Reduce bias:
 Blind studies to limit influence of participants and researchers on interpretation of outcomes
 Placebo control groups
 Crossover studies (each subject acts as own control) to limit confounding bias
 Randomization to limit selection bias and confounding bias
 Matching to reduce confounding bias

Selection bias
 Nonrandom assignment to participation in a study group
 (e.g., Berkson's bias, loss to followup)

Recall bias
 Knowledge of presence of disorder alters recall by subjects
 common in retrospective studies

Sampling bias
 Subjects are not representative of the general population
 results are not generalizable
 Type of selection bias

Latelook bias
 Information gathered at an inappropriate time
 e.g., using survey to study a fatal disease (only those pts still alive will be able to answer survey)

Procedure bias
 Subjects in different groups are not treated the same
 e.g., more attention is paid to treatment group, stimulating greater adherence

Confounding bias
 Occurs when factor is related to both exposure and outcome, but is not on the causal pathway
 factor distorts or confuses effect of exposure on outcome

Leadtime bias
 Early detection confused with ↑ survival
 seen with improved screening (natural history of disease is not changed, but early detection makes it seem as though survival ↑)

Observerexpectancy effect
Occurs when a researcher's belief in the efficacy of a treatment changes the outcome of that treatment

Hawthorne effect
 Occurs when the group being studied changes its behavior owing to the knowledge of being studied
 *Dr. Hawthorne is watching you

Statistical distribution
 Measures of central tendency = mean, median, mode
 Measure of dispersion = standard deviation (SD), standard error of the mean (SEM), Zscore, confidence interval

 Gaussian (aka bellshaped)
 Mean = median = mode

Standard deviation and SEM
 σ = SD
 n = sample size
 SEM ↓ as n ↑

 Positive skew
 Typically, mean > median > mode
 Asymmetry with longer tail on right
 Mode is least affected by outliers in the sample

 Negative skew
 Typically, mean < median < mode
 Asymmetry with longer tail on left

Statistical hypotheses
 Null (H_{0}): hypothesis of no difference
 No association between the disease and the risk factor in the population
 Alternative (H_{1}): hypothesis of some difference
 There is some association between the disease and the risk factor in the population

 Type I error (α)
 Type II error (β)

Type I error (α)
 Stating that there is an effect or difference when non exists
 False positive (accepting the alternative hypothesis when the null hypothesis is true)
 α is the probability of making a type I error
 p is judged against a preset α level of significance (usually <.05)
 If p <.05 then there is less than 5% chance that the data will show something that is not really there
 **α = you saw a difference that did not exist

Type II error (β)
 Stating that there is not an effect or difference when one exists
 False negative (fail to reject the null hypothesis when it is false)
 β is the probability of making a type II error
 **β = you were blind to a difference that did exist

Power (1  β)
 Probability of rejecting null hypothesis when it is in fact false, or the likelihood of finding a difference if one in fact exists
 Increases with:
 ↑ sample size
 ↑ expected effect size
 ↑ precision of measurement
 *If you ↑ sample size, you ↑ power (Power in numbers)

Metaanalysis
 Pools data and integrates results from several similar studies to reach an overall conclusion
 ↑ statistical power
 Limited by quality of individual studies or bias in study selection

Confidence interval
 Range of values in which a specified probability of the means of repeated samples would be expected to fail
 CI = range [mean  Z(SEM)] to [mean + Z(SEM)]
 95% CI corresponds to p = .05
 95% CI, Z = 1.96
 99% CI, Z = 2.58
 *If the 95% CI for a mean difference between 2 variables includes 0, then there is no significant difference and H_{0} is not rejected
 *If the 95% CI for odds ratio or relative risk includes 1, H_{0} is not rejected
 *If the CI between 2 groups do not overlap → significant difference exists
 *If the CIs between 2 groups overlap → usually no significant difference exists

ttest
 Checks difference between the means of 2 groups
 *Mr. T is mean

ANOVA
 Checks differences between the means of 3 or more groups
 * ANOVA = ANalysis Of VAriance of 3 or more groups

Chisquared (
)
 Test checks difference between 2 or more percentages or proportions of categorical outcomes (not mean values)
 = compare percentages or proportions

Pearson's correlation coefficient (r)
 r is always between 1 and +1
 Closer the absolute value of r is to 1, the stronger the linear correlation between the 2 variables
 Coefficient of determination = (value that is usually reported)

Disease prevention
 Primary: Prevent disease occurrence (e.g., HPV vaccination)
 Secondary: Early detection of disease (e.g., Pap smear)
 Tertiary: Reduce disability from disease (e.g., chemotherapy)
 PDR: Prevent, Detect, Reduce disability