Optimal eradication: when to stop looking for an invasive plant

The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.

Presentation and detection of invasive melanoma in a high-risk population

Background: Early detection of melanoma has been encouraged in Queensland for many years, yet little is known about the patterns of detection and the way in which they relate to tumor thickness. Objective: Our purpose was to describe current patterns of melanoma detection in Queensland. Methods: This was a population-based study, comprising 3772 Queensland residents diagnosed with a histologically confirmed melanoma between 2000 and 2003. Results: Almost half (44.0%) of the melanomas were detected by the patients themselves, with physicians detecting one fourth (25.3%) and partners one fifth (18.6%). Melanomas detected by doctors were more likely to be thin (\0.75 mm) than those detected by the patient or other layperson. Melanomas detected during a deliberate skin examination were thinner than those detected incidentally. Limitations: Although a participation rate of 78% was achieved, as in any survey, nonresponse bias cannot be completely excluded, and the ability of the results to be generalized to other geographical areas is unknown. Conclusion: There are clear differences in the depth distribution of melanoma in terms of method of detection and who detects the lesions that are consistent with, but do not automatically lead to, the conclusion that promoting active methods of detection may be beneficial. ( J Am Acad Dermatol 2006;54:783-92.)

Trends for in situ and invasive melanoma in Queensland, Australia, 1982-2002

Objectives Queensland, the north-eastern state of Australia, has the highest incidence of melanoma in the world. Control measures started earlier here than probably anywhere else in the world; early detection programmes started in the 1960s and primary prevention in the 1980s. Data from the population-based Queensland Cancer Registry therefore provide an internationally unique data source with which to assess trends for in situ and invasive melanomas and to consider the implications for early detection and primary prevention. Methods We used Poisson regression to estimate the annual percentage change in rates across 21 years of incidence data for in situ and invasive lesions, stratified by age and sex. Joinpoint analyses were used to assess whether there had been a statistically significant change in the trends. Results In situ melanomas increased by 10.4% (95% CI: 10.1%, 11.1%) per year among males and 8.4% (7.9%, 8.9%) per year among females. The incidence of invasive lesions also increased, but not as quickly; males 2.6% (2.4%, 2.8%), females 1.2% (0.9%, 1.5%). Valid data on thickness was only available for 1991 to 2002 and for this period thin-invasive lesions were increasing faster than thick-invasive lesions (for example, among males: thin 3.8%, thick 2.0%). We found some suggestive evidence of lower proportionate increase for the most recent years for both in-situ and invasive lesions, but this did not achieve statistical significance. Among people younger than 35 years, the incidence of invasive melanoma was stable and there was a suggestion of a birth cohort effect from about 1958. Mortality rates were stable across all ages, and there was a suggestion of decreasing rates among young women, although this did not achieve statistical significance. Conclusion Age-standardised incidence is continuing to increase and this, in combination with a shift to proportionately more in situ lesions, suggests that the stabilisation of mortality rates is due, in large part, to earlier detection. For primary prevention, after a substantial period of sustained effort in Queensland, there is some suggestive, but not definitive, evidence that progress is being made. Incidence rates are stabilising in those younger than 35 years and the proportionate increase for both in situ and invasive lesions appears to be lower for the most recent period compared with previous periods. However, even taking the most favourable view of these trends, primary prevention is unlikely to lead to decreases in the overall incidence rate of melanoma for at least another 20 years. Consequently, the challenge for primary prevention programmes will be to maintain momentum over the long term. If this can be achieved, the eventual public-health benefits are likely to be substantial.

Non-invasive phakometric measurement of corneal and crystalline lens alignment in human eyes

We describe a non-invasive phakometric method for determining corneal axis rotation relative to the visual axis (β) together with crystalline lens axis tilt (α) and decentration (d) relative to the corneal axis. This does not require corneal contact A-scan ultrasonography for the measurement of intraocular surface separations. Theoretical inherent errors of the method, evaluated by ray tracing through schematic eyes incorporating the full range of human ocular component variations, were found to be larger than the measurement errors (β < 0.67°, α < 0.72° and d < 0.08 mm) observed in nine human eyes with known ocular component dimensions. Intersubject variations (mean ± S.D.: β = 6.2 ± 3.4° temporal, α = 0.2 ± 1.8° temporal and d = 0.1 ± 0.1 mm temporal) and repeatability (1.96 × S.D. of difference between repeat readings: β ± 2.0°, α ± 1.8° and d ± 0.2 mm) were studied by measuring the left eyes of 45 subjects (aged 18-42 years, 29 females and 16 males, 15 Caucasians, 29 Indian Asians, one African, refractive error range -7.25 to +1.25 D mean spherical equivalent) on two occasions. © 2005 The College of Optometrists.