An Assessment of Recombinant Human Erythropoietin Effect on Reticulocyte Production Rate and Lifespan Distribution in Healthy Subjects

Abstract

Purpose

An empirical pharmacodynamic model was developed to assess the effect of recombinant human erythropoietin (rHu-EPO) treatment on the reticulocyte production rate and lifespan distribution.

Materials and Methods

Single doses of rHu-EPO at levels 20, 40, 60, 90, 120, and 160 kIU were administered to healthy volunteers (n = 8 per dose level). Erythropoietin plasma concentrations as well as hematologic responses were measured up to 42 days. The hematological data were used to determine explicit relationships between reticulocyte and red blood cell counts (RBC) and the reticulocytes’ production rate and lifespan distribution.

Results

The parameter estimates obtained by simultaneous fitting of the model to the reticulocyte and RBC data revealed that rHu-EPO transiently increased the reticulocyte lifespan from the baseline value of 1.7 days to 3.4 days and the effect lasted for 8.3 days. The dose dependent increase in the reticulocyte production had the maximal value of 77.5 10⁹ cells/l/day and was followed by a rebound that was less than 9% of the baseline value. Both reticulocyte and RBC responses were preceded by a dose-independent lag time of 1.7 days.

Conclusions

The effect of rHu-EPO on the reticulocyte production rate and lifespan distribution was characterized. The results of the present study can be further utilized in building more mechanistic pharmacodynamic models of rHu-EPO stimulatory effects.

Appendices

Appendix A

Derivation of the Precursor–successor Relationship Eq. 12

If the fixed lifespan T _RET0 is assumed for all reticulocytes, then the RBC production is the delayed T _RET0 reticulocyte production rate (11):

$$ k_{{{\text{out}}}} {\left( k \right)} = k_{{\text{R}}} {\left( {t - T_{{{\text{RET}}0}} } \right)} $$

(25)

Thus, similarly to Eq. 11, one can write

$$ {\text{MRBC}}{\left( t \right)} = {\int\limits_{t - T_{{{\text{RBC}}}} }^t {k_{{\text{R}}} {\left( {{\text{z}} - T_{{{\text{RET}}0}} } \right)}{\text{d}}z} } $$

(26)

Changing the variables in the above integral $s = z - T_{{{\text{RET0}}}}$ leads to

$$ {\text{MRBC}}{\left( t \right)} = {\int\limits_{t - T_{{{\text{RET}}0 - }} - T_{{{\text{RBC}}}} }^{t - T_{{{\text{RET}}0}} } {k_{{\text{R}}} {\left( s \right)}{\text{d}}s} } $$

(27)

The interval of integration in Eq. 27, $t - T_{{{\text{RET0}}}} > s > t - T_{{{\text{RET0}}}} - T_{{{\text{RBC}}}}$, can be partitioned to the following subintervals: $t - T_{{{\text{RET}}}} > s > t - 2T_{{{\text{RET}}}} ,\,t - 2T_{{{\text{RET}}}} > s > t - 3T_{{{\text{RET}}}} , \ldots ,t - NT_{{{\text{RET}}}} > s > t - {\left( {N + 1} \right)}T_{{{\text{RET0}}}}$, where N =INT(t/T _RET0) is the integer describing how many times t is bigger than T _RET0. One can now decompose the integral in Eq. 27 into a sum of integrals over these subintervals and a remainder:

$$ {\text{MRBC}}{\left( t \right)} = {\sum\limits_{i = 1}^N {{\int\limits_{t - {\left( {i + 1} \right)} \cdot T_{{{\text{RET0}}}} }^{t - i \cdot T_{{{\text{RET0}}}} } {k{\left( s \right)}{\text{d}}s} }} } + {\int\limits_{t - T_{{{\text{RBC}}}} - T_{{{\text{RET0}}}} }^{t - {\left( {N + 1} \right)} \cdot T_{{{\text{RET0}}}} } {k{\left( s \right)}{\text{d}}s} } $$

