HalfLife Calculation
Bill Denney
Source:vignettes/v06halflifecalculation.Rmd
v06halflifecalculation.Rmd
Introduction
Halflife is calculated by fitting the natural logarithm of concentration by time. The default calculation method is curve stripping (described in more detail below). Manual halflife points with no automated halflife selection can be performed, or specific points can be excluded while still performing curve stripping.
Curve Stripping Method
When automatic point selection is performed for curve stripping, the algorithm described below is used.
Select the Points
All sets of points that are applicable according to the current options are selected.
 Drop all BLQ values, then
 Choose all sets of points that start from the
$T_{last}$
and step back:
 at least 3 points (customizable with
PKNCA.options("min.hl.points")
)  Not including
$T_{max}$
(customizable with
PKNCA.options("allow.tmax.in.half.life")
)
 at least 3 points (customizable with
As a specific example, if measurements were at 0, 1, 2, 3, 4, 6, 8, 12, and 24 hours; if $T_{last}$ is 12 hours; and if $T_{max}$ is 1 hour then the default point sets that would be fit are:
 6, 8, and 12 hours;
 4, 6, 8, and 12 hours;
 3, 4, 6, 8, and 12 hours; and
 2, 3, 4, 6, 8, and 12 hours.
If PKNCA.options("min.hl.points")
were set to
4
, then the 6, 8, and 12 hour set would not be fit. If
PKNCA.options("allow.tmax.in.half.life")
were set to
TRUE
, then 1, 2, 3, 4, 6, 8, and 12 hours would be fit.
Select the Best Fit
After fitting all points, the best fit among the set of possible fit is selected by the following rules:

$\lambda_z > 0$
and at the same time the maximum rsquared must be within an adjusted
$r^2$
factor of the best.
 The adjusted
$r^2$
factor is controlled by
PKNCA.options("adj.r.squared.factor")
and it defaults to 10^{4}.  These rules must be met simultaneously, so if the maximum adjusted $r^2$ is for a line with $\lambda_z \leq 0$, the halflife may end up being unreportable.
 The adjusted
$r^2$
factor is controlled by
 If fitting the loglinear concentrationtime line fails, then it is not the best line.
 If more than one fit still meets the criteria above, then choose the fit with the most points included.
Example
# Perform calculations for subject 1, only
data_conc < as.data.frame(datasets::Theoph)[datasets::Theoph$Subject == 1, ]
# Keep all points
conc_obj <
PKNCAconc(
data_conc,
conc~TimeSubject
)
# Only calculate halflife and parameters required for halflife
current_intervals < data.frame(start=0, end=Inf, half.life=TRUE)
data_obj < PKNCAdata(conc_obj, intervals=current_intervals)
result_obj < pk.nca(data_obj)
## No dose information provided, calculations requiring dose will return NA.
# Extract the results for subject 1
as.data.frame(result_obj)
## # A tibble: 10 × 6
## Subject start end PPTESTCD PPORRES exclude
## <ord> <dbl> <dbl> <chr> <dbl> <chr>
## 1 1 0 Inf tmax 1.12 NA
## 2 1 0 Inf tlast 24.4 NA
## 3 1 0 Inf lambda.z 0.0485 NA
## 4 1 0 Inf r.squared 1.00 NA
## 5 1 0 Inf adj.r.squared 1.00 NA
## 6 1 0 Inf lambda.z.time.first 9.05 NA
## 7 1 0 Inf lambda.z.n.points 3 NA
## 8 1 0 Inf clast.pred 3.28 NA
## 9 1 0 Inf half.life 14.3 NA
## 10 1 0 Inf span.ratio 1.07 NA
Manual Point Selection
Exclusion of Specific Points with Curve Stripping
In some cases, specific points will be known outliers, or there may be another reason to exclude specific points. And, with those points excluded, the halflife should be calculated using the normal curve stripping methods described above.
To exclude specific points but otherwise use curve stripping, use the
exclude_half.life
option as the column name in the
concentration dataset for PKNCAconc()
as illustrated
below.
data_conc$exclude_hl < data_conc$Time == 12.12
# Confirm that we will be excluding exactly one point
stopifnot(sum(data_conc$exclude_hl) == 1)
# Drop one point
conc_obj_exclude1 <
PKNCAconc(
data_conc,
conc~TimeSubject,
exclude_half.life="exclude_hl"
)
data_obj_exclude1 < PKNCAdata(conc_obj_exclude1, intervals=current_intervals)
# Perform the calculations
result_obj_exclude1 < pk.nca(data_obj_exclude1)
## No dose information provided, calculations requiring dose will return NA.
# Results differ when excluding the 12hour point for subject 1 (compare to
# example in the previous section)
as.data.frame(result_obj_exclude1)
## # A tibble: 10 × 6
## Subject start end PPTESTCD PPORRES exclude
## <ord> <dbl> <dbl> <chr> <dbl> <chr>
## 1 1 0 Inf tmax 1.12 NA
## 2 1 0 Inf tlast 24.4 NA
## 3 1 0 Inf lambda.z 0.0482 NA
## 4 1 0 Inf r.squared 1.00 NA
## 5 1 0 Inf adj.r.squared 0.999 NA
## 6 1 0 Inf lambda.z.time.first 5.1 NA
## 7 1 0 Inf lambda.z.n.points 4 NA
## 8 1 0 Inf clast.pred 3.28 NA
## 9 1 0 Inf half.life 14.4 NA
## 10 1 0 Inf span.ratio 1.34 NA
Specification of the Exact Points for Analysis
In other cases, the exact points to use for halflife calculation are known, and automatic point selection with curve stripping should not be performed.
To exclude specific points but otherwise use curve stripping, use the
include_half.life
option as the column name in the
concentration dataset for PKNCAconc()
as illustrated
below.
data_conc$include_hl < data_conc$Time > 3
# Confirm that we will be excluding exactly one point
stopifnot(sum(data_conc$include_hl) == 6)
# Drop one point
conc_obj_include6 <
PKNCAconc(
data_conc,
conc~TimeSubject,
include_half.life="include_hl"
)
data_obj_include6 < PKNCAdata(conc_obj_include6, intervals=current_intervals)
# Perform the calculations
result_obj_include6 < pk.nca(data_obj_include6)
## No dose information provided, calculations requiring dose will return NA.
# Results differ when including 6 points (compare to example in the previous
# section)
as.data.frame(result_obj_include6)
## # A tibble: 10 × 6
## Subject start end PPTESTCD PPORRES exclude
## <ord> <dbl> <dbl> <chr> <dbl> <chr>
## 1 1 0 Inf tmax 1.12 NA
## 2 1 0 Inf tlast 24.4 NA
## 3 1 0 Inf lambda.z 0.0475 NA
## 4 1 0 Inf r.squared 0.999 NA
## 5 1 0 Inf adj.r.squared 0.998 NA
## 6 1 0 Inf lambda.z.time.first 3.82 NA
## 7 1 0 Inf lambda.z.n.points 6 NA
## 8 1 0 Inf clast.pred 3.30 NA
## 9 1 0 Inf half.life 14.6 NA
## 10 1 0 Inf span.ratio 1.41 NA