Abstract
BackgroundIt is often desirable to observe how a disease progresses over time in individual patients, rather than graphing group averages; and since multiple outcomes are typically recorded on each patient, it would be advantageous to visualise disease progression on multiple variables simultaneously.MethodsA variety of vector plots and a path plot have been developed for this purpose, and data from a longitudinal Huntington's disease study are used to illustrate the utility of these graphical methods for exploratory data analysis.ResultsInitial and final values for three outcome variables can be easily visualised per patient, along with the change in these variables over time. In addition to the disease trajectory, the path individual patients take from initial to final observation can be traced. Categorical variables can be coded with different types of vectors or paths (e.g. different colours, line types, line thickness) and separate panels can be used to include further categorical or continuous variables, allowing clear visualisation of further information for each individual. In addition, summary statistics such as mean vectors, bivariate interquartile ranges and convex polygons can be included to assist in interpreting trajectories, comparing groups, and detecting multivariate outliers.ConclusionVector and path plots are useful graphical methods for exploratory data analysis when individual-level information on multiple variables over time is desired, and they have several advantages over plotting each variable separately.
Highlights
It is often desirable to observe how a disease progresses over time in individual patients, rather than graphing group averages; and since multiple outcomes are typically recorded on each patient, it would be advantageous to visualise disease progression on multiple variables simultaneously
This would be useful for exploratory data analysis (EDA), as it would allow for the detection of bivariate or multivariate outliers – patients whose values on any single variable are within the normal range, but whose values on a combination of variables is unusual
Due to the work of Tukey [10], Cleveland [11,12], Cook and Swayne [13], and many others [14], it is widely recognised that to fully appreciate the structure of data it must be examined visually. This is true of multivariate data, and we have developed several variations of a standard vector plot and used these to visualise disease progression in a cohort of patients with Huntington's disease from a recent paper by Michell et al [15], especially the data shown in Figure three of that paper
Summary
It is often desirable to observe how a disease progresses over time in individual patients, rather than graphing group averages; and since multiple outcomes are typically recorded on each patient, it would be advantageous to visualise disease progression on multiple variables simultaneously. Clinical studies typically measure multiple outcomes on patients as well as record information on patient characteristics such as age, sex, genotype, disease severity, and age of onset Many such studies are longitudinal, where initial or baseline values are obtained, and patients are followed over time to observe how the disease progresses. If time is included as a variable 'multivariate' generally refers to multiple observations on a single variable, and the ability to visualise multiple observations on multiple variables for each individual would be of great use in understanding the results of many biomedical studies This would be useful for exploratory data analysis (EDA), as it would allow for the detection of bivariate or multivariate outliers – patients whose values on any single variable are within the normal range, but whose values on a combination of variables is unusual. EDA allows for the detection of novel or interesting relationships in the data – relationships that may not have been predicted beforehand, and which might go unnoticed with standard analytical methods
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