(28)

Equation 11 implies that for any integer i

$$ {\text{RET}}{\left( {t - i \cdot T_{{{\text{RET}}}} } \right)} = {\int\limits_{t - {\left( {i + 1} \right)} \cdot T_{{{\text{RET0}}}} }^{t - i \cdot T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( s \right)}{\text{d}}s} } $$

(29)

Since for t/T _RET < N + 1, the upper limit in the reminder integral in Eq. 28 is less than 0, and for t ≤ T _RBC the lower limit in this integral is less than 0 as well. We assume that prior to erythropoietin treatment the reticulocyte production was at the baseline level, k _R(s) = k _R0 for s < 0. Then the reminder integral in Eq. 28 is equal to

$$ {\int\limits_{t - T_{{{\text{RBC}}}} - T_{{{\text{RET0}}}} }^{t - {\left( {N + 1} \right)} \cdot T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( {\text{z}} \right)}{\text{d}}z = T_{{{\text{RBC}}}} \cdot k_{{{\text{R0}}}} - N \cdot T_{{{\text{RET0}}}} \cdot k_{{{\text{R0}}}} } } $$

(30)

Taking into account the baseline Eqs. 4 and 5 yields

$$ T_{{{\text{RBC}}}} \cdot k_{{{\text{R0}}}} - N \cdot T_{{{\text{RET0}}}} \cdot k_{{{\text{R0}}}} = {\text{MRBC}}_{0} - N \cdot {\text{RET}}_{0} $$

(31)

One can now combine Eqs. 28, 29, 30, 31, and obtain

$$ {\text{MRBC}}{\left( t \right)} - {\text{MRBC}}_{0} = {\sum\limits_{i = 1}^N {{\text{RET}}{\left( {t - iT_{{{\text{RET0}}}} } \right)} - {\text{RET}}_{0} } } $$

(32)

Because RBC is the sum of MRBC and RET, then

$$ \Delta {\text{RBC}}{\left( t \right)} = \Delta {\text{RET}}{\left( t \right)} + {\sum\limits_{i = 1}^N {\Delta {\text{RET}}{\left( {t - iT_{{RET0}} } \right)}} } $$

(33)

and Eq. 12 follows.

APPENDIX B

Derivation of equation for RET(t)

Taking into account Eq. 16 for the reticulocyte conversion rate k _out(t) one can integrate both sides of Eq. 1 from 0 to t and obtain

$$ {\text{RET}}{\left( t \right)} = R{\left( 0 \right)} + {\int\limits_0^t {k_{{\text{R}}} {\left( z \right)}{\text{dz}}} } - {\int\limits_0^t {k_{{\text{R}}} {\left( {{\text{z}} - T_{{{\text{RET0}}}} } \right)}{\left( {1 - \chi {\left( {z - T_{{{\text{RET0}}}} } \right)}} \right)}{\text{d}}z} } - {\int\limits_0^t {k_{{\text{R}}} {\left( {z - T_{{{\text{RET}}}} } \right)}\chi {\left( {z - T_{{{\text{RET}}}} } \right)}{\text{d}}z} } $$

(34)

Changing the variables in the second integral $s = z - T_{{{\text{RET0}}}}$ and in the third integral $s = z - T_{{{\text{RET}}}}$ yields

$$ {\text{RET}}{\left( t \right)} = R{\left( 0 \right)} + {\int\limits_0^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } - {\int\limits_{ - T_{{{\text{RET0}}}} }^{t - T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( s \right)}{\text{d}}z} } + {\int\limits_{ - T_{{{\text{RET0}}}} }^{t - T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( s \right)}\chi {\left( s \right)}{\text{d}}z} } - {\int\limits_{ - T_{{{\text{RET}}}} }^{t - T_{{{\text{RET}}}} } {k_{{\text{R}}} {\left( s \right)}\chi {\left( s \right)}{\text{d}}z} } $$

(35)

