Abstract:
A method and system for providing a drug regimen for a patient that considers both pharmacokinetic and drug resistance testing information to reduce the probability that a drug will become ineffective during treatment due to viral susceptibility to infection. The system uses multiple concentration-time curves to determine trough levels for a drug or drugs, which can be used to determine an appropriate drug regimen for the patient.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to calculating a probability of achieving desired trough concentrations for dosing regimens using anti-infective drugs.  
       BACKGROUND OF THE INVENTION  
       [0002]     Over the past several years, it has become clear that achieving and maintaining adequate antiretroviral drug concentrations is required to produce a durable virologic response. In fact, many studies are either ongoing or in development that will explore therapeutic drug monitoring (TDM) of antiretrovirals in naive and experienced human immunodeficiency virus (HIV)-infected patients. The classic method of applying TDM uses measured drug concentrations to alter a dosing regimen in order to achieve a targeted level of exposure. However, a primary concern when utilizing this method is choosing the appropriate target concentration.  
         [0003]     Some in vivo clinical pharmacodynamic data are available for various antiretrovirals, mostly protease inhibitors (PIs), but efficiently collecting these data is difficult.  
         [0004]     Recently, in vitro phenotypic sensitivity testing of individual patients&#39; viral isolates has become available, enabling clinicians to use susceptibility as a surrogate for concentration-response data. Even so, clinical use of TDM in this country has not been widely used. This is likely due to the logistics of sample collection, difficulty in interpretation of results, and lack of large, prospective studies clearly defining the role of TDM.  
         [0005]     As a result, alternative methods of incorporating antiretroviral pharmacokinetics into therapeutic decisions are being explored. The method gaining the most attention is the inhibitory quotient (IQ), or the C min /IC ratio, where C min  is the measured trough concentration of a particular drug in a patients&#39; regimen and IC is the in vitro drug inhibitory concentration required to block 50%, 90%, or 95% of viral replication (typically the IC50, IC90, or IC95). Several studies have attempted to define the optimal Cmin/IC50 ratio required to produce long-term viral suppression, and the ratio has been linked to clinical outcome.  
         [0006]     Although the IQ concept is appealing, its applicability in the clinic setting remains untested and undefined. There is still a growing clinical need for the development of predictive methods that incorporate pharmacokinetic and viral resistance testing data in order to better manage treatment-experienced patients.  
       SUMMARY OF THE INVENTION  
       [0007]     The present invention provides a method and system for calculating a probability of achieving desired trough concentrations for a desired dosing regimen, which can be used in managing drug treatments for patients.  
         [0008]     The present invention (1) collects pertinent pharmacokinetic parameters for a drug; (2) builds a pharmacokinetic model for each dosing regimen; (3) simulates each dosing regimen model; (4) extracts trough drug levels from each simulation; (5) collects data associated with drug concentrations that reduce viral replication in vitro by a specified percentage; (6) compares the simulated trough levels with a  PB IC 50  and (7) outputs the probabilities of achieving trough levels at or above the  PB IC 50 . 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]     The foregoing and other advantages and features of the invention will become more apparent from the detailed description of exemplary embodiments of the invention given below with reference to the accompanying drawings.  
         [0010]      FIG. 1A  illustrates a plurality of concentration-time curves for a plurality of dosing regimens;  
         [0011]      FIG. 1B  illustrates a plurality of concentration-time curves for a plurality of dosing regimens;  
         [0012]      FIG. 2  is a spreadsheet illustrating a plurality of dosing regimens and a plurality of simulated trough levels for each drug regimen;  
         [0013]      FIG. 3  is a chart illustrating a combination of dosing regimens containing low-dose RTV. APV refers to Amprenavir or fos-Amprenavir; RTV refers to Ritonavir; IDV refers to Indinavir; SQV refers to Saquinavir; LPVr refers to Lopinavir+Ritonavir Combination Product; NFV refers to Nelfinavir; EFV refers to Efavirenz; NVP refers to Nevirapine; ATV refers to Atazanavir; TPV refers to Tipranavir; BID twice daily dosing; QD refers to once daily dosing; and  
         [0014]      FIG. 4  is a schematic diagram of a processing system which implements methods in accordance with the present invention. 
