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Find the best terminal elimination rate constant (lambdaz)

Source: R/find_best_lambdaz.R
find_best_lambdaz.Rd

Identifies the optimal terminal phase for lambdaz estimation using a systematic log-linear regression approach with adjusted R-squared optimization criteria.

Usage

find_best_lambdaz(
  time,
  conc,
  route = "bolus",
  duration = NULL,
  adj_r_squared_threshold = 0.7,
  nlastpoints = 3,
  tolerance = 1e-04
)

Arguments

time

Numeric vector of observation time points.

conc

Numeric vector of concentration measurements corresponding to time points.

route

Administration method specification:

  • "bolus" (default) - Excludes time of maximum concentration (Tmax) point

  • "infusion" - Includes Tmax point in terminal phase evaluation

  • "oral" - Starts regression from Tmax point

duration

Numeric (optional). Duration of infusion administration, in the same time units as time. Required only when route = "infusion". Used to determine the first post-infusion observation time for terminal phase regression.

adj_r_squared_threshold

Minimum acceptable adjusted R-squared value for valid estimation (default = 0.7). Values below this threshold will generate warnings.

nlastpoints

Integer. Minimum number of terminal points (from the end of the profile) to include when evaluating candidate regression segments for \(\lambda_z\). Default is 3.

tolerance

Threshold for considering adjusted R-squared values statistically equivalent (default = 1e-4). Used when selecting between fits with similar goodness-of-fit.

Value

A list containing:

  • lambdaz: Estimated terminal elimination rate constant (\(\lambda_z\)), or NA if no valid fit

  • UsedPoints: Number of data points used in the optimal fit

  • adj.r.squared: Adjusted R-squared value (\(R^2\)) of the optimal regression

  • message: Character vector containing diagnostic messages or warnings

Details

The algorithm implements the following decision logic:

  1. Identifies the time of maximum observed concentration (Tmax)

  2. Defines candidate terminal phases starting from the last 3 measurable concentrations

  3. Iteratively evaluates longer time spans by including preceding data points

  4. For each candidate phase:

    • Performs log-concentration vs. time linear regression

    • Requires negative regression slope (positive \(\lambda_z\))

    • Calculates adjusted R-squared metric

  5. Selects the optimal phase based on:

    • Highest adjusted R-squared value

    • When R-squared differences are < tolerance, selects the fit with more points

  6. Validates final selection against R-squared threshold

Author

Zhonghui Huang

Examples

# Basic usage
time <- c(0.5, 1, 2, 4, 6, 8, 10)
conc <- c(12, 8, 5, 3, 2, 1.5, 1)
find_best_lambdaz(time, conc)
#> $lambdaz
#> [1] 0.1791759
#> 
#> $UsedPoints
#> [1] 4
#> 
#> $adj.r.squared
#> [1] 0.9935461
#> 
#> $message
#> [1] "Selected 4 points (higher Rsquare) Rsquare=0.9935 lambdaz=0.1792"
#> 
#> $slopefit
#> 
#> Call:
#> lm(formula = log(conc[subset]) ~ time[subset])
#> 
#> Coefficients:
#>  (Intercept)  time[subset]  
#>       1.8035       -0.1792  
#> 
#> 

# With infusion route specification
find_best_lambdaz(time, conc, route = "bolus",duration=1)
#> $lambdaz
#> [1] 0.1791759
#> 
#> $UsedPoints
#> [1] 4
#> 
#> $adj.r.squared
#> [1] 0.9935461
#> 
#> $message
#> [1] "Selected 4 points (higher Rsquare) Rsquare=0.9935 lambdaz=0.1792"
#> 
#> $slopefit
#> 
#> Call:
#> lm(formula = log(conc[subset]) ~ time[subset])
#> 
#> Coefficients:
#>  (Intercept)  time[subset]  
#>       1.8035       -0.1792  
#> 
#> 

# Custom threshold settings
find_best_lambdaz(time, conc, adj_r_squared_threshold = 0.8, tolerance = 0.001)
#> $lambdaz
#> [1] 0.1791759
#> 
#> $UsedPoints
#> [1] 4
#> 
#> $adj.r.squared
#> [1] 0.9935461
#> 
#> $message
#> [1] "Selected 4 points (higher Rsquare) Rsquare=0.9935 lambdaz=0.1792"
#> 
#> $slopefit
#> 
#> Call:
#> lm(formula = log(conc[subset]) ~ time[subset])
#> 
#> Coefficients:
#>  (Intercept)  time[subset]  
#>       1.8035       -0.1792  
#> 
#>