T3294
Optimal sampling strategies for the baseline
characterization of testosterone in hypogonadal men
Olivier Barrière, Ph.D1, Mario González-Sales, Ph.D1,2, Julie Desrochers, M.Sc1, Fahima Nekka, Ph.D,2 Pierre-Olivier Tremblay, M.Sc1, Mario Tanguay, Ph.D1
1inVentiv Health Clinical, Montréal, Canada 2Université de Montréal, Montréal, Canada
Purpose
Results
The FDA testosterone bioequivalence guidances recommend that the serum concentrations of testosterone should be corrected for baseline endogenous levels by subtracting the
mean pre-dose baseline value. The timepoints for the baseline computation are specified in 8 out of the 10 testosterone related guidances currently available on the FDA website:
they consist of at least three pre-dose values, e.g. -1.0, -0.5, and 0 hours in 7 of them, and they were recently updated to -12 and 0 hours before dosing in the most recent guidance.
The former approach does not take into account the circadian rhythm, and can over or underestimate the baseline when samples are taken close to the peak or the nadir. The latter
approach is more balanced, so it is less prone to bias but the reduced number of points used for the baseline computation can increase its variance.
Without any constraints, the best estimator based on 3 timepoints (3:00AM, 2:00PM and 11:00PM) has a bias lower than 1 ng/dL with a standard deviation of 20 ng/dL. The best
estimator based on 2 timepoints (5:00AM and 4:00PM) has a bias lower than 1.5 ng/dL with a standard deviation of 24.7 ng/dL.
15
20
25
30
280
5
10
15
20
25
30
2:00
4:00
6:00
8:00
10:00
12:00
14:00
16:00
18:00
20:00
22:00
Testosterone levels [ng/dL]
Probability density
4:00
8:00
12:00
16:00
20:00
-150
23:59
-100
-50
0
50
100
150
Error [ng/dL]
Time [clock time]
200
0.015
0.010
0.005
300
200
0.015
0.010
0.005
0.000
4:00
8:00
12:00
16:00
20:00
-150
23:59
0.000
100
-100
-50
0
50
100
150
0:00
4:00
8:00
Error [ng/dL]
12:00
16:00
20:00
-150
23:59
-100
-50
0
50
100
150
Error [ng/dL]
Time [clock time]
12:00
14:00
16:00
-12h, 0h
18:00
20:00
Testosterone levels [ng/dL]
True
baseline
0
0:00
2:00
4:00
6:00
8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00
0:00
6:00
8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00
22:00
4:00
6:00
8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00
0:00
2:00
4:00
6:00
8:00
10:00
12:00
14:00
16:00
18:00
0h
1.0
1h
17h, 17h30, 18h
20:00
22:00
23:59
Time [clock time]
0:00
2:00
4:00
6:00
8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00
3.0
1h
3.0
1h
2h
2h
3h
3h
3h
4h
4h
4h
2.5
6h
240
18h
200
0h
2h
5h
Testosterone levels [ng/dL]
2:00
The bias can always be reduced to almost zero with an optimal choice of sampling times, but the standard deviation cannot be smaller than 24 ng/dL, 20 ng/dL and 16 ng/dL, when
2, 3 and 4 samples are used, respectively. Assuming that a sample is always taken just before the dose, the times of the other samples can be optimized given the starting time of
the study. Instead selecting the best estimator only, collecting a small group of the top estimators gives a more flexible and robust view.
1h
Estimated
200
baseline
Bias
Accuracy
Trueness
23:59
Closeness
0:00
Starting time of the study [clock time]
12h
2.5
5h
5h
6h
6h
6h
7h
7h
7h
0.8
8h
9h
0.6
10h
11h
12h
13h
0.4
14h
15h
2.0
8h
9h
10h
11h
1.5
12h
13h
14h
15h
1.0
9h
10h
11h
1.5
12h
13h
14h
15h
16h
16h
16h
17h
17h
17h
0.2
18h
2.0
8h
1.0
18h
0.5
12h
Time [clock time]
4:00
240
18h
14:00
2:00
0h
21h
200
30
-60
Variance
Precision
Reproducibility
Repeatability
12:00
-12h, -11.5h, -0.5h, 0h
-30
280
10:00
-16h, -8h, 0h
23:59
Starting time of the study [clock time]
10:00
Probability density
Testosterone levels [ng/dL]
0:00
Time [clock time]
240
8:00
150
60
0:00
9h
6:00
100
0.020
-1h, -0.5h, 0h
35
Time [clock time]
Testosterone levels [ng/dL]
300
100
tmin
200
4:00
50
The pattern -16h, -8h, 0h adequately spans the 24 hours of a day and provide a bias lower than 2.5 ng/dL whatever the starting time of the study, with a standard deviation around 20
ng/dL. If the goal is to limit the confinement period to 12h, the pattern -12h, -11.5h, -0.5h, 0h has a standard deviation decreased by 27% compared to -12h, 0h with a similar bias.
