WO2002065120A1 - Dosage et evaluation de plusieurs medicaments associes - Google Patents

Dosage et evaluation de plusieurs medicaments associes Download PDF

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WO2002065120A1
WO2002065120A1 PCT/US2002/004086 US0204086W WO02065120A1 WO 2002065120 A1 WO2002065120 A1 WO 2002065120A1 US 0204086 W US0204086 W US 0204086W WO 02065120 A1 WO02065120 A1 WO 02065120A1
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dose
combination
desirability
subject
desirability function
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PCT/US2002/004086
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W. Hans Carter, Jr.
Chris Gennings
Vernon M. Chinchilli
Margaret Shih
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Virginia Commonwealth University
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Priority to US10/467,835 priority Critical patent/US7610153B2/en
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/48—Biological material, e.g. blood, urine; Haemocytometers
    • G01N33/50—Chemical analysis of biological material, e.g. blood, urine; Testing involving biospecific ligand binding methods; Immunological testing
    • G01N33/5005—Chemical analysis of biological material, e.g. blood, urine; Testing involving biospecific ligand binding methods; Immunological testing involving human or animal cells
    • G01N33/5091—Chemical analysis of biological material, e.g. blood, urine; Testing involving biospecific ligand binding methods; Immunological testing involving human or animal cells for testing the pathological state of an organism

Definitions

  • the invention generally relates to the titration of multi-modality therapy regimens.
  • the invention provides methods of titrating and evaluating multi-modalitiy therapy regimens using an evolutionary operation (ENOP) approach.
  • ENOP evolutionary operation
  • Dose titration with single compounds is a relatively straightforward process employed by physicians to identify appropriate dose levels which produce improved responses in patients while simultaneously minimizing the adverse side effects a patient may experience. After taking into account a patient's age, weight, and other factors specific to the patient, the physician will prescribe an initial dose which may be increased or decreased as needed, depending on how the patient responds. This titration continues until a favorable balance between the desired response and undesirable side effects is achieved.
  • the difficulty arrives in attempting to translate this approach to determining dosages in the case where multiple drugs and/or other treatment modalities are being prescribed in the treatment of a single disease, or where the consideration of multiple endpoints is needed in the case where a single treatment is prescribed.
  • the ' physician generally either chooses to address the problem empirically, or will employ an ad-hoc approach, varying the levels of one drug while keeping the doses of all the other drugs in the combination fixed.
  • this approach does not account for potential interactions among the drugs, which may be crucial when searching for the most desirable therapy.
  • the present invention provides methodology for titrating a multi-modality therapy regimen in a subject or in a plurality of subjects.
  • an appropriate combination of p modalities for example drugs, radiation, quantifiable amounts of psychotherapy or physical therapy, or other treatment modalities
  • p __2 is selected by a skilled practitioner (e.g. a physician).
  • the methodology of the present invention may also be applied to the titration of a single modality.
  • the combination may be selected to treat a specific disease condition, or may be directed to the treatment of a group of symptoms typically associated with more than one disease condition.
  • the endpoint is one that might reasonably be predicted to occur as a result of the administration of the modality, and the endpoint must be ordinal in nature, i.e. it must be possible to rank order the outcomes from worst to best.
  • the endpoint may also be quantifiable in nature (for example, amenable to a direct numeric measurement) but this is not a necessary condition for the practice of the present invention.
  • the method also involves the formation of a geometric representation (i.e. a geometric figure) of the dose combinations used in the titration.
  • the geometric figure is a simplex which may be represented by a geometric figure with p + 1 vertices. Each of the p + 1 vertices of the simplex corresponds to one of said p + 1 dose combinations.
  • a composite desirability function for each of said p + 1 dose combinations may be determined in the following manner: a particular dose combination is administered to the subject during a predetermined period of time and a measurement of each endpoint is obtained at the end of the indicated time period. The measurements obtained for a given response are assigned to a desirability function.
  • the desirability function may be continuous and differentiable, and must map the measurements to a [0,1] interval where 0 represents a least desirable response and 1 represents a most desirable response.
  • the individual desirability functions are then combined into a composite desirability function and each resulting composite desirability function is associated with the vertex of the simplex corresponding to that particular drug combination.
  • An evolutionary operational direct search algorithm is applied to the simplex.
  • the ENOP procedure is applied to determine the location in dose space that represents a suggested next dose combination by identifying the vertex corresponding to the least desirable composite desirability function and moving from that vertex through dose space to a new location. The new location is the vertex of a new simplex and should be associated with a more desirable outcome.
  • the new vertex is then administered to the subject, the subject's responses are determined and assigned to desirability functions as described, and a new composite desirability function is computed for the new combination.
  • the EVOP procedure is again applied as described above and a next suggested dose combination is determined. This procedure is performed repeatedly until a predetermined criteria is fulfilled. For example, the procedure may be carried out: until a given number of new dose combinations have been generated, administered and the results analyzed; or for a given length of time; or until a predetermined composite desirability function value is attained.
  • the evolutionary operational direct search algorithm that is applied is the ⁇ elder-Mead algorithm.
