Journal of the American Statistical Association, 1983
An exact test of significance of the hypothesis that the row and column effects are independent i... more An exact test of significance of the hypothesis that the row and column effects are independent in an r x c contingency table can be executed in principle by generalizing Fisher's exact treatment of the 2 x 2 contingency table. Each table in a conditional reference set of r x c tables with fixed marginal sums is assigned a generalized hypergeometric probability. The significance level is then computed by summing the probabilities of all tables that are no larger (on the probability scale) than the observed table. However, the computational effort required to generate all r x c contingency tables with fixed marginal sums severely limits the use of Fisher's exact test. A novel technique that considerably extends the bounds of computational feasibility of the exact test is proposed here. The problem is transformed into one of identifying all paths through a directed acyclic network that equal or exceed a fixed length. Some interesting new optimization theorems are developed in the process. The numerical results reveal that for sparse contingency tables Fisher's exact test and Pearson's X 2 test frequently lead to contradictory inferences concerning row and column independence.
Optimization of Pharmaceutical R&D Programs and Portfolios, 2014
Selecting the right dose is critical for the success of any drug development program, and for max... more Selecting the right dose is critical for the success of any drug development program, and for maximizing the value of a product. A well selected dose will have a better chance to demonstrate a desirable risk/benefit profile and thus increase the chance of regulatory success and reimbursement by payors. It will also result in improved patient care and greater benefit to society. Multiple papers have been published within industry’s adaptive design working groups, and these are the key findings.
Abstract: We present an efficient network algorithm for generating exact permutational distributi... more Abstract: We present an efficient network algorithm for generating exact permutational distributions for linear rank tests defined on stratified 2 xc contingency tables. The algorithm can evaluate exact one and two sided p-values, and compute exact confidence intervals ...
Two important and popular time-sharing systems were analysed for the expected waits of requests. ... more Two important and popular time-sharing systems were analysed for the expected waits of requests. These were the Round-Robin and the Dynamic-Priority Multiple-Level systems. The Round-Robin is very complex in all its generality, however with the aid of a realistic simplifying ...
In this paper, we propose an adaptive randomization design for Phase 2 dose-finding trials to opt... more In this paper, we propose an adaptive randomization design for Phase 2 dose-finding trials to optimize Net Present Value (NPV) for an experimental drug. We replace the traditional fixed sample size design (Patel, et al., 2012) by this new design to see if NPV from the original paper can be improved. Comparison of the proposed design to the previous design is made via simulations using a hypothetical example based on a Diabetic Neuropathic Pain Study.
Traditionally, sample size considerations for phase 2 trials are based on the desired properties ... more Traditionally, sample size considerations for phase 2 trials are based on the desired properties of the design and response information from the trials. In this paper, we propose to design phase 2 trials based on program-level optimization. We present a framework to evaluate the impact that several phase 2 design features have on the probability of phase 3 success and the expected net present value of the product. These factors include the phase 2 sample size, decision rules to select a dose for phase 3 trials and the sample size for phase 3 trials. Using neuropathic pain as an example, we use simulations to illustrate the framework and show the benefit of including these factors in the overall decision process.
This article discusses the opportunities and challenges in the application of financially adaptiv... more This article discusses the opportunities and challenges in the application of financially adaptive clinical trials, which combine key aspects of adaptive trial design and financial analytics.
Optimization of Pharmaceutical R&D Programs and Portfolios, 2014
In this chapter we describe a mathematical approach to maximize the Expected Net Present Value (E... more In this chapter we describe a mathematical approach to maximize the Expected Net Present Value (ENPV) of a portfolio over a planning horizon by determining the optimal designs of Phase 3 (Ph3) trials for a given budget. The model is formulated as a Stochastic Integer Programming (SIP) model that incorporates uncertainty regarding availability of drugs in the pipeline. The SIP model provides an optimal policy that specifies the optimal design for each drug for every possible scenario of availability of future drugs for Ph3 trials. It optimizes the trade-off between committing budget to drugs available for Ph3 funding at any point in time and preserving budget for drugs in the development pipeline that will need funding in the future. Optimizing this trade-off is challenging because it is uncertain which drugs will need funding in the future as they may fail to progress to Ph3. This important trade-off is not handled in a consistent, quantitative way in portfolio budgeting models used in practice today. We have also developed a simulation model to assess the technical, regulatory, and commercial risk of the optimal budget allocation policy. We show how our models can be used for dynamic re-optimization of the portfolio when changes in the internal and external environment occur and as new information becomes available. This capability will enable rapid, frequent, and consistent realignment of the strategy to optimize future use of the budget available for reallocation.