MSE = Bias2 + Variance
2:00
0
400
Time [clock time]
1h
0:00
-50
Error [ng/dL]
100
8h 8h30 9h
280
0.000
Probability density
35
Time [hours]
0
8:00
-100
Testosterone levels [ng/dL]
30
Time [hours]
6:00
-150
23:59
Probability density
Testosterone levels [ng/dL]
25
280
4:00
20:00
0.005
500
20
300
400
15
280
2:00
16:00
0.010
200
10
Testosterone profiles were then simulated using this model to determine the optimal sampling times for the baseline estimation with the best trade-off between bias and variance, by
minimizing the mean squared error (MSE) of the base parameter. MSE is the sum of the squared bias and the variance, and thus incorporates both components at the same level.
0:00
12:00
0.015
Applying the former FDA design to a study that starts at 9:00AM can lead to an over-prediction of the baseline with a bias of 33.5 ± 30.3 ng/dL. The latter FDA design has a bias of
7.6 ± 26.4 ng/dL.
0:00
35
8:00
Time [clock time]
amp
260
240
5
Time [hours]
240
4:00
200
Starting time of the study [clock time]
10
0:00
300
100
Starting time of the study [clock time]
5
0.000
100
Bias ± SD [ng/dL]
200
220
240
260
tmax
0.010
0.005
0
Testosterone levels [ng/dL]
280
Time [hours]
0
220
0
35
Testosterone levels [ng/dL]
30
280
25
260
20
240
15
200
0.015
0.020
220
10
300
0.020
400
200
5
Observed 5%, 50% and 95% Percentiles by Bins
Predicted 5%, 50% and 95% Percentiles
200
base
0
Testosterone levels [ng/dL]
Testosterone levels [ng/dL]
280
260
240
220
200
Testosterone levels [ng/dL]
Based on 859 pre-dose PK profiles from 239 hypogonadal men (4556 observations), a kinetic model describing the circadian rhythm of testosterone in hypogonadal men was
previously built. The circadian rhythm is usually described by a standard cosine function, which implies that the increasing and the decreasing behaviors are symmetric. A stretched
cosine function parameterized by base, amp, tmax, and tmin, within a 24 hours cycle, was here defined. It allows the time between tmax and tmin to be different from 12 hours in order to
model the observed slow increase and fast decrease.
Probability density
Methods
400
0.020
Testosterone levels [ng/dL]
The objective of this work is to formally test these sampling strategies and provide optimal sampling times accounting for the circadian behavior for the estimation of the testosterone
baseline, here defined as the average concentration over 24h.
400
16:00
18:00
20:00
22:00
23:59
0:00
2:00
4:00
6:00
8:00
10:00
12:00
14:00
Time [clock time]
16:00
18:00
20:00
22:00
23:59
0.5
19h
19h
19h
20h
20h
20h
21h
21h
21h
22h
0.0
23h
22h
0.0
23h
22h
0.0
23h
-1h -2h -3h -4h -5h -6h -7h -8h -9h -10h -11h -12h -13h -14h -15h -16h -17h -18h -19h -20h -21h -22h -23h
-1h -2h -3h -4h -5h -6h -7h -8h -9h -10h -11h -12h -13h -14h -15h -16h -17h -18h -19h -20h -21h -22h -23h
-1h -2h -3h -4h -5h -6h -7h -8h -9h -10h -11h -12h -13h -14h -15h -16h -17h -18h -19h -20h -21h -22h -23h
Relative optimal times [clock time]
Relative optimal times [clock time]
Relative optimal times [clock time]
Conclusions
© 2015 All Rights Reserved | CONFIDENTIAL
Sampling strategies for the baseline estimation of testosterone in hypogonadal males were extensively tested in terms of bias and variance. The FDA recommendations were
compared to the optimal timepoints and improved patterns were suggested.