  • other direct search algorithms may also be utilized, for example, direct search algorithms based on the construction of complexes rather than simplexes. (See, for example, Box, 1965 and Box, 1969).
  • the advantage of utilizing direct search algorithms is that the use of derivatives is not required, so that no assumptions need be made regarding the underlying relationships between the modalities which are administered and the endpoints being observed.
  • the titration methods of the present invention may be utilized for combined modality therapies that may be active in treating any of a number of diseases and/or conditions, examples of which include but are not limited to cancer, AIDS, arthritis, diabetes, hypertension, and the like. Further, there are diseases and conditions which are cunently treated with a single modality which may in the future be treated with more than one modality. All such conditions are intended to be encompassed in the practice of the present invention.
  • the desirability function which is utilized is continuous and differentiable. However, as a result of the use of direct search algorithms, this need not be the case. However, the desirability function must map the measurements obtained to a [0,1] interval. In a preferred embodiment of the invention, the desirability function is obtained from the logistic cumulative distribution function such as that described by Gibb (1998). The composite desirability function may involve the use of weights for the individual desirability functions.
  • the invention further provides a computerized system including a computer program for carrying out the methods of the present invention. The system includes means for entering into a computer a number p of modalties to be used in the regimen, means for generating a simplex as described, means for determining the composite desirability functions, and means for outputting a new, next dose combination.
  • FIG. 2A and B Examples of desirability functions
  • B minimizing desirability function for increase in body weight, where Y 2*
  • Figure 4A-D Evaluating confidence ellipsoids: A, confidence ellipsoid contains the origin; B, , confidence ellipsoid contains both axes but not the origin; C, confidence ellipsoid contains only one axis; D, , confidence ellipsoid does not contain either axis or the origin.
  • Figure 6 A and B A, Simplex movement for one subject in a two-dimensional dose space. The subject is evaluated at each of three initial dose combinations (1,2,3) [2 pills HCTZ/4 pills DLTZ; 8 pills/4 pills; and 2 pills/12 pills]. The simplex reflects away from the combination producing the least desirable response (in this example, point 1).
  • the final optimized dose combination (F) after 20 steps is 3 pills HCTZ and 19 pills DLTZ, corresponding to a simulated decrease in diastolic blood pressure of 18.4mmHg
  • Figure 7 Pyramid plot of final dose locations for a simulated group of 175 subjects who have completed the 16 steps of titration, using a correlation of 0.7.
  • the desirability function for DBP shown in Figure 5 was used to target a reduction in diastolic blood pressure (DBP).
  • the mean decrease in DBP was 17.7mmHg.
  • the mean final dose combination was 4.6 pills HCTZ and 16.2 pills DLTZ.
  • Figure 8 A and B: A, Asymptotic confidence ellipsoid based on the Wilcoxon signed rank statistic. A group of 175 subjects was simulated using the desirability function for DBP in Figure 5. B, Asymptotic confidence ellipsoid based on the mean. A group of 175 subjects was simulated using the desirability function for DBP in Figure 5.
  • the present invention provides systematic and efficient methodology for titrating combination drug and/or other treatment modality therapies within individual patients and for evaluating the efficacy of such multi-modality therapies.
  • the methods are practical and flexible, and take into account potential interactions between modalities.
  • the methodology uses an evolutionary operation (EVOP) direct-search procedure to titrate doses within individual patients.
  • EVOP approach is used to climb through the dose space to a location of improved patient response.
  • Statistical methodology is also utilized for determining whether there has been an improvement in response to a treatment regimen, and whether a therapeutic synergism exists among the modalities comprising a multi-modality regimen.
  • the treatment modalities which are titrated are drugs.
  • Such modalities include but are not limited to radiation therapy; quantifiable amounts of modalities such as physical therapy, psychotherapy, exercise regimens, acupuncture, skeletal or other body manipulations (e.g. chiropractic manipulation, massage therapy, the wearing of braces, the immobilization of limbs, and the like); nutritional therapy (e.g. administration of vitamins or nutriceuticals); gene therapy techniques, and the like.
  • a "dose” is herein defined as the quantity of a modality that is administered, and may be a dose in the classical sense (e.g.
  • a dose of a substance such as a medication measured as a number of pills, or a quantity of liquid, etc.
  • a dose may be a defined as an amount of a modality that is quantified in terms of time (e.g. hours of psychotherapy per week, minutes exercising at a particular heart rate, or meditating, and the like), or repetitions of a treatment modality (e.g. one session of massage therapy, chiropractic manipulation, or acupuncture, and the like).
  • the purpose of the titrations methods described herein may be to determine the optimal treatment regimen for a patient in order to alleviate the symptoms of a disease.
  • a patient may exhibit symptoms of more than one disease, or of symptoms which are not readily assignable to a particular disease, or of side effects that result from the modalities being administered.
  • some undesirable conditions may not necessarily be categorized as "disease” but would still be amenable to analysis using the methods of the present invention, e.g. a multi-modality treatment regimen for weight loss, or to optimize multi-modality interactions in healthy subjects in clinical trials.