Clinical supply is impacted by decisions and events at every stage of a clinical trial. Protocol ... more Clinical supply is impacted by decisions and events at every stage of a clinical trial. Protocol design, logistics planning, and operational dynamics pose challenges to the management of clinical supply in terms of complexity and uncertainty. In this chapter, we propose a simulation modelling approach to address these issues and support decision-makers in effectively managing clinical supply. The approach is comprehensively described in terms of underlying structure and process, and is illustrated with adaptive trials involving dropping of arms and a Bayesian responsive-adaptive design for dose finding.
Optimization of Pharmaceutical R&D Programs and Portfolios, 2014
In the pharmaceutical industry today, R & D often struggles to generate returns on capital ab... more In the pharmaceutical industry today, R & D often struggles to generate returns on capital above its cost of capital, leading to low to no creation of financial value for investors. Declining returns on R & D investment is a trend that has been unfolding for years given increasingly expensive, long, risky development programs required by regulators and payers for new therapeutics. Once they reach the market, new products face increasingly competitive pressures and decreasing willingness to pay by commercial and government-sponsored insurers. Given these difficulties, funding, particularly of early-stage drugs, has slowed and large pharmaceutical companies and financial sponsors of biotechnology companies have begun questioning the sustainability of the current R & D model. The industry is looking for alternative development and funding options to ensure much-needed new therapies can be brought to market efficiently.
Abstract Successfully advancing Adaptive Licensing requires coordinated planning and action acros... more Abstract Successfully advancing Adaptive Licensing requires coordinated planning and action across multiple stakeholders. The Janus Initiative combines a safe haven multi-stakeholder process with an integrated, best-of-breed quantitative simulation toolset to facilitate biomedical eco-system innovation discussions grounded in case-based realities. The process engages stakeholders from academia, patient advocacy, providers, payers, heath technology assessment, regulators and product sponsors. The quantitative toolset reflects the critical relationships among the parameters, decision domains and metrics relevant to these stakeholders from clinical development through regulatory approval, reimbursement authorization and clinical adoption over the entire product life span. The Janus Initiative, as part of the NEWDIGS program at MIT is moving forward with its first case studies and will continue to develop across multiple therapeutic areas and global regions.
A simple model is developed to evaluate the potential of emission control policies that depend up... more A simple model is developed to evaluate the potential of emission control policies that depend upon meteorological forecasts. An optimal control policy is derived for this model and related analytical results are obtained. A more realistic model leading to a linear programming formulation is discussed and illustrated by means of an example.
This paper studies the one-period, general network distribution problem with linear costs. The ap... more This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. This method is not directly suitable for the solution for large problems, but the exact solution for small problems can be obtained. For the numercial solutions of large problems, the problem has been formulated aa a linear program with column generation. This latter approach is quite robust in the sense that it is eesily extended to incorporate capacity constraints and the multiproduct case. THE PROBLEM The problem can be stated as (1) where (14 subject to j=1, 2 ,. . ., 12, *This work was performed under ONR Contract N00014-67-A-0204-0076 on Multilevel LoQstics Organization Models at the Massachusetts Institute of Technology.
This paper presents two adaptive methods for sample size re-estimation within a unified group seq... more This paper presents two adaptive methods for sample size re-estimation within a unified group sequential framework. The conceptual and practical distinction between these adaptive modifications and more traditional sample size changes due to revised estimates of nuisance parameters is highlighted. The motivation for the adaptive designs is discussed. Having established that adaptive sample size modifications can be made without inflating the type 1 error, the paper concludes with a novel decision theoretic approach for determining the magnitude of the sample size modification.
