Methods in Mathematics and Statistics
A.Y. 2020/2021
Learning objectives
The general objective of the course is to develop in the student the critical ability to evaluate the scientific evidence in support of biomedicine for prevention, diagnosis, treatment and rehabilitation with reference to the integration of laboratory tests for diagnosis, practical efficacy of the therapy, and of prognostic indicators.
In the student's training process, the acquisition of this ability contributes, from an ethical and deontological perspective, to the construction of a mental habitus capable of integrating the knowledge produced by good biomedical and clinical research into the cultural and professional sphere. A habit that is now considered necessary for all professions related to basic and applied biomedical research together with the processes of health technology assessment (HTA).
As specific objectives, the course aims to develop the knowledge and skills related to:
i)statistical methods that make it possible to describe and evaluate the different sources of variability;
ii)diagnostic tests and related measures of reliability and diagnostic relevance;
iii)basic principles of planning observational studies, interpretation of disease occurrence measures and the association between risk factors and disease occurrence;
iv)the relationships between statistics and the foundations of the inductive / deductive scientific method for empirical research, with reference to the planning of observation and experimental studies and methods of statistical inference;
v)basic principles of ethics and the relationship with the methodology of biomedical research with specific reference to experimental studies of therapeutic efficacy.
In the student's training process, the acquisition of this ability contributes, from an ethical and deontological perspective, to the construction of a mental habitus capable of integrating the knowledge produced by good biomedical and clinical research into the cultural and professional sphere. A habit that is now considered necessary for all professions related to basic and applied biomedical research together with the processes of health technology assessment (HTA).
As specific objectives, the course aims to develop the knowledge and skills related to:
i)statistical methods that make it possible to describe and evaluate the different sources of variability;
ii)diagnostic tests and related measures of reliability and diagnostic relevance;
iii)basic principles of planning observational studies, interpretation of disease occurrence measures and the association between risk factors and disease occurrence;
iv)the relationships between statistics and the foundations of the inductive / deductive scientific method for empirical research, with reference to the planning of observation and experimental studies and methods of statistical inference;
v)basic principles of ethics and the relationship with the methodology of biomedical research with specific reference to experimental studies of therapeutic efficacy.
Expected learning outcomes
L'insegnamento si propone di far acquisire agli studenti gli strumenti metodologici necessari per conoscere, saper applicare e valutare, attraverso l'analisi critica della letteratura biomedica:
-i concetti di attendibilità, accuratezza e precisione, ripetibilità e riproducibilità delle misure;
-l'utilità dei test diagnostici e degli indici prognostici;
-le misure di occorrenza di malattia e di associazione con fattori di rischio/beneficio utilizzate in epidemiologia/ricerca clinica;
-l'identificazione delle sorgenti di imprecisione e di inaccuratezza negli studi epidemiologici/clinici;
-la differenza tra studi basati sull'osservazione e sulla sperimentazione insieme ai principali disegni di studio in epidemiologia/ricerca clinica per la valutazione delle relazioni causali insieme alla riflessione sugli aspetti etici della ricerca biomedica
-l'efficacia delle terapie, delle pratiche riabilitative, dei programmi di prevenzione, riportata da studi osservazionali e sperimentali.
-i concetti di attendibilità, accuratezza e precisione, ripetibilità e riproducibilità delle misure;
-l'utilità dei test diagnostici e degli indici prognostici;
-le misure di occorrenza di malattia e di associazione con fattori di rischio/beneficio utilizzate in epidemiologia/ricerca clinica;
-l'identificazione delle sorgenti di imprecisione e di inaccuratezza negli studi epidemiologici/clinici;
-la differenza tra studi basati sull'osservazione e sulla sperimentazione insieme ai principali disegni di studio in epidemiologia/ricerca clinica per la valutazione delle relazioni causali insieme alla riflessione sugli aspetti etici della ricerca biomedica
-l'efficacia delle terapie, delle pratiche riabilitative, dei programmi di prevenzione, riportata da studi osservazionali e sperimentali.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Premise
Short historical overview of quantitative methods in medicine
Role of medical statistics in clinical practice .
Types of studies.
