A New Accurate Method for
Predicting Lithium Clearance and
Daily Dosage Requirements
in Adult Psychiatric Patients
Hisham S. Abou-Auda*1, Mohammad J. Al-Yamani1
Rafiq R. Abou-Shaaban2 and Sahal I. Khoshhal3
1.
Department of Clinical Pharmacy, College of Pharmacy,
King Saud University, P.O. Box 2457, Riyadh-11451, Saudi Arabia.
Tel: 966-1-467-7470, Fax: 966-1-467-6229
E-mail: hisham@ksu.edu.sa
2. College of Pharmacy, Ajman University for Science and
Technology, UAE.
3. Pharmacy Department, King Fahad National Guard Hospital,
Riyadh, Saudi Arabia.
* To whom correspondence should be addressed.
Abstract
Objective: The study goal was to derive new equations for estimating lithium
clearance and daily dosage requirements needed to achieve an intended lithium serum
level for adult psychiatric inpatients and outpatients. Method: Data were
retrospectively collected from 60 adult psychiatric patients (34 males and 26 females,
aged between 18-80 years) in both inpatient and outpatient settings. All variables that
might affect lithium clearance and/or lithium serum concentration were included and
analyzed by stepwise multiple linear regression to produce equations describing
lithium clearance and daily dosage requirements for these patients. The validation of
the developed equations was performed by application to another 60 psychiatric
subjects in both the inpatient and outpatient settings. The bias and accuracy of the new
methods were also compared with those set forth by the empirical method and the a
priori methods developed by Zetin, Pepin, Jermain and Terao and Associates.
Results: The following prediction equations for lithium clearance were obtained:
CLLi(Inpatients)=0.932+0.185CLCr and CLLi(Outpatients)=1.021+0.141CLCr. The
equations derived for daily dosage requirements were: Daily dose (Inpatients,
mg)=350.15+289.92 (desired Lithium level, mmol/L) + 0.84(weight, kg) - 1.76 (Age,
years)+34.43(TCA, yes=1, No=0)+62.1(CLCr, L/h)+13.1(BUN,mmol/L)+ 40.9(sex,
male=1, female=0) and Daily dose (Outpatients, mg)=784.92+530.22(desired Lithium
level, mmol/L) + 8.61(weight, kg) - 12.09 (Age, years) - 11.14 (TCA, yes=1, No=0) 7.63 (CLCr, L/h) - 42.62(BUN, mmol/L) - 23.43 (sex, male=1, female=0). In the
present method, the prediction error for clearance was 10.31% and 6.62% for
inpatients and outpatients, respectively, and the prediction error for daily dosage
requirements was 3.96% and 2.95% for inpatients and outpatients, respectively.
Conclusion: Compared with previously reported methods, the present method proved
to be accurate and can be safely used for the prediction of lithium clearance and daily
dosage requirements in psychiatric inpatients and outpatients.
Key words: Lithium, dosage requirements, clearance, prediction
2
Introduction
Lithium has been used in the treatment of mania and in the prophylaxis of bipolar
disorder and recurrent depression (1,2). Despite a growing number of proposed
alternatives, including several anticonvulsants and antipsychotic drugs, lithium
remains useful in the contemporary treatment of bipolar disorders, and is by far the
agent of choice for long-term maintenance treatment in bipolar disorders (3,4). It has a
narrow therapeutic index at steady state and therapeutic ranges of 0.6–1.2 mmol/L
used by many clinicians do not distinguish between the ranges for the treatment of
mania and maintenance treatment (5-8). Inappropriate dosage can cause poor control
of symptoms and potentially dangerous side-effects. Therefore, the prediction of
optimal dosage to obtain the desired therapeutic level is important. The toxicity of
lithium is closely related to serum lithium levels, and can occur at doses close to its
therapeutic level, therefore, regular clinical and serum level monitoring of lithium is a
requirement for good clinical practice (9,10). In addition, conditions that alter
electrolyte balance may affect lithium levels in patients (11). Lithium removal from
the body is achieved almost exclusively via the renal route. Concomitant medications
with lithium may also contribute to the clinical manifestations of lithium toxicity
since its clearance varies proportionally with glomerular filtration rate (GFR) and is
usually 20-30% of GFR (12). As a result, any medication that increases GFR or
affects electrolyte exchange in the nephron may influence the pharmacokinetic
disposition of lithium. It was also found that lithium clearance is usually reduced in
elderly subjects (13). Concomitant use of diuretics, angiotensin-converting enzyme
inhibitors, calcium channel antagonists, or non-steroid antiinflammatory drugs have
been associated with lithium toxicity through pharmacokinetic interactions (14-17).