Journal of the American Statistical Association, 1983
An exact test of significance of the hypothesis that the row and column effects are independent i... more An exact test of significance of the hypothesis that the row and column effects are independent in an r x c contingency table can be executed in principle by generalizing Fisher's exact treatment of the 2 x 2 contingency table. Each table in a conditional reference set of r x c tables with fixed marginal sums is assigned a generalized hypergeometric probability. The significance level is then computed by summing the probabilities of all tables that are no larger (on the probability scale) than the observed table. However, the computational effort required to generate all r x c contingency tables with fixed marginal sums severely limits the use of Fisher's exact test. A novel technique that considerably extends the bounds of computational feasibility of the exact test is proposed here. The problem is transformed into one of identifying all paths through a directed acyclic network that equal or exceed a fixed length. Some interesting new optimization theorems are developed in the process. The numerical results reveal that for sparse contingency tables Fisher's exact test and Pearson's X 2 test frequently lead to contradictory inferences concerning row and column independence.
Optimization of Pharmaceutical R&D Programs and Portfolios, 2014
Selecting the right dose is critical for the success of any drug development program, and for max... more Selecting the right dose is critical for the success of any drug development program, and for maximizing the value of a product. A well selected dose will have a better chance to demonstrate a desirable risk/benefit profile and thus increase the chance of regulatory success and reimbursement by payors. It will also result in improved patient care and greater benefit to society. Multiple papers have been published within industry’s adaptive design working groups, and these are the key findings.
Abstract: We present an efficient network algorithm for generating exact permutational distributi... more Abstract: We present an efficient network algorithm for generating exact permutational distributions for linear rank tests defined on stratified 2 xc contingency tables. The algorithm can evaluate exact one and two sided p-values, and compute exact confidence intervals ...
Two important and popular time-sharing systems were analysed for the expected waits of requests. ... more Two important and popular time-sharing systems were analysed for the expected waits of requests. These were the Round-Robin and the Dynamic-Priority Multiple-Level systems. The Round-Robin is very complex in all its generality, however with the aid of a realistic simplifying ...
In this paper, we propose an adaptive randomization design for Phase 2 dose-finding trials to opt... more In this paper, we propose an adaptive randomization design for Phase 2 dose-finding trials to optimize Net Present Value (NPV) for an experimental drug. We replace the traditional fixed sample size design (Patel, et al., 2012) by this new design to see if NPV from the original paper can be improved. Comparison of the proposed design to the previous design is made via simulations using a hypothetical example based on a Diabetic Neuropathic Pain Study.
Traditionally, sample size considerations for phase 2 trials are based on the desired properties ... more Traditionally, sample size considerations for phase 2 trials are based on the desired properties of the design and response information from the trials. In this paper, we propose to design phase 2 trials based on program-level optimization. We present a framework to evaluate the impact that several phase 2 design features have on the probability of phase 3 success and the expected net present value of the product. These factors include the phase 2 sample size, decision rules to select a dose for phase 3 trials and the sample size for phase 3 trials. Using neuropathic pain as an example, we use simulations to illustrate the framework and show the benefit of including these factors in the overall decision process.
This article discusses the opportunities and challenges in the application of financially adaptiv... more This article discusses the opportunities and challenges in the application of financially adaptive clinical trials, which combine key aspects of adaptive trial design and financial analytics.
Optimization of Pharmaceutical R&D Programs and Portfolios, 2014
In this chapter we describe a mathematical approach to maximize the Expected Net Present Value (E... more In this chapter we describe a mathematical approach to maximize the Expected Net Present Value (ENPV) of a portfolio over a planning horizon by determining the optimal designs of Phase 3 (Ph3) trials for a given budget. The model is formulated as a Stochastic Integer Programming (SIP) model that incorporates uncertainty regarding availability of drugs in the pipeline. The SIP model provides an optimal policy that specifies the optimal design for each drug for every possible scenario of availability of future drugs for Ph3 trials. It optimizes the trade-off between committing budget to drugs available for Ph3 funding at any point in time and preserving budget for drugs in the development pipeline that will need funding in the future. Optimizing this trade-off is challenging because it is uncertain which drugs will need funding in the future as they may fail to progress to Ph3. This important trade-off is not handled in a consistent, quantitative way in portfolio budgeting models used in practice today. We have also developed a simulation model to assess the technical, regulatory, and commercial risk of the optimal budget allocation policy. We show how our models can be used for dynamic re-optimization of the portfolio when changes in the internal and external environment occur and as new information becomes available. This capability will enable rapid, frequent, and consistent realignment of the strategy to optimize future use of the budget available for reallocation.
