Overview of Statistical Methods

Review of statistical methods
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1. Survival Analysis
   Survival Analysis is used to model time to event data with the purpose of comparing survival function among different groups, the events often refer to death or failure.
   Key definitions include
   
   • survival function
   • hazard function (log normal, log logistic, weibull distribution...)
     
   • cumulative hazard function
   • censoring (left, right, interval)
   • truncation
   Key methods include
   
   • Kaplan-meier estimator (product-limit)
   • Nelson-Aalen estimator
     
   • Life-table estimator
     
   • Logrank test (Mantel-cox test)
   • AFT (Accelerated Failure Time model)
     
   • Cox Proportional Hazards Model (semiparametric model)
   Key software packages
   
   • SAS/PROC LIFEREG
   • SAS/PROC LIFETEST
   • SAS/PROC PHREG
     
   • R/survival (Surv, survfit, survdiff, survreg, coxph)
     
     
2. Logistic regression
   
   Logistic regression (Logit model) is used for prediction of probability of occurrence of an event by fitting data to a logistic curve. The response variable is categorical (binary, ordered, nominal).
   Key definitions include:
   
   • logistic function
   • Sigmoid function
   • Odds, Odds ratio, relative risk, risk difference
   Key methods include:
   
   • Probit model
   • Logit model
   • multinomial logit model
   • proportional odds model (cumulative logit model)
   • generalized linear model
   Key software packages:
   
   • SAS/PROC LOGISTIC
   • SAS/PROC PROBIT
     
   • SAS/PROC GENMOD
   • R/stats (glm)
   • R/nnet (multinom)
   • R/mlogit
   • R/MASS (polr)
     
     
     
3. Categorical Data Analysis
   
   Categorical Data Analysis
   Key definitions:
   
   • Categorical variable (binary, ordinal, nominal; dichotomous, multichotomous)
   • frequency (cell, marginal total)
   • proportion (cell, marginal total)
   • risk, risk difference, relative risk, odds, odds ratio
     
   • frequency table (one variable)
   • contingency table (two variables)
   • multidimensional contingency table (three or more variables)
   • hypergeometric distribution
     
   • binomial distribution
   • multinomial distribution
   • product multinomial distribution
   Key methods:
   
   • measurement of association
   • tests for trend
   • tests and measures of agreement (kappa coefficient)
     
   • Fisher's Exact Test
   • chi-square test
     
   • Cochran-Mantel-Haenszel (CMH) statistics
   • Log linear model
     
   Key software package:
   
   • SAS/TABULATE
     
   • SAS/PROC FREQ
   • SAS/PROC CATMOD
   • SAS/PROC GENMOD
   • SAS/PROC LOGISTIC
   • SAS/PROC PROBIT
   • SAS/PROC CORRESP
   • R/base (table, ftable)
     
   • R/stats (prop.test, chisq.test, fisher.test, mantelhaen.test, glm)
     
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