Viguera et al. (18) analyzed 17 studies on the use of lithium in bipolar disorder to
3
investigate sex differences in response to lithium. They concluded that women may
clear lithium less efficiently than men or probably they vary more in lithium
clearance.
Although a number of studies have examined strategies for determining optimal
lithium dosages in the treatment of patients with bipolar disorder based on single-dose
plasma concentrations (19-33), none of these studies have exclusively gained
recognition as the sole method for lithium monitoring in the routine clinical practice.
The purpose of these methods is eventually to maintain steady-state therapeutic levels
of 0.6-1.2 mmol/L. The most evaluated methods, both retrospectively and
prospectively, were the empirical method (6), the Pepin et al. (21) and the Zetin et al.
(24-26) methods. Browne and Associates (34) retrospectively compared 5 of these
methods and found significant differences in their accuracy for estimating lithium
maintenance dosing requirements in inpatients. When the accuracy of the Pepin
method was tested in 13 healthy volunteers, it was found to be a safe but conservative
method for the prediction of the appropriate daily dose of lithium (35). Markoff and
King (36) compared the Zetin method in 12 patients versus the empirical dosing
method in 21 patients to determine which method would efficiently produce a target
concentration predetermined by the clinician. They concluded that 83% of patients
had reached the desired lithium blood level with Zetin method whereas only 38% had
done so with the empirical method. Other studies (37-39) found no significant
differences between methods or no improvement was noted compared with empirical
method.
Most of the reported predictive a priori methods had never been evaluated in
both psychiatric inpatients and outpatients at the same time. Our observations
indicated a probable difference in lithium clearance and consequently a difference in
4
the predictability of lithium daily dosage requirements between inpatients and
outpatients.
The purpose of this study was to derive new equations for estimating lithium
clearance in inpatients and outpatients. Sex differences in lithium clearance were
considered in this derivation. The bias and accuracy of these equations were compared
with those set forth by Jermain et al. (31), Pepin et al. (21) and the empirical methods.
In addition, new equations for determining lithium daily dosage requirements in adult
psychiatric inpatients and outpatients were derived. The bias and accuracy of the
derived equations were also compared with Pepin et al. (21), Zetin et al. (25) and
Terao et al. (32) methods.
Methods
Patients
Data were collected from King Khalid University Hospital (KKUH) medical
records at Riyadh, Saudi Arabia. Patients were included in the study if they were
adults aged 18-80 years receiving multiple daily doses of lithium carbonate for, at
least, 7 consecutive days prior to the commencement of the study. The patients were
included if they had no evidence of cardiac, respiratory, hepatic or renal
abnormalities. Patients who were on sodium-restricted diet or taking any other
medication that would affect lithium levels were excluded from the study. The period
between lithium serum and body weight and renal function measurements did not
exceed one month. Serum lithium samples were drawn between 12–14 h after the last
dose. The study protocol was approved by King Khalid University Hospital (KKUH),
College of Medicine Research Center (CMRC), King Saud University, Riyadh, Saudi
Arabia.