  • the methods may also be utilized for purposes such as to determine a maximum tolerated dose, for example, in a cancer treatment regimen. The methods may also be utilized in both human and non-human patients. EVOP Direct Search Methods.
  • an evolutionary operational (EVOP) method is utilized to carry out the titration.
  • Traditional applications of EVOP have involved the use of factorial designs (Fisher,1935; Yates, 1935; D.R. Cox, 1958; and Snedecor and Cochran, 1980) to introduce variations in the operating conditions.
  • EVOP makes improvements to the resulting product and has proven useful in optimizing multidimensional relationships without requiring specification of either a model or distribution (Box, 1957; Box and Draper, 1969; Spendley, Hext, and Himsworth, 1962).
  • response surface methods are a static research technique
  • evolutionary operation can be applied as a continuous and automatic production-line method.
  • EVOP EVOP
  • the yield of the product would be continuously monitored, as would the operating conditions, which might consist of the temperature, pressure, and amount of starting material. Minor variants in the operating conditions are then introduced in a factorial pattern. When a significant change in the yield is found in either a positive or negative direction, the operating conditions which produced the change in yield can be identified and subsequently adjusted in the direction of optimizing the yield. The monitoring process would then resume and could be continued indefinitely.
  • EVOP has been effectively adapted to the clinical setting where a combination of modalities is being used for treatment or being evaluated for efficacy. While the multidimensional dose-response relationship is unknown, it can be observed at specific treatment combinations, and a predetermined algorithm can be followed to adjust the therapeutic doses toward improving patient outcome. For example, a patient may make periodic visits to a physician who monitors the patient for improvements in outcome in response to the multiple modalities being prescribed. The physician or researcher can use an EVOP direct search procedure to adjust the doses comprising the treatment combination in response to the patient's continuously evolving condition. The titration is carried out within each patient, allowing every patient to benefit from the therapy if there is any benefit obtainable.
  • the practice of the present invention involves carrying out a within-patient titration.
  • the within-patient titration uses the Nelder-Mead algorithm, which is more flexible than the Spendley, Hext, and Himsworth method, permitting acceleration and adaptation to the response surface.
  • Nelder-Mead algorithm which is more flexible than the Spendley, Hext, and Himsworth method, permitting acceleration and adaptation to the response surface.
  • other flexible direct search EVOP algorithms may also be utilized in the practice of the present invention.
  • a continuous desirability function may be utilized (Gibb, 1998), which incorporates both the main response of interest and additional responses or constraints, as the overall measure of response. In this way, the main response or responses may be improved while simultaneously satisfying multiple additional constraints.
  • the desirability function approach was developed by Harrington (1965) and later modified by Derringer and Suich (1980). Gibb (1998) extended the methodology to desirability functions which are continuous and differentiable. Desirability functions have been successfully used in the industrial setting.
  • Each response of interest is assigned to a continuous desirability function (which may be continuous and differentiable), di, with values ranging from 0 to 1, where a value of 0 designates the response as not at all desirable, while a value of 1 is assigned to the most desirable response.
  • the index i represents the ith desirability function or the ith response of interest.
  • the basic shape of the function is determined by whether one is trying to maximize or minimize the response, or aim for a range of target values. The exact shape of each desirability function is determined in collaboration with physicians or other experts knowledgeable about the disease under study and the therapeutic effects of the treatments being administered.
  • a logistic cumulative distribution function (Gibb, 1998) was used for the desirability, but any function which maps the response to the [0,1] interval could be used.
  • the logistic function the form of the 'bigger-is-better' or maximizing desirability function (Gibb, 1998) is
  • This allows the researcher to incorporate asymmetry into the desirability function.
  • the parameters a i , b and Y J allow the researcher flexibility in defining the desirability function and the degree of conservativeness to incorporate.
  • unweighted desirability functions are utilized.
  • weighted desirability functions may also be employed. This may occur, for example, if a skilled practitioner determines that a particular endpoint is of more import than others. The desirability function representing this endpoint can then be suitably weighted.
  • a physician is treating a type 2 diabetes patient with a combination of a sulfonylurea and metformin.
  • a physician may monitor, including fasting plasma glucose (FPG), glycosylated hemoglobin levels (HbAlc), the patient's lipid profile, weight, and blood pressure, and the number of adverse gastrointestinal and hypoglycemic events the patient experiences.
  • FPG fasting plasma glucose
  • HbAlc glycosylated hemoglobin levels
  • the patient's lipid profile the weight, and blood pressure
  • the number of adverse gastrointestinal and hypoglycemic events the patient experiences.
  • a specific target, maximizing, or minimizing desirability function can be assigned and incorporated into the composite desirability function. Note that this method tends to weight small desirability values heavily so that if any of the individual desirabilities are small, the overall desirability remains small.
  • Table 1 describes three cases which could occur.
  • Case 1 the patient has reasonable fasting plasma glucose values and has experienced minimal weight gain.
  • the glucose value of 140 corresponds to a desirability (dl) of 0.95
  • the weight gain of 10 corresponds to a desirability (d2) of 1.