     
    
     DETAILED DESCRIPTION  
       [0015]     The present invention integrates expected drug exposure information with in vitro susceptibility testing to calculate the probability of achieving desired trough concentrations, particularly those above a measured protein binding-corrected level, such as IC 95  ( PB IC 95 ), IC 50  ( PB IC 50 ), etc. These probabilities can be used to determine which dual PI-based salvage regimen is most likely to be successful in the management of treatment-experienced patients.  
         [0016]     Although the present invention can be used to predict the probability of achieving desired trough levels of any suitable anti-infective agent including, for example, anti-bacterial, antibiotic, antifungal and anti-viral, in exemplary embodiments of the invention described below the anti-infective agent is an anti-viral drug (e.g., an anti-retroviral drug) or combination of such drugs. In particular, it is believed that integration of pharmacokinetic and viral drug resistance testing information maximizes the benefit of antiretroviral therapy in the management of highly treatment-experienced HIV-infected subjects.  
         [0017]     The method can be practiced using a suitable computer such as a personal computer, hand-held computer or PDA. As described below, portions of the software involved can be obtained from commercial sources or can readily be produced by persons skilled in the art to which the invention relates in view of the teachings in this patent specification. In an exemplary embodiment of the invention, which relates to antiretroviral drugs, the steps of the method are as follows:  
         [0018]     In a first step (1) of the method, pertinent pharmacokinetic parameters for the drug or drugs are collected. Such data are available from published literature with which persons skilled in the art are familiar. These data include parameters such as area-under-concentration/time-curve (AUC), oral clearance (CL/F), maximum concentration (C max ), terminal distribution volume (V/F), and others that may be available. These are collected for any regimen where protease inhibitors are used, whether in combination therapy, alone, or with other classes of antiretroviral drugs.  
         [0019]     In a second step (2) of the method, a pharmacokinetic model is built for each regimen. The parameters collected from step 1 are used to create a pharmacokinetic model. Either a one-compartment model or two-compartment model is suitable. As known by persons skilled in the art, commercially available software can be used to build the model. For example, the ADAPT II (release 4) software package available from Biomedical Simulations Resource, Los Angeles, Calif. can be used.  
         [0020]     One-compartment model parameters from step (1) can include: oral clearance (CL/F), terminal distribution volume (V 2 /F), absorption rate constant (k a ), and absorption lag phase (t lag ). Two-compartment parameters can include: total (CL/F tot ) and distributional (CL/F d ) clearance, central (V c /F) and peripheral (V p /F) distribution volumes, and k a  and t lag .  
         [0021]     To account for intersubject pharmacokinetic variability, all clearance and distribution volumes were assigned a coefficient of variation (CV) of 50%. A CV of 50% was also applied to ka and tlag. Standard deviations can be used if obtained in step (1), but it is suitable to use fixed values that accurately represent the true variability across all regimens studied. These CVs may vary though depending upon the drug(s) being studied. A linear standard deviation variance model can be used to describe additional assay variability.  
         [0022]     In a third step (3) of the method, a suitable number of population simulations are performed on each regimen model using a suitable simulation method such as Monte Carlo. This technique calculates multiple scenarios of a model by repeatedly sampling pharmacokinetic parameters from the probability distributions and using those values to generate the concentration-time curves. For example, 100 Monte Carlo simulations can be performed on each model, resulting in the generation of 100 corresponding concentration versus time curves. This is analogous to having 100 patients come into a clinic, take a dose or doses of the drugs of interest, and measuring their blood levels over the course of the dosing interval. At least about 100 simulations is believed to be suitable for purposes of this exemplary embodiment of the invention, but a larger number of simulations (e.g., 1000) would not significantly alter the range of resulting pharmacokinetic parameters and concentration-time curves. These concentration-time data can be used to produce percentile curves, such as the 10th, 25th, 50th (median), 75th, and 90 th , for each dosing regimen, as illustrated in  FIGS. 1A and 1B .  
         [0023]     For each regimen, the 10 th  to 90 th  percentile concentration-time curves are shown, demonstrating the inherent interpatient variability of the drugs of interest. For example, even Efavirenz (EFV), which has a long half-life, has trough concentrations ranging from approximately 600-700 ng/mL (10 th  percentile) to upwards of 4000 ng/mL (90 th  percentile).  
         [0024]     These simulated concentration-time curves serve two important purposes. The first purpose is to aid in the interpretation of antiretroviral plasma drug concentrations. Each plot shown above shows the median concentration-time curve and the variability around that curve. Therefore, if a plasma sample was collected from an individual patient for drug concentration determination, these figures will allow the clinician or other health care professional to determine how that patient compares with the average population. A second purpose is to provide an additional tool for optimization of salvage therapy when used in conjunction with viral drug phenotypic data.  
