Detection of frailty in Weibull lifetime data using Outlier tests

Heterogeneity in lifetime data may be modelled by multiplying an individual's hazard by an unobserved frailty. We test for the presence of frailty of this kind in univariate and bivariate data with Weibull distributed lifetimes, using statistics based on the ordered Cox-Snell residuals from the null model of no frailty. The form of the statistics is suggested by outlier testing in the gamma distribution. We find through simulation that the sum of the k largest or k smallest order statistics, for suitably chosen k , provides a powerful test when the frailty distribution is assumed to be gamma or positive stable, respectively. We provide recommended values of k for sample sizes up to 100 and simple formulae for estimated critical values for tests at the 5% level.

An adaptive approach to implementing bivariate group sequential clinical trial designs

In clinical trials, situations often arise where more than one response from each patient is of interest; and it is required that any decision to stop the study be based upon some or all of these measures simultaneously. Theory for the design of sequential experiments with simultaneous bivariate responses is described by Jennison and Turnbull (Jennison, C., Turnbull, B. W. (1993). Group sequential tests for bivariate response: interim analyses of clinical trials with both efficacy and safety endpoints. Biometrics 49:741-752) and Cook and Farewell (Cook, R. J., Farewell, V. T. (1994). Guidelines for monitoring efficacy and toxicity responses in clinical trials. Biometrics 50:1146-1152) in the context of one efficacy and one safety response. These expositions are in terms of normally distributed data with known covariance. The methods proposed require specification of the correlation, ρ between test statistics monitored as part of the sequential test. It can be difficult to quantify ρ and previous authors have suggested simply taking the lowest plausible value, as this will guarantee power. This paper begins with an illustration of the effect that inappropriate specification of ρ can have on the preservation of trial error rates. It is shown that both the type I error and the power can be adversely affected. As a possible solution to this problem, formulas are provided for the calculation of correlation from data collected as part of the trial. An adaptive approach is proposed and evaluated that makes use of these formulas and an example is provided to illustrate the method. Attention is restricted to the bivariate case for ease of computation, although the formulas derived are applicable in the general multivariate case.

Measuring the discrepancy between fecundity and lifetime reproductive success in a pollinating fig wasp

Lifetime reproductive success in female insects is often egg- or time-limited. For instance in pro-ovigenic species, when oviposition sites are abundant, females may quickly become devoid of eggs. Conversely, in the absence of suitable oviposition sites, females may die before laying all of their eggs. In pollinating fig wasps (Hymenoptera: Agaonidae), each species has an obligate mutualism with its host fig tree species [Ficus spp. (Moraceae)]. These pro-ovigenic wasps oviposit in individual ovaries within the inflorescences of monoecious Ficus (syconia, or ‘figs’), which contain many flowers. Each female flower can thus become a seed or be converted into a wasp gall. The mystery is that the wasps never oviposit in all fig ovaries, even when a fig contains enough wasp females with enough eggs to do so. The failure of all wasps to translate all of their eggs into offspring clearly contributes to mutualism persistence, but the underlying causal mechanisms are unclear. We found in an undescribed Brazilian Pegoscapus wasp population that the lifetime reproductive success of lone foundresses was relatively unaffected by constraints on oviposition. The number of offspring produced by lone foundresses experimentally introduced into receptive figs was generally lower than the numbers of eggs carried, despite the fact that the wasps were able to lay all or most of their eggs. Because we excluded any effects of intraspecific competitors and parasitic non-pollinating wasps, our data suggest that some pollinators produce few offspring because some of their eggs or larvae are unviable or are victims of plant defences.

Communicating thematic data quality with web map services

Geospatial information of many kinds, from topographic maps to scientific data, is increasingly being made available through web mapping services. These allow georeferenced map images to be served from data stores and displayed in websites and geographic information systems, where they can be integrated with other geographic information. The Open Geospatial Consortium’s Web Map Service (WMS) standard has been widely adopted in diverse communities for sharing data in this way. However, current services typically provide little or no information about the quality or accuracy of the data they serve. In this paper we will describe the design and implementation of a new “quality-enabled” profile of WMS, which we call “WMS-Q”. This describes how information about data quality can be transmitted to the user through WMS. Such information can exist at many levels, from entire datasets to individual measurements, and includes the many different ways in which data uncertainty can be expressed. We also describe proposed extensions to the Symbology Encoding specification, which include provision for visualizing uncertainty in raster data in a number of different ways, including contours, shading and bivariate colour maps. We shall also describe new open-source implementations of the new specifications, which include both clients and servers.

Cross layer based protocols for energy aware and critical data delivery related applications using wireless sensor networks

Wireless Sensor Networks (WSNs) have been an exciting topic in recent years. The services offered by a WSN can be classified into three major categories: monitoring, alerting, and information on demand. WSNs have been used for a variety of applications related to the environment (agriculture, water and forest fire detection), the military, buildings, health (elderly people and home monitoring), disaster relief, and area or industrial monitoring. In most WSNs tasks like processing the sensed data, making decisions and generating emergency messages are carried out by a remote server, hence the need for efficient means of transferring data across the network. Because of the range of applications and types of WSN there is a need for different kinds of MAC and routing protocols in order to guarantee delivery of data from the source nodes to the server (or sink). In order to minimize energy consumption and increase performance in areas such as reliability of data delivery, extensive research has been conducted and documented in the literature on designing energy efficient protocols for each individual layer. The most common way to conserve energy in WSNs involves using the MAC layer to put the transceiver and the processor of the sensor node into a low power, sleep state when they are not being used. Hence the energy wasted due to collisions, overhearing and idle listening is reduced. As a result of this strategy for saving energy, the routing protocols need new solutions that take into account the sleep state of some nodes, and which also enable the lifetime of the entire network to be increased by distributing energy usage between nodes over time. This could mean that a combined MAC and routing protocol could significantly improve WSNs because the interaction between the MAC and network layers lets nodes be active at the same time in order to deal with data transmission. In the research presented in this thesis, a cross-layer protocol based on MAC and routing protocols was designed in order to improve the capability of WSNs for a range of different applications. Simulation results, based on a range of realistic scenarios, show that these new protocols improve WSNs by reducing their energy consumption as well as enabling them to support mobile nodes, where necessary. A number of conference and journal papers have been published to disseminate these results for a range of applications.