There is by now a long tradition of using the EM algorithm to find maximum‐likelihood estimates (MLEs) when the data are incomplete in any of a wide range of ways, even when the observed‐data likelihood can easily be evaluated and numerical maximisation of that likelihood is available as a conceptually simple route to the MLEs. It is rare in the literature to see numerical maximisation employed if EM is possible. But with excellent general‐purpose numerical optimisers now available free, there is no longer any reason, as a matter of course, to avoid direct numerical maximisation of likelihood. In this tutorial, I present seven examples of models in which numerical maximisation of likelihood appears to have some advantages over the use of EM as a route to MLEs. The mathematical and coding effort is minimal, as there is no need to derive and code the E and M steps, only a likelihood evaluator. In all the examples, the unconstrained optimiser nlm available in R is used, and transformations are used to impose constraints on parameters. I suggest therefore that the following question be asked of proposed new applications of EM: Can the MLEs be found more simply and directly by using a general‐purpose numerical optimiser? 相似文献
Knee cartilage damage is a common cause of referral for orthopedic surgery. Treatment aims to reduce pain and symptoms by repairing cartilage. Microfracture, the current standard of care, yields good short-term clinical outcomes; however, treatment might fail after 2–3 years. A Chitosan-Beta glycerolphosphate-based medical device (BST-CarGel) is used as an adjunct to microfracture and demonstrates improvements in quantity and quality of repaired tissue, potentially reducing the risk of treatment failure. This study aimed to establish the economic value of BST-CarGel vs microfracture alone in knee cartilage repair from the societal perspective, using Germany as the reference market.
Methods:
A decision tree with a 20-year time-horizon was constructed, in which undesirable clinical events were inferred following initial surgery. These events consisted of pain management, surgery, and total knee replacement. Clinical outcomes were taken from the pivotal clinical trial, supplemented by other literature. Data and assumptions were validated by a Delphi panel. All relevant resource use and costs for procedures and events were considered.
Results:
In a group of patients with all lesion sizes, the model inferred that BST-CarGel yields a positive return on investment at year 4 (with 20-year cumulative cost savings of €6448). Reducing the incremental risk of treatment failure gap between the device and microfracture by 25–50% does not alter this conclusion. Cost savings are greatest for patients with large lesions; results for patients with small lesions are more modest.
Limitations:
Clinical evidence for microfracture and other interventions varies in quality. Comparative long-term data are lacking. The comparison is limited to microfracture and looks only at costs without considering quality-of-life.
Conclusion:
BST-CarGel potentially represents a cost-saving alternative for patients with knee cartilage injury by reducing the risk of clinical events through regeneration of chondral tissue with hyaline characteristics. Since the burden of this condition is high, both to the patient and society, an effective and economically viable alternative is of importance. 相似文献
The largest market in national economies is the labor market. Labor market contracting is characterized by job search, often from unknown wage offer distributions. This paper reports experimental tests of finite horizon models of job search in which the wage offer distribution is unknown. Theoretically-optimal search from an unknown wage offer distribution can have the seemingly paradoxical property that some offers will be accepted that are lower than other offers that will be rejected in the same period of the search horizon. Thus the reservation wage property (or lowest acceptable wage path) may not exist. This can occur because an offer that is a priori relatively high (good news) can imply that it is highly probable that search is from a favorable distribution, and such an offer can look unattractive when it is an a posteriori relatively low offer from a favorable distribution (bad news). This paper reports results from experimental treatments for search from unknown distributions in which the reservation wage property does exist and treatments in which it does not exist. We find that the consistency of search behavior with search theory reported in earlier papers is robust to the presence or absence of the reservation wage property and to whether the draws come from known or unknown distributions. 相似文献
Information security represents the cornerstone of every data processing system that resides in an organisation’s trusted network, implementing all necessary protocols, mechanisms and policies to be one step ahead of possible threats. Starting from the need to strengthen the set of security services, in this article we introduce a new and innovative process named controlled information destruction (CID) that is meant to secure sensitive data that are no longer needed for the organisation’s future purposes but would be very damaging if revealed. The disposal of this type of data has to be controlled carefully in order to delete not only the information itself but also all its splinters spread throughout the network, thus denying any possibility of recovering the information after its alleged destruction. This process leads to a modified model of information assurance and also reconfigures the architecture of any information security management system. The scheme we envisioned relies on a reshaped information lifecycle, which reveals the impact of the CID procedure directly upon the information states. 相似文献