Biostatistics

Research Bias

Selection Bias

  • Attrition bias
  • Berkson bias
  • Healthy worker effect
  • Late-look bias
  • Non-response bias
  • Volunteer bias

Measurement Bias

  • Hawthorne effect
  • Observer bias [Pygmalion effect]
  • Procedure bias
  • Recall bias

Misinterpretation

  • Confounding bias
  • Lead-time bias
  • Length-time bias

Methods to Decrease Confounding Bias

  • Crossover
  • Matching
  • Randomization
  • Restriction
  • Stratification

Observational Studies

  Cross Section Case Control Cohort
Time Time point Retrospective Retrospective
Prospective
Incidence - - +
Prevalence + - -
Causality - + +
Analysis Chi-squared Odds ratio (OR) Relative risk (RR)

Statistical Tests

Independent Variable Dependent Variable Sampling Parametric Test
- Dichotomous Independent - Pearson Chi-squared test & Binomial test
- Polytomous Independent - Pearson Chi-squared test & Multinomial test
- Continuous Independent + Z-test & T-test
Dichotomous Dichotomous Independent - Pearson Chi-squared test & Fisher exact test
Dichotomous Dichotomous Dependent - McNemar Chi-squared test
Dichotomous Polytomous Independent - Pearson Chi-squared test
Dichotomous Continuous Independent - Wilcoxon rank-sum test
Dichotomous Continuous Independent + Z-test & T-test
Dichotomous Continuous Dependent - Wilcoxon signed-rank test
Dichotomous Continuous Dependent + Paired Z-test & T-test
Polytomous Dichotomous Independent - Pearson Chi-squared test
Polytomous Polytomous Independent - Pearson Chi-squared test
Polytomous Continuous Independent - Kruskal-Wallis test
Polytomous Continuous Independent + ANOVA F-test
Polytomous Continuous Dependent - Friedman test
Polytomous Continuous Dependent + Repeated measures ANOVA F-test
Continuous Dichotomous Independent + Logistic regression :: binomial
Continuous Polytomous Independent + Logistic regression :: multinomial
Continuous Continuous Independent - Spearman correlation
Continuous Continuous Independent + Pearson correlation

Statistical Inferences

Inference for Means

Samples One Two
CI
HT

Inference for Proportions

Samples One Two
CI
HT
  • Confidence interval (CI)
  • Hypothesis test (HT)

Sensitivity & Specificity

Sensitivity Specificity
Ture positive True negative
Rule out when negative Rule in when positive
Screening test Confirmation test
High type 1 error Low type 1 error
Low type 2 error High type 2 error

Likelihood Ratios

  • Positive likelihood ratio = sensitivity / (1 - specificity)
  • Negative likelihood ratio = (1 - sensitivity) / specificity

Generalized Linear Models (GLM)

Model Distribution Link
Linear regression Normal Identity
Logistic regression Bernoulli Logit
Poisson regression Poisson Log

Multiple Testing Correction

Correction Control
Bonferroni Family-wise error rate (FWER)
Benjamini-Hochberg False discovery rate (FDR)

Likelihood and Conjugate Priors

Likelihood Conjugate Prior Parameter
Binomial Beta Probability (p)
Geometric Beta Probability (p)
Multinomial Dirichlet Probability (p)
Poisson Gamma Rate (λ)
Exponential Gamma Rate (λ)
Normal Normal Mean (μ)
Normal Inverse gamma Variance (σ2)

Supervised Learning Steps

  • Collection
  • Splitting
  • Preprocessing
  • Modeling
  • Validation
  • Evaluation
  • Prediction