IAI CS2 study plan

Derive the survival function, hazard function and cumulative hazard from a given density, and state the relationships among S(t), f(t), h(t) and H(t) without notes

Distinguish between censoring types (right, left, interval, informative) and explain for each the assumption needed for the Kaplan-Meier estimator to be consistent

Compute and interpret the Kaplan-Meier estimator and Nelson-Aalen estimator by hand for a small dataset containing ties and a censored observation

Derive the mean and variance of the exponential and Weibull lifetime distributions and explain how the shape parameter governs monotone versus non-monotone hazard

Compare Gompertz-Makeham, gamma, log-normal and log-logistic lifetime distributions in terms of hazard shape and the kind of mortality or failure data each fits best

Derive the partial likelihood contribution of a right-censored observation and the full likelihood under parametric survival models, distinguishing the roles of the density and the survival term

Apply the delta method to obtain the approximate variance of a transformed survival probability or cumulative hazard estimate

Explain the actuarial (life table) graduation approach: crude central death rates, exposure-to-risk, and the choice of initial exposed-to-risk

Describe the principle of smoothness in graduation and contrast graduation by parametric formula, by spline, and by standard-table adjustment

Test a graduated set of rates for goodness of fit using chi-square and for smoothness using third-difference statistics, and interpret each test

Derive the Cox partial likelihood, explain why the baseline hazard cancels, and state the proportional hazards assumption formally in terms of the hazard ratio

Interpret Cox regression coefficients as log hazard ratios, construct Wald and likelihood-ratio confidence intervals, and explain how the Efron versus Breslow tie-handling methods differ

Test the proportional hazards assumption using scaled Schoenfeld residuals, a log-minus-log plot, and a time-by-covariate interaction, and state what to do when it fails

Fit and compare exponential, Weibull and Cox models on the same data, and explain when a parametric model gives more efficient estimates than Cox

Explain stratified Cox models and time-dependent covariates, including why time-dependent covariates break the usual interpretation of the baseline hazard

Write the exponential family density in canonical form and derive the mean and variance from the cumulant function for binomial, Poisson and gamma families

Derive the score equations and Fisher information for a generalised linear model, and explain the role of the canonical link in simplifying them

Explain the IRLS algorithm step by step and hand-compute two iterations for a small logistic regression dataset

Diagnose overdispersion in binomial and Poisson models, and fit a quasi-likelihood or negative binomial alternative with correct standard errors

Interpret deviance, Pearson residuals, and the analysis of deviance table for nested GLMs, and explain why deviance residuals are preferred for non-normal responses

Specify priors for GLM coefficients and derive the posterior up to proportionality for a logistic model with a normal prior

Explain conjugacy for the beta-binomial and normal-normal cases, and derive the posterior parameters

Distinguish credible intervals from confidence intervals and explain the role of the prior in small-sample and separated-data settings

Describe the Metropolis-Hastings and Gibbs samplers, state the acceptance ratio, and explain why the target must be the full conditional or a reversible kernel

Diagnose MCMC convergence using trace plots, Gelman-Rubin statistics and effective sample size, and explain the effect of thinning and burn-in

Implement a random-walk Metropolis sampler and a Gibbs sampler for a small Bayesian GLM in R, and explain each line of the code

Fit a Bayesian survival model with a parametric baseline and a prior on the regression coefficients, and interpret the posterior hazard ratios

Explain the difference between a prior predictive and a posterior predictive check and use one on fitted data

Write R code that fits Cox, Weibull and logistic models, extracts coefficients and confidence intervals, and produces a forest plot

Explain how to handle missing data in survival analysis, distinguishing complete-case, multiple imputation and likelihood-based approaches

Reproduce a full survival analysis workflow in R from raw data: cleaning, censoring checks, Kaplan-Meier curves, log-rank test and Cox model

Simulate survival data from a Weibull model with a known covariate effect and check that the fitted model recovers the true parameters within the confidence interval

Apply a parametric graduation to a mortality dataset in R and compare the graduated rates with the crude rates graphically

Explain the log-rank test statistic and its relationship to the Cox score test, and state the null and alternative hypotheses precisely

Interpret output from a standard survival package including the concordance statistic and the global test of proportional hazards

Solve three timed mixed-topic problem sets under exam conditions and mark them against a rubric

List every formula you got wrong in weeks 1 to 7 and re-derive each one from first principles

Explain in writing the differences among Cox, Weibull and accelerated-failure-time models, and when each is preferred

Explain in writing how a GLM, a Bayesian GLM and a survival model share the same likelihood and inference machinery

Produce a final one-page summary sheet covering the key formulas and model-selection rules for all six domains