Statistical Modelling

Emerging data collection protocols in clinical research introduce complexities, which are either not covered by existing generally available software, or more fundamentally, require further statistical methodological development.

The Department accommodates several inter-linked research groups with interests on methodologies and software of Multivariate data modelling, Joint longitudinal and event history modelling, Statistical Genetics and Pharmacogenomics, Prognostic modelling and Causal analysis.

Multivariate data modelling

Multivariate data modelling is often applied to address research questions such as ‘are there a small number of underlying factors explaining the variables in the dataset?’, ‘is there a natural clustering in the dataset?’, ‘can we classify individuals into groups based on their characteristics?’ or ‘can we predict that a person will develop a particular condition/disease by looking at a range of symptoms?’

The multivariate modelling research group has expertise in multivariate methodologies, their application to clinical data, and the development of software in R and in other statistical packages. The group aims to develop methodologies and disseminate concepts among researchers and clinicians.

Commonly applied multivariate techniques are discriminant function analysis, cluster analysis, principal components analysis, factor analysis, multidimensional scaling and MANOVA amongst others.

For further information, contact Prof Marta Garcia-Finana or visit the Liverpool multivariate modelling group website.

Joint longitudinal and event history modelling

Often in health research, patients are followed-up over time to monitor the progression of a disease as it develops using some biomarkers. Hence, the need for joint modelling of combined longitudinally repeated measurements and event-time data to investigate how the patterns over time in biomarkers relate to prognosis for the patient, and in particular to the timing of clinically significant events. However, a major difficulty is how best to merge information from the longitudinally repeated measurements and event history data, especially as the longitudinal data is usually irregularly and imperfectly observed.

Further, although longitudinal data are prevalent throughout the medical literature, joint modelling methods are not routinely used. Often, simpler approaches are used, for example separate analyses of longitudinal and event-time data, because of the ready availability of standard software. These methods potentially suffer from inefficiency or, worse, severe bias through misspecification, for example by failing to take account of informative dropout during the intended follow-up period.

The JoineR collaboration involves (1) Development of novel statistical methods for the analysis of complex longitudinal data structures, (2) Implementation of user-friendly software for new statistical methods, and (3) Dissemination of the modern methods of statistical analysis to the medical research community.

For further information, contact Dr Ruwanthi Kolamunnage-Dona, Dr Maria Sudell, or visit the Joint modelling group website.

Prognostic modelling

Prognosis research provides information crucial to understanding, explaining and predicting future clinical outcomes in people with existing disease or health conditions. In particular, clinical prediction models estimate the risk of existing disease (diagnostic prediction model) or future outcome (prognostic prediction model) for an individual, conditional on their values of multiple predictors (prognostic or risk factors) such as age, sex and biomarkers.

A large number of prediction models are published in the medical literature each year, and most are developed using a regression framework such as logistic and Cox regression. Prediction models are also known as risk scores, prognostic indices, or prognostic scores.

The prognosis research group is focussed on (1) Development and validation (both internal and external) methodologies of prognostic models, (2) Extending areas of clinical application, and (3) Disseminating concepts among researchers and healthcare professionals. The group has expertise in the development of software in R language and in other statistical packages, as well as presentation formats based on stakeholder engagement.

For further information, contact Dr Laura Bonnett or visit the Prognosis Research Group website.

Causal analysis

Understanding whether a treatment, intervention or policy causally affects an outcome variable is often a question of interest in medicine, epidemiology, public health and social sciences. Randomised controlled trials (RCTs) have long been viewed as the goal standard for addressing causal questions. However, nonadherence to treatment is common in general medical practice and trials, with huge economic and clinical consequences. 

In the presence of deviations from randomised treatment in RCTs, the underlying random assignment mechanism, which forms the basis for unbiased hypothesis testing, no longer reflects treatment received, and an intention to treat analysis only provides a causal estimate of the policy of prescribing treatment, rather than of the efficacy of treatment actually received. Regulatory and funding bodies are increasingly recognising the importance of considering adherence in trial efficacy analyses, with growing awareness of appropriate statistical causal methodologies which seek to overcome selection biases associated with simple methods such as per protocol analysis. However, such methodologies are not commonly used in trial settings, as they are unfamiliar to researchers.

Though RCTs are often considered superior to observational studies, the latter more closely reflect real life and are subject to fewer feasibility and ethical issues. Overcoming the  underuse of observational studies in addressing causal questions may save time and money. Projects of interest to the causal analysis research group include 1) Development and application of causal methodologies in both observational studies and randomised trials, 2) Implementation of user-friendly analysis tools to make causal analysis methods easily accessible to researchers and 3) Development of novel methodologies to obtain accurate adherence information to inform causal analyses.

For further information, contact Dr Susanna Dodd or Dr Schadrac Agbla.

Bayesian methods

Bayesian methods offer a different viewpoint to classical frequentist approaches. Rather than treating unknown parameters as fixed quantities, Bayesian approaches treat them as unknown random variables. This enables one to model the uncertainty by defining a probability distribution over the possible values of the unknown parameters (regarded as variables) . Prior to observing data, a prior distribution for each unknown variable is specified based on prior beliefs regarding the likely values of the unknown parameter. After observing data, Bayes theorem is then used to compute the posterior probability for the unknown variables and inferences can then be drawn. 

The Bayesian Methods Group aims to apply and develop Bayesian methodologies, disseminate and discuss concepts among researchers and clinicians, and to foster collaborations. The group has expertise in applying Bayesian methods in various contexts, such a meta-analysis, trial analysis and joint modelling. The group can apply methods using a range of software including, R, Stan, and WinBugs.

The group is open to research staff and students who apply or develop Bayesian methods in their research.


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