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Fit an exponential growth model with a heuristic linear method

Source: R/linear_fits.R
growth.gcFitLinear.Rd

Determine maximum growth rates from the log-linear part of a growth curve using a heuristic approach similar to the ``growth rates made easy''-method of Hall et al. (2013).

Usage

growth.gcFitLinear(
  time,
  data,
  gcID = "undefined",
  quota = 0.95,
  control = growth.control(t0 = 0, tmax = NA, log.x.gc = FALSE, log.y.lin = TRUE,
    min.growth = NA, max.growth = NA, lin.h = NULL, lin.R2 = 0.97, lin.RSD = 0.1, lin.dY
    = 0.05, 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.

quota

(Numeric, between 0 an 1) Define what fraction of \(mu_{max}\) the slope of regression windows adjacent to the window with highest slope should have to be included in the overall linear fit.

control

A grofit.control object created with growth.control, defining relevant fitting options.

log.x.gc

(Logical) Indicates whether ln(x+1) should be applied to the time data for linear and spline fits. Default: FALSE.

log.y.lin

(Logical) Indicates whether ln(y/y0) should be applied to the growth data for linear fits. Default: TRUE

min.growth

(Numeric) Indicate whether only growth values above a certain threshold should be considered for linear regressions.

max.growth

(Numeric) Indicate whether only growth values below a certain threshold should be considered for linear regressions.

t0

(Numeric) Minimum time value considered for linear and spline fits.

tmax

(Numeric) Minimum time value considered for linear and spline fits.

lin.h

(Numeric) Manually define the size of the sliding window . If NULL, h is calculated for each samples based on the number of measurements in the growth phase of the plot.

lin.R2

(Numeric) R2 threshold for growth.gcFitLinear

lin.RSD

(Numeric) Relative standard deviation (RSD) threshold for calculated slope in growth.gcFitLinear

lin.dY

(Numeric) Enter the minimum percentage of growth increase that a linear regression should cover.

biphasic

(Logical) Shall growth.gcFitLinear try to extract growth parameters for two different growth phases (as observed with, e.g., diauxic shifts) (TRUE) or not (FALSE)?

Value

A gcFitLinear object with parameters of the fit. The lag time is estimated as the intersection between the fit and the horizontal line with \(y=y_0\), where y0 is the first value of the dependent variable. Use plot.gcFitSpline to visualize the linear fit.

raw.time

Raw time values provided to the function as time.

raw.data

Raw growth data provided to the function as data.

filt.time

Filtered time values used for the heuristic linear method.

filt.data

Filtered growth values.

log.data

Log-transformed, filtered growth values used for the heuristic linear method.

gcID

(Character) Identifies the tested sample.

FUN

Linear function used for plotting the tangent at mumax.

fit

lm object; result of the final call of lm to perform the linear regression.

par

List of determined growth parameters.

  • y0: Minimum growth value considered for the heuristic linear method.

  • dY: Difference in maximum growth and minimum growth.

  • A: Maximum growth.

  • y0_lm: Intersection of the linear fit with the abscissa.

  • mumax: Maximum growth rate (i.e., slope of the linear fit).

  • tD: Doubling time.

  • mu.se: Standard error of the maximum growth rate.

  • lag: Lag time.

  • tmax_start: Time value of the first data point within the window used for the linear regression.

  • tmax_end: Time value of the last data point within the window used for the linear regression.

  • t_turn: For biphasic growth: Time of the inflection point that separates two growth phases.

  • mumax2: For biphasic growth: Growth rate of the second growth phase.

  • tD2: Doubling time of the second growth phase.

  • y0_lm2: For biphasic growth: Intersection of the linear fit of the second growth phase with the abscissa.

  • lag2: For biphasic growth: Lag time determined for the second growth phase..

  • tmax2_start: For biphasic growth: Time value of the first data point within the window used for the linear regression of the second growth phase.

  • tmax2_end: For biphasic growth: Time value of the last data point within the window used for the linear regression of the second growth phase.

ndx

Index of data points used for the linear regression.

ndx2

Index of data points used for the linear regression for the second growth phase.

control

Object of class grofit.control containing list of options passed to the function as control.

rsquared

R2 of the linear regression.

rsquared2

R2 of the linear regression for the second growth phase.

fitFlag

(Logical) Indicates whether linear regression was successfully performed on the data.

fitFlag2

(Logical) Indicates whether a second growth phase was identified.

reliable

(Logical) Indicates whether the performed fit is reliable (to be set manually).

Details

The algorithm works as follows:

  1. Fit linear regressions (Theil-Sen estimator) to all subsets of h consecutive, log-transformed data points (sliding window of size h). If for example \(h=5\), fit a linear regression to points 1 ... 5, 2 ... 6, 3 ... 7 and so on.

  2. Find the subset with the highest slope \(mu_{max}\). Do the R2 and relative standard deviation (RSD) values of the regression meet the in lin.R2 and lin.RSD defined thresholds and do the data points within the regression window account for a fraction of at least lin.dY of the total growth increase? If not, evaluate the subset with the second highest slope, and so on.

  3. Include also the data points of adjacent subsets that have a slope of at least \(quota \cdot mu{max}\), e.g., all regression windows that have at least 95% of the maximum slope.

  4. Fit a new linear model to the extended data window identified in step 3.

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

  1. Perform a smooth spline fit on the data with a smoothing factor of 0.5.

  2. Calculate the second derivative of the spline fit and perform a smooth spline fit of the derivative with a smoothing factor of 0.4.

  3. Determine local maxima and minima in the second derivative.

  4. Find the local minimum following \(mu_{max}\) and repeat the heuristic linear method for later time values.

  5. Find the local maximum before \(mu_{max}\) and repeat the heuristic linear method for earlier time values.

  6. Choose the greater of the two independently determined slopes as \(mu_{max}2\).

References

Hall, BG., Acar, H, Nandipati, A and Barlow, M (2014) Growth Rates Made Easy. Mol. Biol. Evol. 31: 232-38, DOI: 10.1093/molbev/mst187

Petzoldt T (2022). growthrates: Estimate Growth Rates from Experimental Data. R package version 0.8.3, https://CRAN.R-project.org/package=growthrates.

Theil, H.(1992). A rank-invariant method of linear and polynomial regression analysis. In: Henri Theil’s contributions to economics and econometrics. Springer, pp. 345–381. DOI: 10.1007/978-94-011-2546-8_20

See also

Other growth fitting functions: growth.drFit(), growth.gcBootSpline(), growth.gcFitModel(), growth.gcFitSpline(), growth.gcFit(), growth.workflow()

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 linear fit
TestFit <- growth.gcFitLinear(time, data, gcID = "TestFit",
                 control = growth.control(fit.opt = "l"))

plot(TestFit)