Since for $t < 0{\text{ }}k_{{\text{R}}} {\left( t \right)} = k_{{{\text{R0}}}}$ and χ(t) = 0, the integrals in Eq. 35 can be further simplified to

$$ {\text{RET}}{\left( t \right)} = R{\left( 0 \right)} - T_{{{\text{RET0}}}} k_{{{\text{R0}}}} + {\int\limits_0^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } - {\int\limits_0^{t - T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( s \right)}{\text{d}}z} } + {\int\limits_0^{t - T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( s \right)}\chi {\left( s \right)}{\text{d}}z} } - {\int\limits_0^{t - T_{{{\text{RET}}}} } {k_{{\text{R}}} {\left( s \right)}\chi {\left( s \right)}{\text{d}}z} } $$

(36)

The reticulocytes at time t = 0 are at steady-state, therefore Eq. 4 implies that the first and second term in Eq. 36 cancel each other out. If the first integral is combined with the second, and the third with the fourth, then one obtains

$$ {\text{RET}}{\left( t \right)} = {\int\limits_{t - T_{{{\text{RET0}}}} }^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z + {\int\limits_{t - T_{{{\text{RET}}}} }^{t - T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( z \right)}\chi {\left( z \right)}{\text{d}}z} }} } $$

(37)

which is the exact form of Eq. 17. Assuming the following relationships between the time parameters

$$ T_{{{\text{RET0}}}} < T_{{{\text{TRET}}}} ,{\text{ }}T_{{\text{0}}} + T_{{{\text{RET}}}} < T_{{\text{1}}} {\text{, and }}T_{{\text{1}}} + T_{{{\text{RET}}}} < T_{{\text{2}}} $$

(38)

they can be ordered as follows $T_{{\text{0}}} < T_{{\text{0}}} + T_{{{\text{RET0}}}} < T_{{\text{0}}} + T_{{{\text{RET}}}} < T_{{\text{1}}} < T_{{\text{1}}} + T_{{{\text{RET0}}}} < T_{{\text{1}}} + T_{{{\text{RET}}}} < T_{{\text{2}}} < T_{{\text{2}}} + T_{{{\text{RET0}}}}$. Consequently, an arbitrary t value must fall into one of the following intervals:

t ≤ T₀, then

$$ {\text{RET}}{\left( t \right)} = {\text{RET}}_{{\text{0}}} $$

(39)

T₀ < t ≤ T₀ + T_RET0, then

$$ {\text{RET}}{\left( t \right)} = {\int\limits_{t - T_{{{\text{RET0}}}} }^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } = {\int\limits_{t - T_{{{\text{RET0}}}} }^{T_{0} } {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } + {\int\limits_{T_{{\text{0}}} }^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } = k_{{{\text{R0}}}} {\left( {T_{0} - t + T_{{{\text{RET0}}}} } \right)} + k_{{{\text{R1}}}} {\left( {t - T_{0} } \right)} $$

(40)

T₀ + T_RET0 < t ≤ T₀ + T_RET, then

$$ {\text{RET}}{\left( t \right)} = {\int\limits_{t - T_{{{\text{RET0}}}} }^{T_{0} } {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } + {\int\limits_{T_{0} }^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } + {\int\limits_{T_{{\text{0}}} }^{t - T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( z \right)}\chi {\left( z \right)}{\text{d}}z} } = {\int\limits_{T_{0} }^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } = k_{{{\text{R1}}}} {\left( {t - T_{0} } \right)} $$

(41)

T₀ + T_RET < t ≤ T₁, then

$$ {\text{RET}}{\left( t \right)} = k_{{{\text{R1}}}} T_{{{\text{RET0}}}} + k_{{{\text{R1}}}} {\left( {T_{{{\text{RET}}}} - T_{{{\text{RET0}}}} } \right)} = k_{{{\text{R1}}}} T_{{{\text{RET}}}} $$

(42)