         [0025]     In a fourth step (4) of the method, the range of trough drug levels is extracted from the concentration-time curves for each regimen. Since 100 simulations were performed for each regimen, there are 100 trough drug levels available from each regimen. The trough drug level is the lowest amount of drug in the body just before the next dose is taken. So, for a regimen that is administered every 12 hours, the trough level will generally occur 12 hours after the last dose. The trough levels are important because research has shown strong relationships between trough levels (for protease inhibitors and NNRTIs like efavirenz) and clinical outcome, i.e., low trough levels cause viral resistance to develop and ultimately the drug regimen will fail.  
         [0026]     In a fifth step (5) of the method, data representing drug concentration that reduces viral replication in vitro by a specified percentage are collected. ViroLogic, Inc. of San Francisco, Calif. is a commercial source of data representing drug concentration that reduces viral replication in vitro by 50% (IC 50 ) (ViroLogic&#39;s PHENOSENSE™ report), but the data could be obtained in any other manner or from any other source that may provide it. The IC 50  represents how resistant a virus may be; the higher the IC 50  the more drug it will take to prevent viral replication.  
         [0027]     When using an IC 50  to target plasma drug levels, it should be adjusted to account for plasma protein binding. The IC 50  data are corrected for protein binding to produce a  PB IC 50 . Any suitable method known in the art can be used to correct IC 50 s for protein binding. Several methods include dividing the IC 50  by the known free-fraction of drug, quantitating the free drug level in plasma, and determining a protein binding correction factor based on in vitro protein binding studies using 50% human serum (HS).  
         [0028]     Several well-conducted studies examining this issue have been published, and it is suitable to use the average value across different studies. Using data from some of these studies, and taking IDV as an example, 50% binding would lead to an appropriate correction factor of 2 (i.e. 100 ng/mL divided by 0.5 equals 200 ng/mL). IDV, however, is 60% bound to plasma proteins, so the conversion factor must be slightly higher than 2.0. Results from a 100% HS study state the conversion factor to be 3.5, which is likely an overestimate. The average value across four such studies for IDV is 2.4, which is believed to be a reasonable estimate.  
         [0029]     The following table lists as an example the results of four studies involving eight drugs and the average correction factor for each of these drugs:  
                                                                   TABLE 1                           PROTEIN-BINDING CORRECTION       FACTORS FOR PIs AND NNRTIs            Drug   50% HS   50% HS   50% HS   100% HS   Average                    IDV   2   2   2.1   3.5   2.4       APV   6   7   3.8   10.5   6.8       LPV   5       3.9   14.2   7.7       RTV   20   20   10.2   29.7   20.0       SQV   25   26   14.7   28.0   23.4       NFV   35   37   21.9   90.6   46.1       EFV           11.2   25.5   18.4       NVP           1.3   1.2   1.3                  
 
         [0030]     The average value in the last column for a particular drug is multiplied by the IC 50  derived from the PHENOSENSE™ report. In this regard, the IC 50  becomes a protein-binding corrected IC 50  ( PB IC 50 ). It is the  PB IC 50  that is compared with the range of simulated trough drug levels in order to determine the probability of achieving a trough drug levels above the  PB IC 50  for each regimen examined. These  PB IC 50 &#39;s can then be compared directly to the simulated concentration-time curves in order to estimate the probability that the trough concentration of a particular drug regimen will be at or above the  PB IC 50 . In other words, one can determine the probability of achieving an IQ of 1.0 for a particular drug regimen.  
