Perform a smooth spline fit on growth data

growth.gcFitSpline performs a smooth spline fit on the dataset and determines the highest growth rate as the global maximum in the first derivative of the spline.

Usage

growth.gcFitSpline(
  time,
  data,
  gcID = "undefined",
  control = growth.control(biphasic = FALSE)
)

Arguments

time: Vector of the independent variable (usually time).
data: Vector of dependent variable (usually: growth values).
gcID: (Character) The name of the analyzed sample.
control: A grofit.control object created with growth.control, defining relevant fitting options.
biphasic: (Logical) Shall growth.gcFitSpline try to extract growth parameters for two different growth phases (as observed with, e.g., diauxic shifts) (TRUE) or not (FALSE)?

Value

A gcFitSpline object. The lag time is estimated as the intersection between the tangent at the maximum slope and the horizontal line with \(y = y_0\), where y0 is the first value of the dependent variable. Use plot.gcFitSpline to visualize the spline fit and derivative over time.

time.in: Raw time values provided to the function as time.
data.in: Raw growth data provided to the function as data.
raw.time: Filtered time values used for the spline fit.
raw.data: Filtered growth values used for the spline fit.
gcID: (Character) Identifies the tested sample.
fit.time: Fitted time values.
fit.data: Fitted growth values.
parameters: List of determined growth parameters.

A: Maximum growth.
dY: Difference in maximum growth and minimum growth.
mu: Maximum growth rate (i.e., maximum in first derivative of the spline).
tD: Doubling time.
t.max: Time at the maximum growth rate.
lambda: Lag time.
b.tangent: Intersection of the tangent at the maximum growth rate with the abscissa.
mu2: For biphasic growth: Growth rate of the second growth phase.
tD2: Doubling time of the second growth phase.
lambda2: For biphasic growth: Lag time determined for the second growth phase.
t.max2: For biphasic growth: Time at the maximum growth rate of the second growth phase.
b.tangent2: For biphasic growth: Intersection of the tangent at the maximum growth rate of the second growth phase with the abscissa.
integral: Area under the curve of the spline fit.

spline: smooth.spline object generated by the smooth.spline function.
spline.deriv1: list of time ('x') and growth ('y') values describing the first derivative of the spline fit.
reliable: (Logical) Indicates whether the performed fit is reliable (to be set manually).
fitFlag: (Logical) Indicates whether a spline fit was successfully performed on the data.
fitFlag2: (Logical) Indicates whether a second growth phase was identified.
control: Object of class grofit.control containing list of options passed to the function as control.

Details

If biphasic = TRUE, the following steps are performed to define a second growth phase:

Determine local minima within the first derivative of the smooth spline fit.
Remove the 'peak' containing the highest value of the first derivative (i.e., \(mu_{max}\)) that is flanked by two local minima.
Repeat the smooth spline fit and identification of maximum slope for later time values than the local minimum after \(mu_{max}\).
Repeat the smooth spline fit and identification of maximum slope for earlier time values than the local minimum before \(mu_{max}\).
Choose the greater of the two independently determined slopes as \(mu_{max}2\).

References

Matthias Kahm, Guido Hasenbrink, Hella Lichtenberg-Frate, Jost Ludwig, Maik Kschischo (2010). grofit: Fitting Biological Growth Curves with R. Journal of Statistical Software, 33(7), 1-21. DOI: 10.18637/jss.v033.i07

Examples

# Create random growth dataset
rnd.dataset <- rdm.data(d = 35, mu = 0.8, A = 5, label = 'Test1')

# Extract time and growth data for single sample
time <- rnd.dataset$time[1,]
data <- rnd.dataset$data[1,-(1:3)] # Remove identifier columns

# Perform spline fit
TestFit <- growth.gcFitSpline(time, data, gcID = 'TestFit',
                 control = growth.control(fit.opt = 's'))

plot(TestFit)