  • This high desirability suggests that the patient is doing well with the current treatment.
  • the patient has a less desirable glucose value of 155, which corresponds to a desirability of 0.19, and a weight gain of 30 lbs, which corresponds to a desirability of 0.5.
  • This patient has an overall desirability of 0.31, which indicates that changes to the patient's current therapeutic regimen may be needed to improve the treatment of this patient.
  • the last example is of a patient with a high serum glucose value which is further outside the desirable limits, corresponding to a desirability of 0.05, but one who has experienced no weight gain and so has a weight gain desirability of 1. Although this patient is doing well in terms of preventing weight gain, the glucose level is objectionably high, so the overall desirability decreases to 0.22.
  • desirability functions can be useful for both the multiple drug case and the single agent case where multiple endpoints are being monitored.
  • desirability functions can provide the physician or researcher with a more objective way of evaluating the overall effect of a therapy and can provide information about individual clinical endpoints and side effects.
  • EVOP direct-search methods we can titrate combination therapies within individual subjects and make inferences about the efficacy of the combination.
  • the Nelder-Mead simplex algorithm was used to carry out the within-patient titration.
  • the first step of the procedure is to establish an initial simplex, a geometric figure with a fixed number of vertices. In the p-dimensional case, where p is the number of drugs comprising the combination under evaluation, the number of vertices required for the simplex is p+1.
  • the simplex adapts its form, moving away from the vertex with the lowest response toward the direction of maximum response.
  • the simplex is a triangle.
  • Each vertex A, B, and C of the triangle represents a different dose level of the two-drug combination.
  • the subject's response is measured at each of these three dose combinations, and the composite desirability resulting from the administration of each combination is compared, with the simplex reflecting away from the least desirable response, through the centroid of the face created by the remaining vertices to a new point.
  • the simplex can also extend, contract, or perform a shrinkage contraction, depending on the contour of the response surface (see Table 2).
  • the Nelder-Mead algorithm is run on a continuous scale, and therefore the new dose combination determined by the algorithm is not given in units of whole pills or whole dose units.
  • the dose combinations are adjusted to whole units (e.g. whole pills).
  • the new dose combination to be administered is determined by either rounding to the nearest whole dose unit, or more conservatively, by rounding down to the dose unit.
  • the initial simplex step size which specifies how far apart the initial dose combinations are, and the reflection and expansion coefficients used by the Nelder-Mead procedure, which determine how far the simplex can move or expand in one step, are decided in collaboration with the physician expert, and can be modified to be more or less conservative depending on factors such as the therapeutic index of the drug involved.
  • the step size of the initial simplex will depend on the potency and toxicity of the drugs under study, with smaller initial step sizes prudent for compounds of higher potency and/or toxicity. In the case where the drugs are already being used in combination in practice, a reasonable starting combination would be the number of pills or dose units with which the practicing physician generally initiates therapy. With a new and yet untested combination of drugs, where one cannot draw from previous experience, a more conservative approach is advisable.
  • Each subject begins the process by being evaluated at each of the p+1 combinations of p drugs in the regimen.
  • the subject receives the initial combination and the response is recorded.
  • the subject receives the second combination, which is determined by the initial step size, and the response is measured after a time interval sufficient to preclude carryover effects. This continues for each of the p+1 drug combinations.
  • EVOP may not be practical due to the time required in setting up the initial simplex.
  • the new simplex is formed, determining the next dose combination to be administered. This process repeats until the subject has passed through a fixed number of steps or until other specific stopping criteria are reached and further titration is deemed unnecessary.
  • the simplex movement can be continuously monitored by the physician, and the reflection, expansion, and contraction coefficients can be modified if the simplex expands to a dose with which physician is uncomfortable. Otherwise, a dose constraint can be put in as a boundary to prevent the simplex from moving above a certain dose in one or more dimensions.
  • the last simplex is evaluated and the combination producing the most desirable response is determined to be the 'best' treatment combination. Possible stopping criteria include running the process until convergence to a 'best' treatment or until an 'acceptable' response is reached. Since disease processes are dynamic and often chronic, the physician may continue to periodically monitor subjects after the initial optimized dose level is reached, and may restart the titration process if changes in the patient's status are observed. Inference about the Patient Population
  • the methodology of the present invention may also be applied to the analysis of multi-modality therapies in a large test population.
  • the initial and final dose locations and corresponding initial and final responses are used to determine whether there has been an improvement in response and whether a therapeutic synergism exists among the drugs comprising the combination.
  • the set of final treatment dose combinations observed from the n subjects enrolled in a study can be considered a sample from a multivariate distribution.
  • the first goal can be accomplished by identifying it as a one-sample location problem on paired responses which can easily be addressed using existing tests, which are described below.
  • the second goal can be accomplished by construction of a p- dimensional confidence ellipsoid about the central location of the 'cloud' of final dose combinations in the p-dimensional dose space. Both a parametric approach and nonparametric approach are described below. Based on the estimated confidence ellipsoid, we can evaluate whether a therapeutic synergism (Mantel, 1974) exists between all treatments comprising the combination, and we can also estimate a region of improved therapy (Carter, 1982).