         [0031]     In a sixth step (6) of the method, the  PB IC 50  is compared with the simulated trough drug levels. In the exemplary embodiment of the invention, the comparison is performed using a spreadsheet program such as MICROSOFT EXCEL, but in other embodiments this step can be integrated with the other steps in a single software program or can be performed by computer in any other suitable manner. The plasma drug trough levels from the simulated concentration-time data are input to the spreadsheet. The IC 50 s, in μM units, are entered directly from the ViroLogic PHENOSENSE™ report. As described in further detail below, the spreadsheet automatically converts the IC 50 s to ng/mL (using standard conversion factors), corrects for protein binding based on the average values listed in Table 1 above, and determines the probability of achieving an IQ of 1.0 (i.e., a C min / PB IC 50  ratio of 1.0), 2.0, or 5.0. Briefly, all of the plasma drug trough values from the pharmacokinetic simulations for each regimen ( FIGS. 1A and 1B ) are listed in ascending order and assigned a rank. In this case, the total rank is 100, since 100 simulations were conducted. As described in further detail below, a simple logical test is written in the column next to the troughs such that if the trough value in a particular cell is greater than the PBIC 50 , its assigned rank is converted to a percentage of the total rank. As an example, it is assumed that the range of 100 simulated troughs for a particular PI in a RTV-enhanced regimen is from 300 to 5000 ng/mL. The  PB IC 50  for this PI is 1700 ng/mL, and the first trough in the list that is at or above 1700 ng/mL is, for example, rank number 60; thus, 100 (total number of trough levels) minus the rank 60 (which equals the first trough at or above 1700 ng/mL) divided by 100 is 40%. Therefore, there is a 40% probability of achieving a trough level at or above the patient&#39;s  PB IC 50  for this particular dual PI regimen. The same methods are applied to 2× the  PB IC 50  and 5× the  PB IC 50  to determine IQs of 2.0 and 5.0, respectively.  
         [0032]     As illustrated in  FIG. 2  below, the EXCEL spreadsheet has multiple groups of four columns (columns A-Q being visible in that portion of the spreadsheet screen display shown in  FIG. 2 ). Each group of four columns represents one of the regimens. Row 1 lists the column header labels. Column A is labeled “Rank” and contains a list of numbers from 1 to 100 in ascending order. Therefore, cell A2 (i.e., the cell at column A, row 2) contains the number 1, cell A3 contains the number 2, and so on, with the last cell in column A, cell A101, containing the number 100. The first group of four columns, B-D, relate to a first regimen, the next group of four columns, F-I, relate to a second regimen, and so on.  
         [0033]     In the example illustrated in  FIG. 2 , column B is labeled “APV/RTV 600/100 BID,” and lists the 100 simulated trough levels for this regimen in ascending order. Column C is labeled “PROB AR6-1,” which stands for the probability of the APV/RTV 600/100 BID regimen being greater than the corresponding value in column B. This is the most important column. The formula written in this column is: =IF(B2&gt;$BE$3,(1−(A2−1)/$A$101),“”). Where the cell B2 is the first simulated trough level for this particular regimen, the cell BE3 is where the protein binding corrected IC 50  ( PB IC 5 O) for APV is listed (top section of the output table), the cell A2 is the first rank (i.e. 1) and the cell A101 is the last rank (i.e. 100). This formula then indicates which trough levels listed in column B are above the PBIC50, and lists them in column C. Therefore, the highest value (percentage) in Column C is displayed in the bottom section of the output table under that particular regimen for that particular IQ level. In this example, regimen APV/RTV 600/100 mg BID (IQ=1.0) is displayed in cell AY24. Another formula is written in cell AY24: =MAX(C2:C101), which then calculates the maximum value listed in column C and displays it in cell AY24.  
         [0034]     Additional drugs and regimens are contemplated. Examples of various regimens used in the invention include, but are not limited to: 
        APV/RTV 600/100 BID     APV/RTV 1200/200 QD     IDV/RTV 800/200 BID     IDV/RTV 800/100 BID     IDV/RTV 400/400 BID     SQV/RTV 1600/200 QD     SQV/RTV 1000/100 BID     SQV/RTV 400/400 BID     LPV/RTV 400/100 BID     NFV 1250 BID     EFV 600 QD     NVP 400 QD     ATV-RTV 300/100 QD     LPVr-APV 400/100/600 BID     APV-LPVr 600/400/100BID     ATV/RTV 300/100 mg QD     LPV/RTV/SQV 400/100/1000 mg BID     APV/RTV/IDV 700/100/600 mg BID     SQV/RTV/ATV (multiple doses)     LPV/RTV/ATV (multiple dose)     LPV/RTV/IDV (400/100/600 mg BID     TPV/RTV 500/200 mg BID        
 
         [0057]     To produce an IQ of 2.0 and 5.0, the  PB IC 50  is multiplied by 2 or 5, respectively. These are displayed in cells BG3 and BG5, respectively. Column D is labeled “AR6-1 IQ=2” and column E is labeled “AR6-1 IQ=5”. The exact same formula is written in these 2 columns as in column C, except the  PB IC 50  is now from cells BF3 (2×PBIC50) and BG3 (5×PBIC50). Again, the highest percentage listed under columns D and E are displayed in the bottom sections of the output table. For APV/RTV 600/100 mg BID, these correspond to cells AY32 (IQ=2.0) and AY40 (IQ=5.0). The equation: =MAX(D2:D101) is written in cell AY32 and the equation: =MAX(E2:E101) is written in cell AY40, which correspond to the maximum percentages in columns D and E, respectively.  
