Optimal Budget-Constrained Sample Allocation for Selection Decisions with Multiple Uncertain Attributes

A decision-maker, when faced with a limited and fixed budget to collect data in support of a multiple attribute selection decision, must decide how many samples to observe from each alternative and attribute. This allocation decision is of particular importance when the information gained leads to uncertain estimates of the attribute values as with sample data collected from observations such as measurements, experimental evaluations, or simulation runs. For example, when the U.S. Department of Homeland Security must decide upon a radiation detection system to acquire, a number of performance attributes are of interest and must be measured in order to characterize each of the considered systems. We identified and evaluated several approaches to incorporate the uncertainty in the attribute value estimates into a normative model for a multiple attribute selection decision. Assuming an additive multiple attribute value model, we demonstrated the idea of propagating the attribute value uncertainty and describing the decision values for each alternative as probability distributions. These distributions were used to select an alternative. With the goal of maximizing the probability of correct selection we developed and evaluated, under several different sets of assumptions, procedures to allocate the fixed experimental budget across the multiple attributes and alternatives. Through a series of simulation studies, we compared the performance of these allocation procedures to the simple, but common, allocation procedure that distributed the sample budget equally across the alternatives and attributes. We found the allocation procedures that were developed based on the inclusion of decision-maker knowledge, such as knowledge of the decision model, outperformed those that neglected such information. Beginning with general knowledge of the attribute values provided by Bayesian prior distributions, and updating this knowledge with each observed sample, the sequential allocation procedure performed particularly well. These observations demonstrate that managing projects focused on a selection decision so that the decision modeling and the experimental planning are done jointly, rather than in isolation, can improve the overall selection results.

HIV Reverse Transcriptase Fidelity And Inhibition Are Modulated By Divalent Cations In A Concentration-Dependent Manner In Vitro

Human immunodeficiency virus (HIV) rapidly evolves through generation and selection of mutants that can escape drug therapy. This process is fueled, in part, by the presumably highly error prone polymerase reverse transcriptase (RT). Fidelity of polymerases can be influenced by cation co-factors. Physiologically, magnesium (Mg2+) is used as a co-factor by RT to perform catalysis, however, alternative cations including manganese (Mn2+), cobalt (Co2+), and zinc (Zn2+) can also be used. I demonstrate here that fidelity and inhibition of HIV RT can be influenced differently, in vitro, by divalent cations depending on their concentration. The reported mutation frequency for purified HIV RT in vitro is typically in the 10-4 range (per nucleotide addition), making the enzyme several-fold less accurate than most polymerases. Paradoxically, results examining HIV replication in cells indicate an error frequency that is ~10 times lower than the error rate obtained in the test tube. Here, I reconcile, at least in part, these discrepancies by showing that HIV RT fidelity in vitro is in the same range as cellular results, in physiological concentrations of free Mg2+ (~0.25 mM). At low Mg2+, mutation rates were 5-10 times lower compared to high Mg2+ conditions (5-10 mM). Alternative divalent cations also have a concentration-dependent effect on RT fidelity. Presumed promutagenic cations Mn2+ and Co2+ decreases the fidelity of RT only at elevated concentrations, and Zn2+, when present in low concentration, increases the fidelity of HIV-1 RT by ~2.5 fold compared to Mg2+. HIV-1 and HIV-2 RT inhibition by nucleoside (NRTIs) and non-nucleoside RT inhibitors (NNRTIs) in vitro is also affected by the Mg2+ concentration. NRTIs lacking 3'-OH group inhibited both enzymes less efficiently in low Mg2+ than in high Mg2+; whereas inhibition by the “translocation defective RT inhibitor”, which retains the 3ʹ-OH, was unaffected by Mg2+ concentration, suggesting that NRTIs with a 3ʹ-OH group may be more potent than other NRTIs. In contrast, NNRTIs were more effective in low vs. high Mg2+ conditions. Overall, the studies presented reveal strategies for designing novel RT inhibitors and strongly emphasize the need for studying HIV RT and RT inhibitors in physiologically relevant low Mg2+ conditions.