The U.S. pharmaceutical industry spent upwards of $18 billion on marketing drugs in 2005; detailing and drug sampling activities accounted for the bulk of this spending. To stay competitive, pharmaceutical managers need to maximize the return on these marketing investments by determining which physicians to target as well as when and how to target them. In this paper, we present a two-stage approach for dynamically allocating detailing and sampling activities across physicians to maximize long-run profitability. In the first stage, we estimate a hierarchical Bayesian, nonhomogeneous hidden Markov model to assess the short- and long-term effects of pharmaceutical marketing activities. The model captures physicians' heterogeneity and dynamics in prescription behavior. In the second stage, we formulate a partially observable Markov decision process that integrates over the posterior distribution of the hidden Markov model parameters to derive a dynamic marketing resource allocation policy across physicians. We apply the proposed approach in the context of a new drug introduction by a major pharmaceutical firm. We identify three prescription-behavior states, a high degree of physicians' dynamics, and substantial long-term effects for detailing and sampling. We find that detailing is most effective as an acquisition tool, whereas sampling is most effective as a retention tool. The optimization results suggest that the firm could increase its profits substantially while decreasing its marketing spending. Our suggested framework provides important implications for dynamically managing customers and maximizing long-run profitability.pharmaceutical marketing, marketing resource allocation, long-term effect of marketing activities, hidden Markov model, Bayesian estimation, dynamic programming

The accuracy of intensivists' early clinical predictions of duration of mechanical ventilation is limited, particularly for identifying patients who will require prolonged mechanical ventilation.

Companies in diverse industries must decide the pricing policy of their inventories over time. This decision becomes particularly complex when customers are forward looking and may defer a purchase in the hope of future discounts and promotions. With such uncertainty, many customers may end up not buying or buying at a significantly lower price, reducing the firm’s profitability. Recent studies show that a way to mitigate this negative effect caused by strategic consumers is to use a posted or preannounced pricing policy. With that policy, firms commit to a price path that consumers use to evaluate their purchase timing decision. In this paper, we propose a class of preannounced pricing policies in which the price path corresponds to a price menu contingent on the available inventory. We present a two-period model, with a monopolist selling a fixed inventory of a good. Given a menu of prices specified by the firm and beliefs regarding the number of units to be sold, customers decide whether to buy upon arrival, buy at the clearance price, or not to buy. The firm determines the set of prices that maximizes revenues. The solution to this problem requires the concept of equilibrium between the seller and the buyers that we analyze using a novel approach based on ordinary differential equations. We show existence of equilibrium and uniqueness when only one unit is on sale. However, if multiple units are offered, we show that multiple equilibria may arise. We develop a gradient-based method to solve the firm’s optimization problem and conduct a computational study of different pricing schemes. The results show that under certain conditions the proposed contingent preannounced policy outperforms previously proposed pricing schemes. The source of the improvement comes from the use of the proposed pricing policy as a barrier to discourage strategic waiting and as a discrimination tool for those customers waiting.Millennium Nucleus Information and Coordination in Networks ICM/FIC RC130003 CONICYT FBO16 CONICYT through grant FONDECYT 113067

BACKGROUND: Spontaneous breathing trials (SBTs) are increasingly performed. Significant changes in monitored breathing variables and the timing of those changes during the trial have important implications for its outcome determination and supervision. We aimed to study the magnitude and timing of change in breathing variables during the course of a 30-min SBT. METHODS: Breathing variables were continuously measured and averaged by minute during the SBT in 32 subjects with trial success and 8 subjects with trial failure from a general ICU population. Percentage changes in breathing variables during the trial and proportions of subjects showing a > 20% change at different time points relative to the second minute of the trial were calculated. RESULTS: The commonly monitored breathing variables (frequency, tidal volume, their ratio, and minute ventilation) showed median coefficients of variation of < 15% throughout the trial and a median change of less than ؎ 20% by the end of the trial. Changes in a detrimental direction of > 20% at the end of the trial but not already present at 10 min were noted in < 5% of all subjects. CONCLUSIONS: During the course of a 30-min SBT, breathing variables remain relatively constant, and potentially significant changes in these variables after 10 min into the trial are uncommon. These findings should be considered when addressing aspects of duration and supervision of SBTs in weaning protocols.

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