traj (version 3.0.0)

trajMeasures: Compute Measures for Identifying Patterns of Change in Longitudinal Data

Description

trajMeasures computes up to 20 measures for each longitudinal trajectory. See Details for the list of measures.

Usage

trajMeasures(
  Data,
  Time = NULL,
  ID = FALSE,
  measures = c(1:10, 12:20),
  midpoint = NULL,
  cap.outliers = FALSE
)
# S3 method for trajMeasures
print(x, ...)
# S3 method for trajMeasures
summary(object, ...)

Value

An object of class trajMeasures; a list containing the values of the measures, a table of the outliers which have been capped, as well as a curated form of the function's arguments.

Arguments

Data

a matrix or data frame in which each row contains the longitudinal data (trajectories).

Time

either NULL, a vector or a matrix/data frame of the same dimension as Data. If a vector, matrix or data frame is supplied, its entries are assumed to be measured at the times of the corresponding cells in Data. When set to NULL (the default), the times are assumed equidistant.

ID

logical. Set to TRUE if the first columns of Data and Time corresponds to an ID variable identifying the trajectories. Defaults to FALSE.

measures

a vector containing the numerical identifiers of the measures to compute. The default, c(1:10,12:20), excludes the measure which require specifying a midpoint.

midpoint

specifies which column of Time to use as the midpoint in measure 11 Can be NULL, an integer or a vector of integers of length the number of rows in Time. The default is NULL, in which case the midpoint is the time closest to the median of the Time vector specific to each trajectory.

cap.outliers

logical. If TRUE, extreme values of the measures will be capped. Defaults to FALSE.

x

object of class trajMeasures.

...

further arguments passed to or from other methods.

object

object of class trajMeasures.

Details

Each trajectory must have a minimum of 3 observations, otherwise it is omitted from the analysis. The 20 measures and their numerical identifiers are listed below. Please refer to the vignette for the specific formulas used to compute them.

1. Maximum
   

2. Minimum
   

3. Range
   

4. Mean value
   

5. Standard deviation
   

6. Slope of the affine approximation
   

7. Intercept of the affine approximation
   

8. Proportion of variance explained by the affine approximation
   

9. Rate of intersection with the best affine approximation
   

10. Net variation per unit of time
    

11. Late variation to early variation contrast
    

12. Total variation per unit time
    

13. Spikiness
    

14. Maximum of the first derivative
    

15. Minimum of the first derivative
    

16. Standard deviation of the first derivative
    

17. First derivative's net variation per unit of time
    

18. Maximum of the second derivative
    

19. Minimum of the second derivative
    

20. Standard deviation of the second derivative
    

If 'cap.outliers' is set to TRUE, Nishiyama's improved Chebychev bound for continuous distributions is used to determine extreme values for each measure, corresponding to a 0.3% probability threshold. Extreme values beyond the threshold are then capped to the 0.3% probability threshold (see vignette for more details).

References

Leffondre K, Abrahamowicz M, Regeasse A, Hawker GA, Badley EM, McCusker J, Belzile E. Statistical measures were proposed for identifying longitudinal patterns of change in quantitative health indicators. J Clin Epidemiol. 2004 Oct;57(10):1049-62. doi: 10.1016/j.jclinepi.2004.02.012. PMID: 15528056.

Nishiyama T, Improved Chebyshev inequality: new probability bounds with known supremum of PDF, arXiv:1808.10770v2 stat.ME https://doi.org/10.48550/arXiv.1808.10770

Examples

if (FALSE) {
data("trajdata")
trajdata.noGrp <- trajdata[, -which(colnames(trajdata) == "Group")] #remove the Group column

m1 = trajMeasures(trajdata.noGrp, ID = TRUE, measures = 19, midpoint = NULL)
m2 = trajMeasures(trajdata.noGrp, ID = TRUE, measures = 19, midpoint = 3)

identical(m1$measures, m2$measures)
}