T₁ < t ≤ T₁ + T_RET0, then

$$ {\text{RET}}{\left( t \right)} = {\int\limits_{t - T_{{{\text{RET0}}}} }^{T_{1} } {k_{{\text{R}}} {\left( {\text{z}} \right)}{\text{dz}}} } + {\int\limits_{{\text{T}}_{{\text{1}}} }^{\text{t}} {{\text{k}}_{{\text{R}}} {\left( z \right)}{\text{d}}z} } + {\int\limits_{t - T_{{{\text{RET}}}} }^{t - T_{{{\text{RET0}}}} } {k_{{\text{R}}} {\left( z \right)}\chi {\left( z \right)}{\text{d}}z} } = {\int\limits_{t - T_{{{\text{RET}}}} }^{T_{1} } {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } + {\int\limits_{T_{{\text{1}}} }^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } = k_{{{\text{R1}}}} {\left( {T_{1} - t + T_{{{\text{RET}}}} } \right)} + k_{{{\text{R2}}}} {\left( {t - T_{{\text{1}}} } \right)} $$

(43)

T₁ + T_RET0 < t ≤ T₁ + T_RET, then

$$ {\text{RET}}{\left( {\text{t}} \right)} = {\int\limits_{{\text{t}} - {\text{T}}_{{{\text{RET0}}}} }^{\text{t}} {{\text{k}}_{{\text{R}}} {\left( {\text{z}} \right)}{\text{dz}}} } + {\int\limits_{{\text{t}} - {\text{T}}_{{{\text{RET}}}} }^{{\text{T}}_{1} } {{\text{k}}_{{\text{R}}} {\left( {\text{z}} \right)}{\text{dz}}} } = {\text{k}}_{{{\text{R2}}}} {\text{T}}_{{{\text{RET0}}}} + {\text{k}}_{{{\text{R1}}}} {\left( {{\text{T}}_{1} - {\text{t}} + {\text{T}}_{{{\text{RET}}}} } \right)} $$

(44)

T₁ + T_RET < t ≤ T₂, then

$$ {\text{RET}}{\left( t \right)} = k_{{{\text{R2}}}} T_{{{\text{RET0}}}} $$

(45)

T₂ < t ≤ T₂ + T_RET0, then

$$ {\text{RET}}{\left( t \right)} = {\int\limits_{t - T_{{{\text{RET0}}}} }^{T_{2} } {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } + {\int\limits_{T_{2} }^t {k_{{\text{R}}} {\left( z \right)}{\text{d}}z} } = k_{{{\text{R2}}}} {\left( {T_{2} - t + T_{{{\text{RET0}}}} } \right)} + k_{{{\text{R0}}}} {\left( {t - T_{2} } \right)} $$

(46)

T₂ + T_RET0 ≤ t, then

$$ {\text{RET}}{\left( t \right)} = k_{{{\text{R0}}}} T_{{{\text{RET0}}}} $$

(47)

Arranging terms in Eqs. 39, 40, 41, 42, 43, 44, 45, 46, 47 yields Eq. 10. A similar derivation holds for Eq. 20, except that one needs to consider the cases determined by the intervals T ₀ < T ₁ < T ₂ < T _RBC and use Eq. 8.

APPENDIX C

NONMEM control stream and data file for estimation of T _RET0 from Eq. 12

$PROB Estimation of TRET

$INPUT ID TIME CMT MDV DV RET RBC DOSE

$DATA C:\data_1041.csv IGNORE=#

$PRED

TRET = THETA(1)*EXP(ETA(1))

"OPEN(2,FILE=’C:\nmv\run\fdata’)

"REWIND 2

"DO WHILE (.NOT.EOF(2))