Introduction to Health Technology Assessment
The variability of biological phenomena
Measurement scales
Sources of variability
Variability within and between subjects
Maesurement errors
Accuracy and precision
Elements of descriptive statistics
Graphical representations
Measures of location and dispersion
Measures of correlation
Data transformations and empirical distributions.
Diagnostic and screening tests
The diagnostic test with dichotomous response vs more categories.
Properties of a test and informative contribution (screening and confirmatory)
Sensitivity and specificity, positive and negative predictive values (PPV,NPV) .
Odds and likelihood ratios for the calculation of PPV and NPV .
The Fagan nomogram and its practical application in the development and evaluation of diagnostic tests
Introduction to Probability
i ) expected proportion of a population study ;
ii ) the inherent properties of a system;
iii ) subjective opinion of the researcher.
iv) Intuitive introduction to probability models
Statistical inference 1: parameter estimation in statistical models
Sample variability and sampling distributions.
Empirical sample proportions.
The concept of estimation of the parameters of a probability model .
Intuitive introduction to the results of the central limit theorem
Empirical derivation of the Gaussian distribution
Point estimates and standard errors.
Confidence intervals .
Study of the association between risk factors and disease.
Probability and risk of a disease
Measures of prevalence and incidence.
Relative risk and odds ratio between exposed and not exposed to a risk factor.
Measures in cohort and case-control studies
Statistical Inference 2: Test of statistical hypotheses .
Application of the statistical test for comparison between groups with different treatment .
The statistical significance
The power of a statistical test
Comparison between statistical significance and clinical relevance.
The general linear model
Simple linear model
Method for estimating least squares and maximum likelihood
Inference on the regression coefficients and ANOVA of the model
Explained variability and coefficient of determination
Multiple regression model
Interpretation of the regression coefficients
Partial determination coefficients
Model fitting: residual analysis and identification of influential observations
Assesement of a medical intervention.
Etical issues in observational and experimental studies
Clinical trials of phase I, II and III
Target population and inclusion criteria .
Random assignment to treatment.
Measures of effectiveness of treatments
Confounding and interaction ( treatment response)
Short historical overview of quantitative methods in medicine
Role of medical statistics in clinical practice .
Types of studies.
Introduction to Health Technology Assessment
The variability of biological phenomena
Measurement scales
Sources of variability
Variability within and between subjects
Maesurement errors
Accuracy and precision
Elements of descriptive statistics
Graphical representations
Measures of location and dispersion
Measures of correlation
Data transformations and empirical distributions.
Diagnostic and screening tests
The diagnostic test with dichotomous response vs more categories.
Properties of a test and informative contribution (screening and confirmatory)
Sensitivity and specificity, positive and negative predictive values (PPV,NPV) .
Odds and likelihood ratios for the calculation of PPV and NPV .
The Fagan nomogram and its practical application in the development and evaluation of diagnostic tests
Introduction to Probability
i ) expected proportion of a population study ;
ii ) the inherent properties of a system;
iii ) subjective opinion of the researcher.
iv) Intuitive introduction to probability models
Statistical inference 1: parameter estimation in statistical models
Sample variability and sampling distributions.
Empirical sample proportions.
The concept of estimation of the parameters of a probability model .
Intuitive introduction to the results of the central limit theorem
Empirical derivation of the Gaussian distribution
Point estimates and standard errors.
Confidence intervals .
Study of the association between risk factors and disease.
Probability and risk of a disease
Measures of prevalence and incidence.
Relative risk and odds ratio between exposed and not exposed to a risk factor.
Measures in cohort and case-control studies
Statistical Inference 2: Test of statistical hypotheses .
Application of the statistical test for comparison between groups with different treatment .
The statistical significance
The power of a statistical test
Comparison between statistical significance and clinical relevance.
The general linear model
Simple linear model
Method for estimating least squares and maximum likelihood
Inference on the regression coefficients and ANOVA of the model
Explained variability and coefficient of determination
Multiple regression model
Interpretation of the regression coefficients
Partial determination coefficients
Model fitting: residual analysis and identification of influential observations
Assesement of a medical intervention.
Etical issues in observational and experimental studies
Clinical trials of phase I, II and III
Target population and inclusion criteria .
Random assignment to treatment.
Measures of effectiveness of treatments
Confounding and interaction ( treatment response)
Prerequisites for admission
No preliminary knowledge is requested
Teaching methods
The teaching methods consider lectures, exercises, seminars and non-formal teaching activities in small groups oriented to the acquisition of practical skills.
