Dynamic longitudinal discriminant analysis using multiple longitudinal markers of different types

Abstract

There is an emerging need in clinical research to accurately predict patients’ disease status and disease progression by optimally integrating multivariate clinical information. Clinical data are often collected over time for multiple biomarkers of different types (e.g. continuous, binary and counts). In this paper, we present a flexible and dynamic (time-dependent) discriminant analysis approach in which multiple biomarkers of various types are jointly modelled for classification purposes by the multivariate generalized linear mixed model. We propose a mixture of normal distributions for the random effects to allow additional flexibility when modelling the complex correlation between longitudinal biomarkers and to robustify the model and the classification procedure against misspecification of the random effects distribution. These longitudinal models are subsequently used in a multivariate time-dependent discriminant scheme to predict, at any time point, the probability of belonging to a particular risk group. The methodology is illustrated using clinical data from patients with epilepsy, where the aim is to identify patients who will not achieve remission of seizures within a five-year follow-up period.

Identifying patients who will not reachieve remission after breakthrough seizures

“…We considered four variables that were recorded at each follow‐up visit and modeled the changes in these variables over time using a multivariate generalized linear mixed model . Separate models were fitted to patients who are known to have achieved another remission period of 12 months within 2 years following breakthrough and those who did not.…”

Dynamic classification using credible intervals in longitudinal discriminant analysis

“…In this approach, a patient's group membership (remission/refractory) does not change and is based on their observed condition at 5 years from initial diagnosis. Good levels of classification accuracy were achieved by Hughes et al, with sensitivity and specificity showing values above 90%. However, a positive predictive value (PPV) of 59% was reported, which implies that 41% of patients who were classified using the LoDA approach as not achieving remission of seizures did in fact achieve remission.…”

“…Fieuws et al presented a multivariate LoDA method for both continuous and binary longitudinal markers. An alternative multivariate LoDA method for longitudinal markers of different types (continuous, counts, and binary), which is robustified against possible model misspecification, was recently developed by Hughes et al These models use the longitudinal history of patients of known prognosis to develop a classification procedure that can be used to classify new patients based on their own longitudinal data. For each patient, a probability of belonging to each prognostic group is calculated and used in an allocation scheme to assign the new patient to a group.…”

“…The approach of Hughes et al aimed to identify those patients who will fail to achieve remission from seizures within a 5‐year follow‐up period. Patients who achieve a continuous 12‐month period free from seizures within 5 years of diagnosis are regarded as being in “remission,” whereas patients who do not are referred to as “refractory.” Clinical interest is in being able to assess, each time a patient attends follow‐up, their risk of ultimately belonging to the refractory group.…”

“…In all of the LoDA procedures referenced above, point estimates , g =0,…, G −1, of the group membership probabilities are used to derive the prediction , ie, to assign a new patient to a group. However, the precision of these estimated probabilities may be different for different patients and also at different occasions.…”