Clinical supply is impacted by decisions and events at every stage of a clinical trial. Protocol ... more Clinical supply is impacted by decisions and events at every stage of a clinical trial. Protocol design, logistics planning, and operational dynamics pose challenges to the management of clinical supply in terms of complexity and uncertainty. In this chapter, we propose a simulation modelling approach to address these issues and support decision-makers in effectively managing clinical supply. The approach is comprehensively described in terms of underlying structure and process, and is illustrated with adaptive trials involving dropping of arms and a Bayesian responsive-adaptive design for dose finding.
Optimization of Pharmaceutical R&D Programs and Portfolios, 2014
In the pharmaceutical industry today, R & D often struggles to generate returns on capital ab... more In the pharmaceutical industry today, R & D often struggles to generate returns on capital above its cost of capital, leading to low to no creation of financial value for investors. Declining returns on R & D investment is a trend that has been unfolding for years given increasingly expensive, long, risky development programs required by regulators and payers for new therapeutics. Once they reach the market, new products face increasingly competitive pressures and decreasing willingness to pay by commercial and government-sponsored insurers. Given these difficulties, funding, particularly of early-stage drugs, has slowed and large pharmaceutical companies and financial sponsors of biotechnology companies have begun questioning the sustainability of the current R & D model. The industry is looking for alternative development and funding options to ensure much-needed new therapies can be brought to market efficiently.
Abstract Successfully advancing Adaptive Licensing requires coordinated planning and action acros... more Abstract Successfully advancing Adaptive Licensing requires coordinated planning and action across multiple stakeholders. The Janus Initiative combines a safe haven multi-stakeholder process with an integrated, best-of-breed quantitative simulation toolset to facilitate biomedical eco-system innovation discussions grounded in case-based realities. The process engages stakeholders from academia, patient advocacy, providers, payers, heath technology assessment, regulators and product sponsors. The quantitative toolset reflects the critical relationships among the parameters, decision domains and metrics relevant to these stakeholders from clinical development through regulatory approval, reimbursement authorization and clinical adoption over the entire product life span. The Janus Initiative, as part of the NEWDIGS program at MIT is moving forward with its first case studies and will continue to develop across multiple therapeutic areas and global regions.
A simple model is developed to evaluate the potential of emission control policies that depend up... more A simple model is developed to evaluate the potential of emission control policies that depend upon meteorological forecasts. An optimal control policy is derived for this model and related analytical results are obtained. A more realistic model leading to a linear programming formulation is discussed and illustrated by means of an example.
This paper studies the one-period, general network distribution problem with linear costs. The ap... more This paper studies the one-period, general network distribution problem with linear costs. The approach is to decompose the problem into a transportation problem that represents a stocking decision, and into decoupled newsboy problems that represent the realization of demand with the usual associated holding and shortage costs. This approach leads to a characterization of optimal policies in terms of the dual of the transportation problem. This method is not directly suitable for the solution for large problems, but the exact solution for small problems can be obtained. For the numercial solutions of large problems, the problem has been formulated aa a linear program with column generation. This latter approach is quite robust in the sense that it is eesily extended to incorporate capacity constraints and the multiproduct case. THE PROBLEM The problem can be stated as (1) where (14 subject to j=1, 2 ,. . ., 12, *This work was performed under ONR Contract N00014-67-A-0204-0076 on Multilevel LoQstics Organization Models at the Massachusetts Institute of Technology.
This paper presents two adaptive methods for sample size re-estimation within a unified group seq... more This paper presents two adaptive methods for sample size re-estimation within a unified group sequential framework. The conceptual and practical distinction between these adaptive modifications and more traditional sample size changes due to revised estimates of nuisance parameters is highlighted. The motivation for the adaptive designs is discussed. Having established that adaptive sample size modifications can be made without inflating the type 1 error, the paper concludes with a novel decision theoretic approach for determining the magnitude of the sample size modification.
Uploads
Papers by Nitin Patel