  • the multivariate sampling model involves n independent, identically distributed p-component random vectors x l3 ..., x n , each with the p-variate distribution function , where F (t, - ⁇ precede ..., t p - ⁇ p ), where F is absolutely continuous with continuous marginal distribution functions F ⁇ t j - ⁇ j ), ..., F p (t p - ⁇ p ).
  • the vector of location parameters ⁇ [ ⁇ , ⁇ 2 ... ⁇ p ] contains the marginal medians, and if each Fj is symmetric, ⁇ is also the vector of marginal means.
  • a parametric inferential approach would be to assume a form for F and to construct the confidence ellipsoid for ⁇ .
  • Finding ⁇ - is equivalent to finding ⁇ j such that the signed rank statistic
  • R y ⁇ j is the rank of
  • v w is a pxp matrix
  • the ellipsoids can be evaluated using the approach described by Carter, et al. (1982).
  • the confidence ellipsoid is evaluated along a grid of points on each single axis.
  • the evolutionary operation direct search titration methodology is suitably applied to the treatment of chronic conditions or diseases with long time courses. This allows sufficient time for the establishment of the initial simplex and for titration to a maintenance therapy. Since disease processes are dynamic, EVOP can be continued indefinitely to track the patient's progress. After an initial maintenance dose is identified, the physician can continue to periodically monitor the patient, and the titration process can be restarted when changes to the patient's status are observed.
  • a condition which would favor the use of the methods of the present invention include but are not limited to those having an easily and rapidly measured response, a lengthy time; and a condition where dose escalation within a patient is reasonable.
  • diseases or syndromes which may benefit from this treatment approach include but are not limited to hypertension, diabetes, rheumatoid arthritis, asthma, AIDS, and some cancers.
  • the responses being monitored are easily measurable and reproducible. For example, they might consist of laboratory tests or measurements that are already performed periodically as part of the regular standard of care so as to minimize additional discomfort or inconvenience to the patient. Accuracy and reproducibility of measurement are also important to ensure that the simplex is moving purposefully according to the clinical endpoint (or signal) rather than moving haphazardly in response to a large variability in the measurement (or noise).
  • Suitable clinical endpoints include but are not limited to blood pressure, fasting plasma glucose, forced expiratory volume, the reported number of side effects a patient is experiencing each week, and the like. Those of skill in the art will recognize that many suitable endpoints exist which may be measured in the practice of the present invention, and all such endpoints are intended to be encompassed in the scope of the instant invention.
  • EVOP may not be appropriate. A sufficient time interval between measurements must be allowed to preclude any carryover effects from the previous treatment. Otherwise, the time required to set up the initial simplex may become impractical, and the subsequent simplex movement may be too slow to be of benefit in treating the patient.
  • EVOP titration may also be problematic when the number of therapies in a combination is extremely large. In this case, establishing the initial simplex may become cumbersome due to time constraints, and problems with patient compliance are more likely. EVOP may also be of limited application when the course of a disease is too brief to provide substantial information. Theoretically, there is no limit to the number of different modalities which can be titrated by the methods of the present invention. Limitations on the number will likely arise rather as a result of practical clinical considerations and will be determined by a skilled practitioner on a case by case basis.
  • multi-modality therapies are titrated by the methods of the present invention.
  • the present invention also contemplates a computer program for use in carrying out the practice of the present invention.
  • Such a computer program could be written and adapted for use in any of many known devices which are employed by suitable practitioners of the invention, for example, physicians. Examples of such devices include but are not limited to PCs, laptop computers, palm pilots, pocket PCs, personal digital devices, and the like. Further, many such devices are also currently under development. Details of exemplary embodiments of the methodology are given in the examples 5. below, but should not in any way be considered limiting.
  • EXAMPLE 1 A comparison of multi-drug titration with glyburide and metformin 0 to treatment with Glucovance
  • Type 2 diabetes accounts for 90-95% of all patients diagnosed with diabetes. An additional 15 million people have impaired glucose tolerance, 5 putting them at a high risk for developing type 2 diabetes. Diabetes is currently the 4th leading cause of death by disease in the U.S., the leading cause of blindness in adults 20- 74 years old, and the leading cause of end-stage renal disease. Sixty to seventy percent of diabetics have some form of mild to severe neuropathy, and diabetes is associated with a 2 to 4 fold increase in risk for both heart disease and stroke. The considerable morbidity 0 and mortality associated with this disease is estimated to cost $98 billion each year in direct medical costs and indirect costs to industry (Centers for Disease Control, 1998).
  • the sulfonylureas are a group of agents that increase insulin secretion by stimulating pancreatic beta cells (Lebovitz, 1992). They are effective in lowering glycemia in about 50 percent of patients who are unable to control their glycemia with diet and exercise alone (Ertel, 1997). The effectiveness declines as the failure of the beta cells progresses, resulting in a secondary failure rate of 3 to 10 percent per year (Ertel, 1997). The average decrease in HbAlc is 1 to 2 percent (Pharmacological intervention in: Medical management of type 2 diabetes. 1998). There is a small risk of hypoglycemia with use of the sulfonylureas and a modest associated weight gain. The effects on the lipid profile are minimal, with minor decreases in triglyceride levels. Treatment should be initiated at the lowest recommended dose and increased every four to seven days until the desired effect or maximum dose is reached.