" READ(2,*) X1,X2,X3,X4,X5,X6,X7,X8

" IF(X1.EQ.ID.AND.CMT.EQ.1) THEN

" IF (X2.EQ.0) RT0=X6

" IF (X2.EQ.2) RT2=X6

" IF (X2.EQ.3) RT3=X6

" IF (X2.EQ.4) RT4=X6

" IF (X2.EQ.5) RT5=X6

" IF (X2.EQ.6) RT6=X6

" IF (X2.EQ.7) RT7=X6

" IF (X2.EQ.8) RT8=X6

" IF (X2.EQ.9) RT9=X6

" IF (X2.EQ.11) RT11=X6

" IF (X2.EQ.13) RT13=X6

" IF (X2.EQ.15) RT15=X6

" IF (X2.EQ.17) RT17=X6

" IF (X2.EQ.19) RT19=X6

" IF (X2.EQ.21) RT21=X6

" IF (X2.EQ.23) RT23=X6

" IF (X2.EQ.25) RT25=X6

" IF (X2.EQ.27) RT27=X6

" IF (X2.EQ.28) RT28=X6

" IF (X2.EQ.31) RT31=X6

" IF (X2.EQ.32) RT32=X6

" IF (X2.EQ.34) RT34=X6

" IF (X2.EQ.35) RT35=X6

" IF (X2.EQ.40) RT40=X6

" IF (X2.EQ.42) RT42=X6

" IF (X2.EQ.0) RBC0=X7

"ENDIF

"ENDDO

"CLOSE(2)

" RB=RBC0

" IF(DOSE.GT.0) THEN

" I=0

" DO WHILE (TIME−I*TRET.GE.0.0)