5
A total of 60 patients (34 males and 26 females) met the study criteria. Of these,
53 patients were Saudi nationals (28 males and 25 females). The mean age (±SD) was
38.83±9.87 years (range, 21-77 years) and the mean body weight was 71.39±17.04 kg
(range, 33–120 kg). Only 7 (11.7%) patients were smokers. Fifty three (88.3%)
patients were diagnosed with bipolar affective disorder, 3 (5%) with schizoaffective
disorder and the rest were affected by other psychiatric conditions. Only 3 (5%)
patients were taking tricyclic antidepressant agents. Twenty eight (46.7%) patients
have family history of psychiatric illness. Lithium serum levels were measured both
as inpatients and outpatients for 47 (78.3%) patients, as only outpatients for 9 (15%)
and as only inpatients for the rest. Lithium dose in these patients averaged
1016.7±216.2 mg/day (range, 375–1800 mg/day) and their average lithium serum
level was 0.61±0.13 mmol/L (range, 0.3–1.0 mmol/L) for the outpatient setting. On
the other hand, lithium dose averaged 1016.2±230.1 mg/day (range, 375-1800
mg/day) and lithium serum level was 0.58±0.18 mmol/L (range, 0.06–1.21 mmol/L)
for these patients in the inpatient setting. BUN averaged 11.36±3.28 mg/dL (range,
6.02–22.13 mg/dL) and 10.85±3.13 mg/dL (range, 4.76-19.05 mg/dL) for inpatients
and outpatients, respectively. The mean serum creatinine level was 0.92±0.17 mg/dL
(range, 0.63–1.37 mg/dL) and 0.92±0.20 mg/dL (range, 0.49–1.86 mg/dL) for
inpatients and outpatients, respectively.
Data Analysis
Data were collected from patient medical records at King Khalid University
Hospital (KKUH), Riyadh, Saudi Arabia, using a specially designed collection form.
The total body clearance (CL) of lithium (L/h) in these patients was estimated from
the following relationship:
6
CL Li 
F  D  8.12 

24 Css 
 300 
(Eqn. 1)
where F is the oral bioavailability (usually 100%), Css is the average steady-state
serum concentration of lithium (mmol/L) and D is the daily dose (mg/day) of lithium
carbonate. The creatinine clearance was calculated from Cockcroft and Gault equation
(40).
Data collected from the 60 patients retrospectively (both in the inpatient and
the outpatient settings) were applied to published a priori methods either to determine
lithium clearance or lithium daily dosage regimen. The methods applied for clearance
determination are the empirical (7), Pepin et al. (21) and the Jermain et al. (31)
methods. The methods applied for daily dosage requirements determinations are Pepin
et al. (21), Zetin et al. (25) and Terao et al. (32) methods. The calculated daily dose
requirement required to produce the lithium levels observed in these patients was
compared with the daily dose actually used by these patients during the course of the
treatment.
The empirical method assumes that lithium clearance (CLLi) is one fourth of
the creatinine clearance (CLCr) and each 300 mg of lithium increases lithium level by
0.3 mmol/L. On the other hand, the equation used by Pepin et al. was
[CLLi=0.235×CLCr]. The Jermain et al. method (31) utilized a one-compartment open
model equation and population pharmacokinetic modeling to produce the following
estimate of CLLi:
CLLi  0.0093  LBW  0.0885 CLCr
where LBW is the lean body weight and was calculated from the following
relationship:
W
LBWMales  1.10W  128  
H
7
2
LBWFemales
W
 1.07W  148  
H
2
where W=the total body weight (kg) and H=the height (cm). The ideal body weight
(IBW) is calculated as: IBWMales  50  2.3  H  and
IBWFemales  45.5  2.3  H 
where H is the height in inches.
The daily dosage requirements and serum concentrations were calculated also
by the following formula used by Pepin et al. (21):
min
 300   Css  Vd 
D
1  e k d 


 kd  
 8.12   F  e



where D=daily dosage of lithium (mg), Cmin
ss =the desired steady-state trough
concentration (mmol/L), Vd=the apparent volume of distribution (L) (calculated as
CLLi/kd), F=the oral bioavailability of lithium (1.0),  =dosing interval (24 h) and
kd=elimination rate constant (h–1) [calculated as ln(2)/lithium t½].
The Terao et al. method (32) was given by the following formula:
Daily lithium dose (mg)  100.5  752.7  CLi   3.6  Age   7.2  W  13.7  BUN 
where CLi is the expected lithium concentration in mg/L, age in years, W is weight in
kg and BUN is the blood urea nitrogen in mg/dL.