  • Glyburide is a second generation sulfonylurea, administered twice a day in doses ranging from 1.25mg to 5mg, with a maximum daily dose of 20mg.
  • Metformin is the only biguanide currently approved for use in the U.S. by the FDA. It acts on the liver to decrease hepatic glucose production and also promotes insulin sensitivity in both the liver and peripheral tissues (UKPDS Group, 1998). Treatment with metformin has been shown to decrease fasting and postprandial glycemia by 60-70mg/dL (Cusi and DeFranso, 1998), with an average decrease in HbAlc of 1.5 to 2 percent (Cusi and DeFranso, 1998). Metformin shows initial effectiveness in approximately 75 to 80 percent of type 2 diabetes patients (Lebovitz, 1992) and does not cause hypoglycemia.
  • metformin cannot be used when the creatinine clearance is greater than 1.4mg/dL in women, and greater than 1.5mg/dL in men.
  • Metformin is also contramdicated in cardiac failure and pulmonary disease patients or anybody with a disease condition which interferes with lactate removal.
  • Treatment with metformin is usually initiated at a dose of 500 mg, which may be increased in 500 mg increments every one to two weeks, with the maximum effect seen at a dose of 2000mg per day.
  • Glucovance is a combination of the sulfonylurea, glyburide, and the biguanide, metformin.
  • Glucovance is available in fixed combination doses of 1.25mg glyburide/250mg metformin, 2.5mg/500mg, and 5mg/500mg, with a maximum daily dose of
  • a logistic regression analysis was performed using data from the study of 806 drug-naive type 2 diabetes patients printed in the package insert ((Bristol-Myers Squibb, 2000) to determine whether there was an interaction effect between the 2.5mg of glyburide and 500mg of metformin.
  • the likelihood ratio ⁇ 2 statistic associated with the test of additivity i.e. no interaction
  • was 5.975 with a p-value of 0.0145, indicating the presence of a significant interaction between the two drugs.
  • the coefficient of the interaction term was negative (-0.887), indicating that the interaction was antagonistic between the two drugs at the given doses. It should be noted that these were the starting doses given to the patients for a period of 4 weeks, after which the dose could be increased up to a maximum of four tablets daily.
  • the methodology of the present invention may be applied as follows: A 20 week pilot study is conducted. Ten newly diagnosed type 2 diabetes patients, men and women, are enrolled using the following eligibility criteria: Inclusion Criteria
  • Subjects who have previously been treated with other diabetes therapies Subjects with hepatic or renal impairment (creatinine > 1.4mg/dL in women, > 1.5mg/dL in men) Subjects with concomitant CHF or pulmonary disease
  • Each subject begins the study by rotating through each of three starting drug combinations.
  • baseline values of fasting plasma glucose (FPG), 2-hour postprandial plasma glucose (PPG), fingerstick HbAlc, and HbAlc are recorded.
  • Each dose combination is administered for a period of 2 weeks.
  • the patient is instructed to keep a daily journal of his or her fasting glucose measurements and 2-hour postprandial glucose measurements.
  • the fasting glucose measurements and 2-hour postprandial glucose measurements recorded by the patient over the previous one week, are reported to and averaged by the physician, along with a fingerstick HbAlc measurement.
  • the number of reported hypoglycemic episodes and the number of reported negative GI effects over the previous one week are also recorded.
  • the averaged fasting and 2-hour postprandial glucose measurements, the fingerstick HbAlc, the number of hypoglycemic episodes, and the number of GI complaints are reported to the physician over the telephone at the end of the second week.
  • the measurements are combined into a single desirability measure (Appendix 4.A) and the Nelder-Mead algorithm (Appendix 4.B) is used to determine the next dose combination to be administered to the patient. If the physician is uncomfortable with the algorithm determined dose, the physician adjusts the dose, and the actual dose prescribed by the physician is recorded, together with the algorithm determined dose.
  • the following treatment dose is again determined by the Nelder- Mead algorithm, using the adjusted dose information.
  • the study continues for a period of 20 weeks.
  • the dose combination for each patient is titrated until an average fasting glucose of ⁇ 150 or an average 2 -hour postprandial glucose of ⁇ 180 is achieved or until the end of the study period.
  • bi-monthly reports with data collection and monitoring will continue for the duration of the study period.
  • the patient keeps a diary of daily fasting glucose and 2-hour postprandial glucose measurements. The measurements recorded by the patient over the previous one week will be averaged and recorded at each visit. Fingerstick HbAlc is also measured at each visit. Serum HbAlc is measured at the initial visit and final visit.
  • a 4 by 5 factorial grid of treatment doses was used, with 4 twice-a-day doses of hydrochlorothiazide ranging from 0 to 25 mg, and 5 twice-a-day doses of diltiazem hydrochloride ranging from 0 to 180 mg.
