Course syllabus for Fundamentals of Statistical Modeling

Grunderna i statistisk modellering

Specific entry requirements

A Bachelor's degree or professional degree of at least 180 credits or the equivalent. The applicant must have completed a total of at least 60 credits in mathematics, statistics, and programming, of which univariate calculus, multivariate calculus, numerical methods, probability theory and statistics, and programming in a general-purpose programming language such as C++, Python, or Java. Proficiency in English equivalent to the Swedish upper secondary school course English 6/English B.

Outcomes

The course aims to equip the student with knowledge and understanding of tools for advanced statistical modeling and knowledge and understanding of how to apply these tools in biology, medicine, and health science. Upon completion of the course, the student should be able to:

Regarding knowledge and understanding

• Explain the relationship between cumulative distribution, probability mass/density, quantile, sparsity, cumulative hazard, and hazard functions,
• Explain the concepts of joint, marginal, and conditional distributions,
• Explain the differences between inference for sampled populations and unsampled populations and describe the general and specific assumptions underlying these two types of inference.

Regarding competence and skills

• Develop statistical models as mathematical functions for joint, marginal, and conditional probability distributions, both marginally and conditionally on covariates,
• Estimate parametric, semi-parametric, and non-parametric distribution functions,
• Propose a suitable statistical model for assessing a specific research hypothesis within biomedical research, estimate the model using standard statistical software, evaluate the fit of the model, and interpret the results.

Regarding judgement and approach

• Exhibit critical thinking and judgment in assessing the quality and validity of the statistical aspects of biomedical research studies.

Content

The course introduces students to a unified, general framework for data analyses as a statistical approach to science. It details the steps and potentials of creating statistical models for joint, marginal, and conditional probability distributions, possibly conditional on covariates; describes the similarities with other areas of science, such as physics and engineering; presents relevant summary measures and visual representations; clarifies the scientific importance of differentiating inferences on sampled populations from inferences on unsampled populations; explains the general and specific assumptions underlying the two types of inferences; introduces a framework to build, estimate, and evaluate statistical models; uses one single computational tool, the nonlinear optimized implemented in the “nlm” R function and in the “ml” Stata command.

The course focuses on real-life applications where all measured variables can take on a finite set of possible values, thus correcting the inherent biases of traditional methods like ordinary least-squares and maximum likelihood estimators. The course shows the connection of the unified, general framework to some popular statistical methods, like linear regression, logistic regression, Poisson regression, quantile regression, Cox regression, flexible parametric survival models, competing event models, mixed effects models, latent class analysis, group trajectory models, and more.

The students grow their knowledge of the foundations and philosophy of data analysis and statistical practice and learn to see any other statistical methods as special cases of a unified, general framework. They will also be prepared to pursue more advanced studies in statistics.

Teaching methods

The central teaching methods of the course are lectures, technology-supported learning (especially computer-based data analysis), self-studies, and group work. The course emphasizes active learning, i.e. applying knowledge in practice and critical reflection.

Examination

The examination consists of assignments (with written and/or oral presentation) and an individual written examination. The deliverable elements of the assignments (e.g., holding an oral presentation or submitting a written report) are to be completed before the end of the course according to the times specified in the schedule.

Compulsory participation
It is compulsory to attend the introduction to the course and the sessions in which the assignments are presented/discussed.

The examiner assesses if and, in that case, how absence from compulsory components can be compensated. The student must participate in all compulsory parts or compensate for absence in accordance with the examiner's instructions, in order to pass the course. Absence from a compulsory activity may result in the student not being able to compensate the absence until the next time the course is given.

Limit to the number of examinations
A student who does not pass the first examination is entitled to participate in five more examinations. If the student does not pass after four examinations, he/she is recommended to retake the course at the next regular course date, and may, after that, participate in two more examinations. If the student has failed six examinations, no additional examination or new admission is provided.

Physically attending or otherwise commencing an examination is regarded as an examination session. Handing in a blank exam is considered taking part in an examination session. An examination, for which the student registered but did not participate, is not counted as an examination session.

Adaption of examination
If there are special grounds, or a need for adaptation for a student with a disability, the examiner may decide to deviate from the syllabus' regulations on the examination form, number of examinations, the possibility of supplementation or exemptions from compulsory sections of the course. Content and learning outcomes as well as the level of expected skills, knowledge and abilities may not be changed, removed, or reduced.

Other directives

The course language is English

Literature and other teaching aids

Study material and reference articles will be provided during the course.