         [0058]     In a seventh step (7) of the method, the probabilities of achieving trough levels at or above the  PB IC 50  are output to the computer display, as illustrated below with regard to an example in which there are 12 different regimens.  
         [0059]     The top section of this exemplary output display lists the drug names (col. 1) and the IC 50 &#39;s obtained from ViroLogic or other source (col. 2), as a person would enter them into the spreadsheet or other software program at step (5) of the method, described above. In the third column, the spreadsheet or program has converted the IC 50  from μM to ng/mL, and in the last column has corrected the IC 50  for protein binding ( PB IC 50 ).  
         [0060]     Note that combination regimens containing low-dose RTV are displayed in the output shown in  FIG. 3  using only the active protease inhibitor (e.g., there are 3 different dosing regimens for SQV/RTV, but the probability value in the output refers to only SQV) because the combination regimens listed in  FIG. 3  all contain ritonavir (RTV) at various dosages, and RTV is not considered an active component of the drug regimen because it is commonly used clinically to enhance or “boost” the plasma drug levels of other drugs, such as other protease inhibitors, in order to achieve significantly higher drug levels relative to a single, unboosted protease inhibitor. Additional dual protease inhibitor plus NNRTI regimens, such as LPV/RTV plus EFV and APV/RTV plus EFV, can be added to the output. For these combination regimens, the probabilities are listed for both active components (LPV and EFV) and displayed as such in the output table.  
         [0061]     It is the  PB IC 50  for each drug that the spreadsheet or other program then compares with the simulated trough levels for each regimen to determine the probability, or likelihood, of achieving an IQ of 1.0. The bottom section of  FIG. 3  in this exemplary output display shows the computed percentages. This is the information that a clinician would use to help guide the decision-making process when choosing the next salvage therapy regimen for their patient.  
         [0062]     In the illustrated example, the bottom section of  FIG. 3  can be interpreted as follows. Both the EFV and NVP regimens would be expected to achieve trough levels above the  PB IC 50  essentially 100% of the time, even though some viral drug resistance is present. The dual protease inhibitor-containing (PI-containing) regimens of APV/RTV (87 to 93%), IDV/RTV (88-92%), and LPV/RTV (100%) all have high probabilities of achieving trough levels at or above the  PB IC 50  for each respective enhanced PI regimen at various doses. Others PI regimens, such as SQV/RTV (0-2%) and NFV (1%) have very little chance of achieving the desired trough levels due to the high degree of viral drug resistance present in this subjects isolate. This procedure, which incorporates known pharmacokinetic data and viral drug susceptibility, allows the clinician and patient more choices than the phenotyping alone would provide when determining treatment options for PI and NNRTI-resistant virus.  
         [0063]     A clinician can base a decision of the subsequent treatment regimen upon the results computed in accordance with the present invention. For example, a clinician can choose to treat a patient with the regimen having the highest probability. However, as persons skilled in the art to which the invention relates will recognize, other factors may influence the regimen choice, such as past history of the patient (e.g., intolerability to particular drugs). Consequently, a clinician may choose a regimen not having the highest probability. The invention provides the clinician the full range of treatment options available to make an intelligent choice once the clinician has considered both the pharmacokinetics of the drugs and viral susceptibility inherent within this process.  
         [0064]      FIG. 4  shows a processor system  400 , which includes a computer application  408  that implements methods in accordance with the present invention. Application  408  is used to generate the various concentrations versus time curves and dosing regimens of  FIGS. 1-3  for use by a clinician in creating a treatment regimen for a patient. System  400  includes a processor  402  having a central processing unit (CPU) that communicates with various devices over a bus  404 . Some of the devices connected to the bus  404  provide communication into and out of the system  400 , for example, an input/output (I/O) device  406  and an imager device  408 . Other devices connected to the bus  404  provide memory, illustratively including a random access memory (RAM)  410 , hard drive  412 , and one or more peripheral memory devices such as a floppy disk drive  414  and compact disk (CD) drive  416 .  
         [0065]     It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope or spirit of the invention. Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.