  • Mild-to-moderate essential hypertension was defined as supine diastolic blood pressure in the range of 95 to 110 mm Hg.
  • the goal of treatment was to achieve a supine diastolic blood pressure of less than 90 mm Hg, with no limiting adverse experience.
  • 261 patients completed the six- week treatment protocol, with 13 to 17 patients randomized to each treatment group.
  • DBP diastolic blood pressure
  • a desirability function was defined for each of the three responses, DBP, CHO, and GLU.
  • the three functions, dl-d3 (Figs 5A-5C), were combined into an overall unweighted composite desirability function, D (d ! *d 2 *d 3 ) 1/3 .
  • the Nelder-Mead simplex procedure was used to carry out the within-patient titration using the composite desirability.
  • the Nelder-Mead algorithm is run on a continuous scale to maintain the flexibility allowed by simplexes of differing shapes. Therefore, at each step, to determine the next dose combination, the doses output by the algorithm are rounded to the nearest whole dose unit. As discussed, it is also possible to round down to the nearest integer value.
  • the starting dose for the initial simplex was chosen to be the same as the smallest combination dose used in the original study: 6.25mg (2 pills) of HCTZ and 60mg (4 pills) of DLTZ.
  • the initial step size was chosen to be this initial dose combination increased by 6 pills in the HCTZ axis and by 8 pills in the DLTZ axis.
  • a mixed effects model with a first order autoregressive co variance structure was used.
  • the covariance between two observations w time intervals apart on the same subject is ⁇ 2 p w , where p is the correlation between adjacent observations within the same subject, and w is the number of time intervals between the observations.
  • the root MSE for DBP, ⁇ DBP was 6.2 mm Hg, and 0.35 mmol/L was used for both CHO, ⁇ CH0 , and GLU, ⁇ GLU .
  • FIG. 6A is an example showing the simplex movement for a single subject. The titration was continued for 20 steps. At the last step, the final simplex was evaluated and the dose combination associated with the most desirable response was taken as the final treatment combination. This subject arrived at a final dose combination of 3 pills HCTZ and 19 pills DLTZ, with a simulated decrease in DBP of 18.4mmHg.
  • Figure 6B demonstrates the simplex movement for the same subject starting with a smaller initial step size increase of 4 pills in the HCTZ axis and 6 pills in the DLTZ axis, with titration continuing for 20 steps.
  • the final dose combination reached was 3 pills of HCTZ and 18 pills of DLTZ, similar to that obtained with the larger step size.
  • the corresponding decrease in DBP was 15.7mmHg.
  • Figure 7 demonstrates the final dose locations for a simulated group of 175 subjects who have completed the titration process
  • Figure 8 A shows the asymptotic confidence ellipsoid about the central location estimate for the Wilcoxon Signed Rank statistic
  • Figure 8B shows the confidence ellipsoid about the mean.
  • Table 4 shows the percentage of confidence ellipsoids which included the origin, included the hydrochlorothiazide axis only, included the diltiazem axis only, or included both axes, also using the desirability for DBP alone.
  • the final central dose locations for diltiazem and hydrochlorothiazide are also given in the far right columns, using both the mean and the Wilcoxon Signed Rank statistics as measures of central location. Using Mardia's test, in many instances the multivariate distribution of the final dose locations for each simulation showed some departure from normality, suggesting the nonparametric approach to be most appropriate.
  • Table 3 Proportion of improved responses using the Fisher sign test or Wilcoxon signed-rank test. Simulations were done using the desirability function for diastolic blood pressure alone (di). The mean decrease in DBP is shown in the far right column.
  • Table 4 Evaluation of the confidence ellipsoids using a parametric and nonparametric approach. Simulations were done using the desirability function for diastolic blood pressure alone (di). The columns show the percentage of confidence ellipsoids containing the origin, containing the HCTZ axis only, containing the DLTZ axis only, or containing both axes. The rightmost columns show the final dose locations for HCTZ and DLTZ using either the mean or Wilcoxon signed-rank statistic as the measure of central location.
  • Table 5 Proportion of improved responses using the Fisher sign test or Wilcoxon signed-rank test. Simulations were done using the composite desirability function (D). The correlation between successive DBP measurements was varied from 0.1 to 0.8, while the correlations for both CHO and GLU were fixed at 0.7. The rightmost columns show the mean decrease in diastolic blood pressure, the mean change in cholesterol and the mean change in serum glucose.
  • Table 6 Evaluation of the confidence ellipsoids using a parametric and nonparametric approach. Simulations were done using the composite desirability function (D). The correlation between successive DBP measurements was varied from 0.1 to 0.8, while the correlations for both CHO and GLU were fixed at 0.7. The columns show the percentage of confidence ellipsoids (SE) containing the origin, containing the HCTZ axis only, containing the DLTZ axis only, or containing both axes. The rightmost columns show the final dose locations for HCTZ and DLTZ using either the mean or Wilcoxon signed-rank statistic as the measure of central location.