Validation of Equations
For equations’ validations, the predicted clearance and daily dosage
requirements were correlated with the observed clearance and dosage in another 60
subjects who received different doses of lithium.
Statistical Analysis
The differences between various methods were evaluated by one-way analysis
of variance (ANOVA) at the 0.05 level of significance. The predictive performance of
8
all methods for clearance and daily dosage requirements was determined by
calculating the percent error (41) as follows:
 YY
%Error  100 
 Y 


where Y is the predicted value and Y is the observed value. The bias of prediction
was determined by the mean prediction error (MPE):
Y
n
MPE 
i
Y
i 1

n
and precision of prediction was measured by mean absolute error (MAE) and root
mean square error (RMSE):
n
MAE 
Y
i
Y
i 1
n

 n
  Yi  Y
RMSE   i 1
n




2






1
2
The statistical significance of bias and precision was tested using ANOVA.
The data were analyzed using the Statistical Package for Social Sciences (SPSS)
version 13.0 for Windows (SPSS Inc., Chicago, Illinois).
Results and Discussion
The data from 60 psychiatric patients were utilized to develop new equations
for the prediction of lithium clearance and daily dosage requirements by performing
stepwise linear regression. Lithium clearance was correlated with creatinine clearance.
In addition to sex-dependent variability in lithium clearance, we have reasons to
believe that lithium clearance may also vary between inpatients and outpatients. Many
9
factors may contribute to this difference; including noncompliance, activity, nonrestricted diet and disease severity. Poor compliance may prove to be a detrimental
factor in causing lithium clearance changes. The fluctuation in serum levels is quite
common, particularly with erratic treatment compliance (42-44). Furthermore,
Hopkins and Associates (11) suggested that lithium clearance might increase during
manic depression episodes and consequently lithium levels would decrease. Also the
changes in salt intake, diet and caffeine intake may alter serum lithium levels.
Caffeine can increase the excretion of lithium, thereby decreasing lithium
concentrations. Furthermore, Schaub et al. (45) found that many of the psychiatric
patients who had been receiving lithium for years did not have sufficient knowledge
about lithium therapy especially older patients. Therefore, disregarding these
influences on lithium clearance might produce a biased estimate of lithium daily
dosage requirements.
The correlation between creatinine clearance (L/h, independent variable) vs.
lithium clearance (L/h, dependent variable) was evaluated by multiple linear
regression. The regression equations which gave the best correlation coefficient (r)
were the following:
 For inpatients:
CLLi  Males   1.415  0.124 CLCr
CLLi  Females   0.534  0.228 CLCr
 For outpatients:
CLLi  Males   1.055  0.137 CLCr
CLLi  Females   0.979  0.148 CLCr
10
Since the calculation of creatinine clearance by Cockroft and Gault method
accounts for gender differences, these equations were further simplified to produce a
lithium clearance value combined for both males and females as follows:
CLLi  Inpatients   0.932  0.185 CLCr
CLLi  Outpatients   1.021  0.141 CLCr
Figure 1 shows the relationship between lithium clearance and creatinine clearance in
60 adult psychiatric inpatients.
