Logistic Regression and Survival Analysis

Code:

M6026

Acronym:

M6026

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2024/2025 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Doctoral Program in Applied Mathematics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PDMATAPL	1	Official Study Plan	1	-	3	21	81

Teaching language

Portuguese and english

Objectives

The aim of the course is to introduce different methods for estimation of parameters in logistic regression models under different contexts. 



Remark: The students were interested in studying  logistic regression models hence no survival analysis will be considered in this edition of the course.

Learning outcomes and competences

Upon completion of the course, students should be able to know, master and implement in R the methods for estimating parameters in logistic regression models with a linear predictor, with a partially linear predictor and with mixed effects (fixed and random).
These skills will enable better modelling of regression phenomena with a binary response that do not necessarily follow the more usual linear structure. 



Remark: The students were interested in studying  logistic regression models hence no survival analysis will be considered in this edition of the course.

Working method

Presencial

Program

Logistic regression as a generalized linear model. Estimation by maximum likelihood - Fisher method and the iteratively reweighted least squares method.
Logistic regression with a partially linear model. Estimation by local quasi-likelihood. Estimation by profile likelihood, backfitting, estimating equations and Speckman algorithm.
Logistic regression with a linear predictor and fixed and random effects. Estimation by penalized quasi-likelihood.

Remark: The students were interested in studying  logistic regression models hence no survival analysis will be considered in this edition of the course.

Mandatory literature

Rita Gaio; Apontamentos sobre a unidade curricular

Complementary Bibliography

McCullagh , P.; Generalized linear models. ISBN: 0-412-31760-5
Wolfgang Härdle , Axel Werwatz , Marlene Müller , Stefan Sperlich; Nonparametric and Semiparametric Models, Springer Series in Statistics, 2004
Fahrmeir, Kneib, Lang, Marx; Regression, Springer, 2021
Hosmer , David W.; Applied logistic regression. ISBN: 0-471-61553-6

Teaching methods and learning activities

Tutorial classes, with directed study interspersed with presentations by the teacher. The topics and problems proposed are discussed weekly and accompanied by material provided by the teacher.

Two individual written assignments with an oral presentation are foreseen.

Software

R

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Participação presencial	5,00
Apresentação/discussão de um trabalho científico	47,50
Trabalho escrito	47,50
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Apresentação/discussão de um trabalho científico	10,00
Estudo autónomo	36,00
Frequência das aulas	21,00
Trabalho escrito	14,00
Total:	81,00

Eligibility for exams

Written assignments and class attendance.

Calculation formula of final grade

Oral participation - maximum of 1 point;
Mark of assignment 1 / mark of assignment 2 - maximum of 20 points;
Final mark: 0.475*(mark from assignment 1) + 0.475*(mark from assignment 2) + (mark from oral participation)

Classification improvement

The student can only improve the mark for one of the assignments and the topic must be different from the one initially covered.