Learning objectives

This page lists the chapter-specific and overall learning objectives for the course

Introduction

At the end of this chapter, students should be able to

  • Understanding the role of uncertainty in decision making.
  • Understanding the importance of signal-to-noise ratio as a measure of evidence.
  • Formulating the null and alternative hypotheses attached to a problem statement.
  • Understanding and correctly interpreting \(p\)-values and confidence intervals;

Linear regression

At the end of the chapter, students should be able to

  • interpret the coefficients of a linear model (binary, continuous and categorical variables);
  • fit the model by least squares (using dedicated software), correctly accounting for categorical variables;
  • test for statistical significance of model parameters as well as global significance;
  • obtain predictions from a linear model using software; understand the distinction between estimated mean and predicted values;
  • interpret the coefficients of the log-linear model on a meaningful scale;
  • interpret and test the significance of interaction terms between continuous and categorical variables, as well as between two categorical variables;
  • conceptualize the notion of collinearity and understand its impacts on statistical inference.
  • test for equality of means in multiple (sub-groups) and also mean differences between groups with one or two factors;
  • list the assumptions of the linear model and understand their meaning;
  • use graphical diagnostic tools to validate the model assumptions.

Likelihood-based modelling

At the end of the chapter, students should be able to:

  • understand what the likelihood represents;
  • derive the maximum likelihood estimator of a simple model;
  • understand the maximum likelihood principle;
  • perform likelihood ratio tests for two nested models using software output;
  • use information criteria to compare two non-nested models. Generalized linear models At the end of the chapter, students should be able to
  • write the equation linking predictors and parameters for Poisson, binomial and normal generalized linear models with canonical link function;
  • understand the relationship between mean and variance in generalized linear models;
  • interpret parameters of the Poisson and negative binomial models;
  • test for overdispersion in Poisson models using likelihood ratio tests;
  • assess the quality of the fit of a Poisson model using the deviance statistic;
  • test independence in contingency tables using a saturated Poisson model.
  • interpret software output for generalized linear models and the respective merits of different functions;
  • interpret parameters of logistic regression models in terms of log-odds.
  • model success rate for aggregated data using a Poisson regression with an offset or a binomial generalized linear regression and correctly interpret the rates.

Correlated and longitudinal data

At the end of the chapter, students should be able to

  • understand how correlation appears in grouped or longitudinal data;
  • correctly calculate summary statistics for repeated data;
  • adjust models with compound symmetry, first-order autoregressive or unstructured correlation structures;
  • write correlation and covariance models for main models and understand their parametrization;
  • perform tests to compare covariance structures (for nested models) or using information criteria;
  • understand group heteroscedasticity and how to account for it.

Linear mixed models

At the end of the chapter, students should be able to

  • understand the concept of group-effect;
  • know in which context to use random group-effects as opposed to fixed group-effects (covariates constant within group, large number of groups with few observations in each);
  • write down the equation of the mixed model with random-intercept(s) and random-slope(s);
  • write down the model assumptions (linearity, covariance within-group and between-group, etc.);
  • write the covariance matrix of observations given parameter estimates (sum of covariance matrices of random effects and errors);
  • distinguish between the adequate structures for correlated and longitudinal data;
  • distinguish predicted (marginal) mean and individual predictions with random effects (conditional);
  • obtain predictions for new observations from mixed models using dedicated software.

Introduction to survival analysis

At the end of the chapter, students should be able to

  • explain key concepts (truncation, censoring) arising in survival analysis in your own word and provide examples of the latter;
  • recognize scenarios with random right censoring;
  • interpret a Kaplan–Meier nonparametric estimate of the survival function;
  • compare and test for equality of survival curves using a score test;
  • interpret the coefficients of the Cox proportional hazard model and check for their significance.

Global objectives

At the end of the course, students should be able to de

  • set up a database in a format suitable for a regression analysis (e.g., in long format).
  • choose an adequate regression model for data.
  • criticise the quality of model fit.
  • synthetise the conclusions of a regression model.
  • compare different regression models based on their respective benefits.
  • formulate practical recommandations based on a regression model.