The variables chosen by the stepwise linear regression analysis for the
prediction of lithium daily dosage requirements (mg) were lithium concentration
(mmol/L), age (years), weight (kg), tricyclic antidepressants (TCA, yes=1, no=0),
CLCr (L/h), blood urea nitrogen (BUN, mmol/L) and sex (male=1, female=0). The
determination coefficients (r2) with this combination of variables were 0.59
(p=0.00458, ANOVA) and 0.746 (p=0.00017, ANOVA) for inpatients and
outpatients, respectively. The resulting regression equations for the prediction of daily
dosage requirements of lithium carbonate (mg) in these patients were as follows:
 For inpatients:
Daily dose  350.15  289.92  desired lithium level   0.84  weight 
 1.76  Age   34.43  TCA   62.1  CL Cr 
 13.1  BUN   40.9  sex 
 For outpatients:
Daily dose  784.92  530.22  desired lithium level   8.61  weight 
 12.09  Age   11.14  TCA   7.63  CL Cr 
 42.62  BUN   23.43  sex 
11
If the patients are not concomitantly administering tricyclic antidepressants, a
simplified version of both equations could be used for the preliminary estimation of
daily dosage requirements of lithium for both sexes:
Daily dose  382.54  348.29  desired lithium level   67.19  CLCr 
Comparison with other methods
When the developed equations were applied to another set of data for other 60
psychiatric patients, the predicted total body clearance of lithium was found to be
2.09±0.045 L/h and 1.88±0.051 L/h for inpatients and outpatients, respectively,
compared with the observed values of 2.09±0.112 L/h and 1.98±0.086 L/h for
inpatients and outpatients, respectively. The lithium clearance calculated by Pepin et
al. method averaged 1.46 L/h and 1.44 L/h for inpatients and outpatients, respectively.
On the other hand, the empirical and Jermain et al. methods produced estimates of
1.56 L/h and 1.026 L/h for inpatients, and 1.53 L/h and 1.0 L/h for outpatients,
respectively. Table 1 shows the lithium clearance values predicted by various
methods. All methods, with the exception of our method, tended to under-estimate
lithium clearance for both inpatients and outpatients. The Jermain et al. method
proved to be the least accurate among all methods for the prediction of lithium
clearance and the empirical method produced better estimates of clearance than Pepin
et al. method (Table 2).
The predicted daily dosage requirements in the 60 psychiatric patients by the
Pepin et al. method averaged 1140.3±87.0 mg (range, 90.7–4008.1 mg) compared
with 1014.5±19.9 mg (range, 650.8–1498.4 mg) predicted by our method for
inpatients. On the other hand, Zetin and Terao methods predictions of daily dosage
requirements averaged 1088.7±26.1 mg (range, 611.8-1571.3 mg) and 743.8±26.1 mg
12
(range, 228.6-1196.0 mg), respectively. One-way ANOVA for the mean prediction
error (MPE), mean absolute error (MAE) and root mean square error (RMSE) showed
statistically significant differences (p<0.001) between all methods. The post hoc
pairwise comparisons using Student-Neuman-Keuls and Duncan tests revealed that
Zetin method was not significantly different from our method with respect to MPE
and MAE. Table 2 shows the bias and precision of prediction of both lithium
clearance and daily dosage requirements predicted by various methods for psychiatric
inpatients. Our method proved to be statistically superior to all other methods
described in this study for the prediction of lithium clearance as well as the prediction
of daily dose. Figure 2 shows a plot of predicted dose by the current method as a
function of the administered dose for 60 inpatients. The Terao et al. method extremely
underpredicted the daily dosage requirements for these patients by almost 25%,
whereas Pepin and Zetin methods overpredicted the dosage by about 13%. The
deviation in our method was less than 4%.
Similar analysis was performed for outpatients revealed that the empirical,
Jermain and Pepin methods also significantly underpredicted lithium clearance for
outpatients (Table 1). The deviation in our method was less than 7%, while the
deviation in Jermain method exceeded 44% (Table 3). The Pepin method predicted
the lithium daily dosage requirements to be 1212.4±99.9 mg (range, 440.3-3408.0
mg) compared with 1003.7±26.3 mg (range, 651.1-1463.4 mg) predicted by our
method with a deviation of less than 3% from the observed dose actually prescribed
for these patients, whereas the deviation in Pepin method was more than 18%. Again,
the Terao and Associates method significantly underpredicted the dose. Conversely,
dosage prediction by Jermain method was reasonably unbiased for these patients
compared with other a priori methods, but it still falls short when compared with the
13
present method (Table 3). Figure 3 shows a plot of predicted dose by the current
method versus administered dose for 60 outpatients. On the other hand, the reduced
predictive equation for the estimation of lithium daily dosage requirements also
proved to be useful if the clinician had no access to all patient variables or when a
quick estimate of the dose is desired. Compared with the full equations, it has been
found that estimating the dose using the reduced equation will only underestimate the
daily dose by less than 2% and 9.8% for the inpatients and outpatients, respectively.