" X=TIME−I*TRET

" IF (0.LT.X.AND.X.LE.2) RB=RB+RT0+(RT2−RT0)/(2−0)*(X−0)−RT0

" IF (2.LT.X.AND.X.LE.3) RB=RB+RT2+(RT3−RT2)/(3−2)*(X−2)−RT0

" IF (3.LT.X.AND.X.LE.4) RB=RB+RT3+(RT4−RT3)/(4−3)*(X−3)−RT0

" IF (4.LT.X.AND.X.LE.5) RB=RB+RT4+(RT5−RT4)/(5−4)*(X−4)−RT0

" IF (5.LT.X.AND.X.LE.6) RB=RB+RT5+(RT6−RT5)/(6−5)*(X−5)−RT0

" IF (6.LT.X.AND.X.LE.7) RB=RB+RT6+(RT7−RT6)/(7−6)*(X−6)−RT0

" IF (7.LT.X.AND.X.LE.8) RB=RB+RT7+(RT8−RT7)/(8−7)*(X−7)−RT0

" IF (8.LT.X.AND.X.LE.9) RB=RB+RT8+(RT9−RT8)/(9−8)*(X−8)−RT0

" IF (9.LT.X.AND.X.LE.11) RB=RB+RT9+(RT11−RT9)/(11−9)*(X−9)−RT0

" IF (11.LT.X.AND.X.LE.13) RB=RB+RT11+(RT13−RT11)/(13−11)*(X−11)−RT0

" IF (13.LT.X.AND.X.LE.15) RB=RB+RT13+(RT15−RT13)/(15−13)*(X−13)−RT0

" IF (15.LT.X.AND.X.LE.17) RB=RB+RT15+(RT17−RT15)/(17−15)*(X−15)−RT0

" IF (17.LT.X.AND.X.LE.19) RB=RB+RT17+(RT19−RT17)/(19−17)*(X−17)−RT0

" IF (19.LT.X.AND.X.LE.21) RB=RB+RT19+(RT21−RT19)/(21−19)*(X−19)−RT0

" IF (21.LT.X.AND.X.LE.23) RB=RB+RT21+(RT23−RT21)/(23−21)*(X−21)−RT0

" IF (23.LT.X.AND.X.LE.25) RB=RB+RT23+(RT25−RT23)/(25−23)*(X−23)−RT0

" IF (25.LT.X.AND.X.LE.27) RB=RB+RT25+(RT27−RT25)/(27−25)*(X−25)−RT0

" IF (27.LT.X.AND.X.LE.28) RB=RB+RT27+(RT28−RT27)/(28−27)*(X−27)−RT0

" IF (28.LT.X.AND.X.LE.31) RB=RB+RT28+(RT31−RT28)/(31−28)*(X−28)−RT0

" IF (31.LT.X.AND.X.LE.32) RB=RB+RT31+(RT32−RT31)/(32−31)*(X−31)−RT0

" IF (32.LT.X.AND.X.LE.34) RB=RB+RT32+(RT34−RT32)/(34−32)*(X−32)−RT0

" IF (34.LT.X.AND.X.LE.35) RB=RB+RT34+(RT35−RT34)/(35−34)*(X−34)−RT0

" IF (35.LT.X.AND.X.LE.40) RB=RB+RT35+(RT40−RT35)/(40−35)*(X−35)−RT0

" IF (40.LT.X.AND.X.LE.42) RB=RB+RT40+(RT42−RT40)/(42−40)*(X−40)−RT0

" I=I+1

" ENDDO

" ENDIF

IPRED=RB+ERR(1)

Y = IPRED

IRES = DV − IPRED

$THETA (0,,15) ;TRET

$OMEGA 0.00 FIX

$SIGMA 0.02

$EST NSIGDIG=3 MAX=9999 PRINT=1 NOABORT POSTHOC METHOD=1

$COV PRINT=E

$TABLE ID TIME CMT IPRED IRES DOSE RET

NOPRINT FILE=C:\1041.txt

The following file data_1041.txt contains records for Subject 1041. The missing values for RET were calculated by the linear interpolation of the neighboring reticulocyte measurements

#ID	TIME	CMT	MDV	DV	RET	RBC	DOSE
1041	0	1	0	5.145	0.054	5.145	40
1041	2	1	0	5.55	0.072	5.55	40
1041	3	1	0	5.49	0.135	5.49	40
1041	4	1	0	5.36	0.192	5.36	40
1041	5	1	0	5.2	0.253	5.2	40
1041	6	1	0	5.26	0.245	5.26	40
1041	7	1	0	5.5	0.291	5.5	40
1041	8	1	0	5.4	0.349	5.4	40
1041	9	1	0	5.69	0.218	5.69	40
1041	11	1	0	5.44	0.132	5.44	40
1041	13	1	0	5.37	0.103	5.37	40
1041	15	1	0	5.27	0.092	5.27	40
1041	17	1	0	5.45	0.070	5.45	40
1041	19	1	0	5.55	0.093	5.55	40
1041	21	1	0	5.39	0.072	5.39	40
1041	23	1	0	5.49	0.083	5.49	40
1041	25	1	0	5.55	0.084	5.55	40
1041	27	1	1	0	0.108	0	40
1041	28	1	0	5.49	0.120	5.49	40
1041	31	1	1	0	0.111	0	40
1041	32	1	1	0	0.108	0	40
1041	34	1	1	0	0.101	0	40
1041	35	1	1	0	0.098	0	40
1041	40	1	1	0	0.082	0	40
1041	42	1	0	5.22	0.076	5.22	40

APPENDIX D

NONMEM control stream for estimation of T ₀, ΔT, ΔT ₁, Δk _R1, and Δk _R2

$PROB RHUEPO EFFECT ON RET AND RBC

$INPUT ID TIME CMT MDV DV RET RBC DOSE

$DATA C:\data_1034.csv IGNORE = #

$PRED

T0 = THETA(1)*EXP(ETA(1))

DT1 = THETA(2)

DT = THETA(3)

DT2 = THETA(4)

DKR1 = THETA(5)

DKR2 = THETA(6)

"OPEN(2,FILE=’C:\nmv\run\fdata’)

"REWIND 2

"DO WHILE (.NOT.EOF(2))

" READ(2,*) X1,X2,X3,X4,X5,X6,X7,X8

" IF(X1.EQ.ID.AND.CMT.EQ.1) THEN

" IF (X2.EQ.0) THEN

" RT0=X6

" RBC0=X7

" TT=RT0/(RBC0−RT0)*120.0

" ENDIF

" ENDIF

"ENDDO

" CLOSE(2)