  • SE percentage of confidence ellipsoids
  • Tables 7 and 8 show the results of changing the initial step size from an increase of 6 pills in the HCTZ axis and 8 pills in the DLTZ axis, to an increase of only 5 pills/7 pills, or 4 pills/6 pills over the initial dose combination.
  • Tables 7 and 8 show the results of changing the initial step size from an increase of 6 pills in the HCTZ axis and 8 pills in the DLTZ axis, to an increase of only 5 pills/7 pills, or 4 pills/6 pills over the initial dose combination.
  • Tables 7 A comparison of initial step sizes.
  • SE confidence ellipsoids
  • Tables 9 and 10 display the results of changes to the sample size. Simulations were run with sample sizes of 25, 50, 175, and 300 subjects, using the desirability function for DBP alone. The between-observations correlation was fixed at 0.7, and the titration was continued for 16 steps. In general, changes to the sample size did not appear to significantly affect the outcomes. In Table 9, the decrease in the DBP remains similar across cases and there is a significant improvement in the response for all cases. In Table 10, the final dose combinations also remain similar across the cases.
  • Table 9 Sample size comparison. Simulations were done using the desirability function for diastolic blood pressure alone (dl), with 16 steps, p-0.7. The table shows the proportion of improved responses using the Fisher sign test or the Wilcoxon signed-rank test. The effect of increasing the sample size is shown, with the mean decrease in diastolic blood pressure given in the rightmost column.
  • SE confidence ellipsoids
  • Tables 11 and 12 show that sharpening the peak desirability as with da, increasing the width of the desirability function as with db, or decreasing the width and sharpening the peak simultaneously as with dc, did not result in any appreciable change in the outcome with respect to either response or dose location. There was little or no change in the decrease in DBP or final dose combinations, indicating that the process is robust, or relatively insensitive, to small changes in the definition of the desirability function. So while the desirability function has to be defined carefully, there is some room for variation when deciding on the parameters.
  • Table 11 A comparison of desirability functions. The table shows the proportion of improved responses using the Fisher sign test or the Wilcoxon signed-rank test. The parameters for the modified desirability functions are shown, with the mean decrease in diastolic blood pressure given in the rightmost column.
  • Table 12 A comparison of desirability functions.
  • the columns show the percentage of confidence ellipsoids (SE) containing the origin, containing the HCTZ axis only, containing the DLTZ axis only, or containing both axes.
  • SE confidence ellipsoids
  • the parameters for the modified desirability functions are shown, with the rightmost columns giving the final dose locations for HCTZ and DLTZ using either the mean or Wilcoxon signed-rank statistic as the measure of central location.
  • Lebovitz HE Stepwise and combination drug therapy for the treatment of NIDDM. Diabetes Care 1994;17:1-3.
  • Lebovitz HE Rationale in the management of non-insulin-dependent diabetes. In: Leslie RD, Robbins DC, eds. Diabetes: clinical science in practice. New York: Cambridge University Press, 1995:450-64.

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Abstract

L'invention concerne le dosage de plusieurs médicaments associés ou des protocoles de traitement chez des sujets individuels. Ce dosage est réalisé au moyen d'une procédure d'analyse directe par processus évolutif (EVOP), telle que le simplex de Nelder-Mead. Des fonctions de convenance sont incorporées pour définir la réponse d'intérêt principale et les réponses ou contraintes additionnelles. On décrit une méthodologie statistique qui permet de déterminer si le traitement par médicaments associés dosé a donné lieu à une amélioration de la réaction du patient, et d'évaluer s'il existe une synergie thérapeutique. Des inférences peuvent être établies sur l'efficacité des médicaments associés, ou des médicaments pris séparément, ou des protocoles de traitement mettant en oeuvre ces médicaments associés. Cette approche offre à chaque patient la possibilité de bénéficier de l'association de médicaments faisant l'objet de l'étude; elle permet également d'envisager simultanément plusieurs résultats.
PCT/US2002/004086 2001-02-13 2002-02-13 Dosage et evaluation de plusieurs medicaments associes WO2002065120A1 (fr)

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EP1628589A2 (fr) * 2003-06-03 2006-03-01 Dimensional Dosing Systems, Inc. Procede et appareil ameliores de dosage de traitement a base d'agent therapeutique unique ou d'agents therapeutiques multiples

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US5647663A (en) * 1996-01-05 1997-07-15 Wisconsin Alumni Research Foundation Radiation treatment planning method and apparatus
US6222093B1 (en) * 1998-12-28 2001-04-24 Rosetta Inpharmatics, Inc. Methods for determining therapeutic index from gene expression profiles

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1628589A2 (fr) * 2003-06-03 2006-03-01 Dimensional Dosing Systems, Inc. Procede et appareil ameliores de dosage de traitement a base d'agent therapeutique unique ou d'agents therapeutiques multiples
EP1628589A4 (fr) * 2003-06-03 2007-04-25 Dimensional Dosing Systems Inc Procede et appareil ameliores de dosage de traitement a base d'agent therapeutique unique ou d'agents therapeutiques multiples

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