In conclusion, the present method proved to be superior to all reported
methods in predicting the daily dosage requirements and clearance of lithium for our
patients. These new predictive equations were safely applied to patients with no
noticeable adverse effects.
14
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Table 1. Lithium clearance predicted by various methods. The observed lithium
clearance in 60 patients was 2.09±0.112 L/h (range, 0.58 – 3.29 L/h)
for inpatients and 1.88±0.0.45 L/h (range, 0.57 – 5.07 L/h) for
outpatients.
Method
Lithium Clearance (L/h)
Mean±SEM (Range)
Inpatients
Outpatients
Empirical
1.56 ± 0.064
(0.73 – 3.02)
1.53 ± 0.08
(0.61 – 2.92)
Jermain
1.026 ± 0.031
(0.53 – 1.58)
1.00 ± 0.036
(0.53 – 1.52)
Pepin
1.46 ± 0.06
(0.69 – 2.84)
1.44 ± 0.076
(0.58 – 2.74)
Abou-Auda et al.
(This method)
2.088 ± 0.051
(1.22 – 3.29)
1.88 ± 0.045
(1.37 – 2.67)
18
Table 2: Bias and precision of prediction of lithium clearance and daily dosing regimen of various methods (mean±SEM) compared
with the method described in this study for inpatients.
% Error
MPE*
MAE**
RMSE***
Empirical
-19.53±3.72
-0.53±0.104
0.63±0.09
0.89±0.51
Jermain
-46.37±2.69
-1.066±0.107
1.07±0.105
1.29±0.67
Pepin
-24.36±3.50
-0.618±0.103
0.68±0.10
0.95±0.54
Abou-Auda et al.
(This Method)
10.31±5.77
0.002±0.10
0.49±0.07
0.69±0.45
Pepin
13.39±6.39
143.13±74.39
357.97±57.37
534.92±355.38
Zetin
12.45±4.66
68.36±32.64
181.13±20.98
229.36±110.72
Terao
-23.13±3.39
-265.72±33.51
282.64±30.49
352.85±161.56
3.96±3.32
0.68±26.6
142.9±16.86
184.57±95.99
Parameter
Method
Clearance
Daily Dose
Abou-Auda et al.
(This Method)
* Mean Prediction Error
** Mean Absolute Error
*** Root Mean Square Error
19
Table 3: Bias and precision of prediction of lithium clearance and daily dosing regimen of various methods (mean±SEM) compared
with the method described in this study for outpatients.
% Error
MPE*
MAE**
RMSE***
Empirical
-16.37±3.56
0.34±0.073
0.47±0.05
0.58±0.24
Jermain
-44.34±2.75
-0.902±0.068
0.91±0.07
0.99±0.35
Pepin
21.39±3.34
-0.437±0.071
0.52±0.055
0.624±0.255
Abou-Auda et al.
(This Method)
6.62±4.80
0.004±0.063
0.334±0.035
0.40±0.165
Pepin
18.47±7.20
208.74±82.93
374.48±66.79
546.5±110.06
Zetin
8.76±3.92
47.79±26.68
147.24±17.55
190.95±94.92
Terao
-18.83±3.34
-218.43±27.74
248.08±20.59
280.17±108.30
2.95±3.12
0.026±23.47
111.5±15.5
148.46±72.16
Parameter
Method
Clearance
Daily Dose
Abou-Auda et al.
(This Method)
* Mean Prediction Error
** Mean Absolute Error
*** Root Mean Square Error
20
Figures’ Captions
Figure 1:
Relationship between lithium clearance and creatinine clearance in 60
adult psychiatric inpatients.
Figure 2:
A plot of predicted dose by the current method described in this study
versus administered dose for 60 inpatients.
Figure 2:
A plot of predicted dose by the current method described in this study
versus administered dose for 60 outpatients.
21