KR0=RT0/TT

KR1=KR0+DKR1

KR2=KR0−DKR2

T1=T0+DT1

T2=T1+DT2

TR=TT+DT

CH0=0

CH1=1

CH2=0

X=TIME

IT1=0

IT2=0

IT3=0

IT4=0

IF (X.LE.T0) IT1=KR0*X

IF (X.GT.T0.AND.X.LE.T1) IT1=KR1*(X−T0)+KR0*T0

IF (X.GT.T1.AND.X.LE.T2) IT1=KR2*(X−T1)+KR1*(T1−T0)+KR0*T0

IF (X.GT.T2) IT1=KR0*(X−T2)+KR2*(T2−T1)+KR1*(T1−T0)+KR0*T0

X=TIME−TT

IF (X.LE.T0) IT2=KR0*X

IF (X.GT.T0.AND.X.LE.T1) IT2=KR1*(X−T0)+KR0*T0

IF (X.GT.T1.AND.X.LE.T2) IT2=KR2*(X−T1)+KR1*(T1−T0)+KR0*T0

IF (X.GT.T2) IT2=KR0*(X−T2)+KR2*(T2−T1)+KR1*(T1−T0)+KR0*T0

X=TIME−TT

IF (X.LE.T0) IT3=KR0*CH0*X

IF (X.GT.T0.AND.X.LE.T1) IT3=KR1*CH1*(X−T0)+KR0*CH0*T0

IF (X.GT.T1.AND.X.LE.T2) THEN

IT3=KR2*CH2*(X−T1)+KR1*CH1*(T1−T0)+KR0*CH0*T0

ENDIF

IF (X.GT.T2) THEN

IT3=KR0*CH0*(X−T2)+KR2*CH2*(T2−T1)+KR1*CH1*(T1−T0)+KR0*CH0*T0

ENDIF

X=TIME−TR

IF (X.LE.T0) IT4=KR0*CH0*X

IF (X.GT.T0.AND.X.LE.T1) IT4=KR1*CH1*(X−T0)+KR0*CH0*T0

IF (X.GT.T1.AND.X.LE.T2) THEN

IT4=KR2*CH2*(X−T1)+KR1*CH1*(T1−T0)+KR0*CH0*T0

ENDIF

IF (X.GT.T2) THEN

IT4=KR0*CH0*(X−T2)+KR2*CH2*(T2−T1)+KR1*CH1*(T1−T0)+KR0*CH0*T0

ENDIF

R=IT1−IT2+IT3−IT4

RB=IT1−KR0*TIME+RBC0

IPRED=0

IF(CMT.EQ.1) IPRED=RB+ERR(1)

IF(CMT.EQ.2) IPRED=R+ERR(2)

Y = IPRED

IRES = DV − IPRED

$THETA

(0,1.5,5) ;T0

(0,7.0 ,20) ;DT1

(0,2,20) ;DT

42 FIX ;DT2

(0,0.04, 0.1) ;DKR1

(0,0.01,0.05) ;DKR2

$OMEGA 0.0 FIX

$SIGMA

0.01 ; RBC

0.01 ; RET

$ESTIMATION NSIGDIG=3 MAX=999 PRINT=1 NOABORT POSTHOC METHOD=1

$COV PRINT=E

$TABLE ID TIME CMT IPRED DOSE RET RBC

NOPRINT

FILE=C:\1034.txt

#ID	TIME	CMT	MDV	DV	RET	RBC	DOSE
1034	0	1	0	4.925	0.079	4.925	160
1034	0	2	0	0.079	0.079	4.925	160
1034	2	1	0	5.38	0.126	5.38	160
1034	2	2	0	0.126	0.126	5.38	160
1034	3	1	0	5.59	0.149	5.59	160
1034	3	2	0	0.149	0.149	5.59	160
1034	4	1	0	5.49	0.189	5.49	160
1034	4	2	0	0.189	0.189	5.49	160