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. Pharmacy Department, King Fahad National Guard Hospital, Riyadh, Saudi Arabia. * To whom correspondence should be addressed. Abstract 2 Introduction Lithium has been used in the treatment of mania and in the prophylaxis of bipolar disorder and recurrent depression (Jefferson 1987, Speirs 1978). 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 (Baldessarini 1996, Johnson 1996). 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 (Amdisen 1975, Amdisen 1977, American Psychiatric Association 1994, American Psychiatric Association 2002). 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 (Moscovich 1993, Johnson 2002). In addition, conditions that alter electrolyte balance may affect lithium levels in patients (Hopkins 2000). 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 (Thomsen 1997). 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 (Hewick 1977). Concomitant use of diuretics, angiotensin-converting enzyme inhibitors, calcium 3 channel antagonists, or non-steroid antiinflammatory drugs have been associated with lithium toxicity through pharmacokinetic interactions (Timmer 1999, Finley 1995, Jefferson 1981). Viguera et al. (Viguera 2000) analyzed 17 studies on the use of lithium in bipolar disorder to 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 (Cooper 1973, Cooper 1976, Amdisen 1977, Pepin 1980, Slattery 1980, Slattery 1981, Zetin 1983, Zetin 1986, Kook 1985, Cummings 1988, Dugas 1983, Gengo 1981, Perry 1983, Perry 1986, Jermain 1991, Terao 1999, Gervasoni 2003), 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 (Ref), the Pepin et al. (Pepin 1980) and the Zetin et al. (Zetin 1983, Zetin 1986, Zetin 1990) methods. Browne and Associates (Brown 1989) 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 (Stip 2001). Markoff and King (Markoff and King 1992) 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 4 level with Zetin method whereas only 38% had done so with the empirical method. Other studies (Hagino 1998, Wright 2000, Markins 1994) 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 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. (Jermain 1991), Pepin et al. (Pepin 1980) 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. (Pepin 1980), Zetin et al. (Zetin 1986) and Terao et al. (Terao 1999) 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 5 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. 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. Fortyfour (73.3%) patients were diagnosed with bipolar affective disorder, 9 (15%) with manic depressive illness, 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: CL Li F D 8.12 24 Css 300 6 (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 (Cockroft & Gault 1976). 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 (Amdisen 1977), Pepin et al. (Pepin 1980) and the Jermain et al. (Jermain 1991) methods. The methods applied for daily dosage requirements determinations are Pepin et al. (Pepin 1980), Zetin et al. (Zetin 1986) and Terao et al. (Terao 1999) 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 (Jermain 1991) utilized a onecompartment 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: 2 LBWMales W 1.10W 128 H 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.: 7 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 hr) and kd=elimination rate constant (hr–1) [calculated as ln(2)/lithium t½]. The Terao et al. method (Terao 1999) 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 all methods for clearance and daily dosage requirements was determined by calculating the percent error (Sheiner 1981) as follows: YY %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 i 1 n 8 Y n Yi Y RMSE i 1 n 2 1 2 The statistical significance of bias and precision was tested using ANOVA. Results 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. The correlation between creatinine clearance (L/hr, independent variable) vs. lithium clearance (L/hr, 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 These equations were further simplified to produce for both males and females as follows: CLLi Inpatients 0.932 0.185 CLCr CLLi Outpatients 1.021 0.141 CLCr The variables chosen by the stepwise linear regression analysis for the prediction of daily dosage requirements (mg) were lithium concentration (mmol/L), age (years), weight (kg), tricyclic antidepressants (TCA, yes=1, no=0), CLCr (L/hr), 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 9 resulting regression equations for the prediction of daily dosage requirements of lithium carbonate (mg) in these patients 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 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 the same 60 psychiatric patients, the predicted total body clearance of lithium was found to be 2.09±0.045 L/hr and 1.88±0.051 L/hr for inpatients and outpatients, respectively, compared with the observed values of 2.09±0.112 L/hr and 1.98±0.086 L/hr for inpatients and outpatients, respectively. The lithium clearance calculated by Pepin et al. method averaged 1.46 L/hr and 1.44 L/hr for inpatients and outpatients, respectively. On the other hand, the empirical and Jermain et al. methods produced estimates of 1.56 L/hr and 1.026 L/hr for inpatients, and 1.53 L/hr and 1.0 L/hr for outpatients, respectively. Table 1 shows the lithium clearance values predicted by various methods. All methods, with the exception of our method, tended to underestimate 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 10 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 (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. 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. 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The observed lithium clearance in 60 patients was 2.09±0.112 (range, 0.58 – 3.29) for inpatients and 1.88±0.0.45 (range, 0.57 – 5.07) for outpatients. Method Lithium Clearance (L/hr) 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) 15 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 the 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 16 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 the 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 17 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. 18 19 20 21