The preparation of documents and / or research with the use of telematic supports is also considered
In detail:
- Frontal lessons supported by slides.
- Group exercises
- Professional training activity carried out on PC with open source software R Commander. Bibliographic research methods on portals and certified search engines for medicine.
to learn how to correctly apply descriptive and interpretative models to real data sets, to critically use diagnostic tests, through the application of the concepts of norm and probability in biomedicine, and finally to evaluate the results of biomedical research, also through the critical analysis of literature.
The preparation of documents and / or research with the use of telematic supports is also considered
In detail:
- Frontal lessons supported by slides.
- Group exercises
- Professional training activity carried out on PC with open source software R Commander. Bibliographic research methods on portals and certified search engines for medicine.
to learn how to correctly apply descriptive and interpretative models to real data sets, to critically use diagnostic tests, through the application of the concepts of norm and probability in biomedicine, and finally to evaluate the results of biomedical research, also through the critical analysis of literature.
Teaching Resources
A specific text is not indicated but some possible reference texts
M. Pagano e K. Gauvreau Biostatistica (2ª edizione)
Editore: Idelson-Gnocchi 2003
M. Bland Statistica medica (Idee & strumenti)
Editore: Apogeo 2009
JF. Jekel, DL. Katz, JG. Elmore, DMG. Wild Epidemiologia Biostatistica e Medicina Preventiva (3ª edizione)
Editore: Masson 2009
Statistica medica : intervalli di confidenza nella ricerca biomedica / D. G. Altman ... [et al.] ; edizione italiana a cura di F. Cavallo. - 2. ed.-Torino : Minerva medica, 2004. - , 238 p..
La medicina basata sulle evidenze scientifiche: come praticare e insegnare l'EBM / D. L. Sackett °et al. - 2. ed. riv. e ampliata, ed. italiana / a cura di Marco Bobbio. - Torino : Centro scientifico, °2002. - XVI, 248 p.
The course slides and additional materials presented in class are available on the Ariel teaching website
M. Pagano e K. Gauvreau Biostatistica (2ª edizione)
Editore: Idelson-Gnocchi 2003
M. Bland Statistica medica (Idee & strumenti)
Editore: Apogeo 2009
JF. Jekel, DL. Katz, JG. Elmore, DMG. Wild Epidemiologia Biostatistica e Medicina Preventiva (3ª edizione)
Editore: Masson 2009
Statistica medica : intervalli di confidenza nella ricerca biomedica / D. G. Altman ... [et al.] ; edizione italiana a cura di F. Cavallo. - 2. ed.-Torino : Minerva medica, 2004. - , 238 p..
La medicina basata sulle evidenze scientifiche: come praticare e insegnare l'EBM / D. L. Sackett °et al. - 2. ed. riv. e ampliata, ed. italiana / a cura di Marco Bobbio. - Torino : Centro scientifico, °2002. - XVI, 248 p.
The course slides and additional materials presented in class are available on the Ariel teaching website
Assessment methods and Criteria
The exam requires and having participated profitably in small group activities for the non-formal teaching part, evaluated with the presentation and discussion of the reports.
The exam includes a written test divided into two parts of 1) Statistics and 2) Evidence Assessment organized as follows:
1) problem solving (simple calculation exercises related to the topics covered in each module of the course);
2) interpretation of the results of an original in-depth study on the themes of practical teaching
Students, equipped with a suitable calculator as an aid to solving the proposed exercises, can freely consult any paper material they deem appropriate for taking the exam.
The results of the exam are communicated through the Ariel teaching website
The exam includes a written test divided into two parts of 1) Statistics and 2) Evidence Assessment organized as follows:
1) problem solving (simple calculation exercises related to the topics covered in each module of the course);
2) interpretation of the results of an original in-depth study on the themes of practical teaching
Students, equipped with a suitable calculator as an aid to solving the proposed exercises, can freely consult any paper material they deem appropriate for taking the exam.
The results of the exam are communicated through the Ariel teaching website
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/07 - MATHEMATICAL PHYSICS
Practicals: 32 hours
Lessons: 32 hours
Lessons: 32 hours
Professor:
Biganzoli Elia
Professor(s)