How special is a 'special' interval: modeling departure from length-biased sampling in renewal processes

Length-biased sampling occurs in renewal processes when the probability that an interval is selected is proportional to the length of the interval. This can occur when intervals are selected because they contain an event that is independent of the renewal process and occurs with constant hazard. For example, if the times between donations for repeat blood donors are independent and identically distributed, and if the donor seroconverts to HIV (develops antibodies that indicate infection with human immunodeficiency virus), then the interval between the last HIV seronegative and first HIV seropositive test is expected to be longer than that donor's previous time intervals between donations. We develop hypothesis tests to determine if the relationship between the typical and length-biased intervals is as expected, or if there is departure from length-biased sampling. We further develop a regression method to determine if there are covariates that explain the departure from length-biased sampling. Our approach is motivated by the question of whether there is evidence that repeat blood donors who develop antibodies to HIV or other viral infections change their donation pattern in some way because of seroconversion.     

Variance estimation for statistics computed from single recurrent event processes

This article is concerned with variance estimation for statistics that are computed from single recurrent event processes. Such statistics are important in diagnosis for each individual recurrent event process. The proposed method only assumes a semiparametric form for the first-order structure of the processes but not for the second-order (i.e., dependence) structure. The new variance estimator is shown to be consistent for the target parameter under very mild conditions. The estimator can be used in many applications in semiparametric rate regression analysis of recurrent event data such as outlier detection, residual diagnosis, as well as robust regression. A simulation study and application to two real data examples are used to demonstrate the use of the proposed method.     

Calibration of sampling techniques and determination of sample size for the estimation of egg and larval populations of Helicoverpa spp. (Lepidoptera: Noctuidae) on irrigated soybean

Abstract  Informed spray decisions require accurate assessments of the target pest's density. Currently, no advice is provided to farmers on the best method for sampling soybean for insect pests, although spray thresholds for Helicoverpa larvae are provided. This article describes the results of a trial designed to calibrate relative sampling techniques for Helicoverpa larvae; visual inspection of plants in situ in the field, beat cloth, sweep net and D-vac sampling were compared with an absolute measure of population density. The absolute measure was derived from the bagging and removal of whole plants in the field, followed by subsequent examination in the laboratory. Analysis of the distribution of Helicoverpa larvae collected by the different samples was then used to calculate the number of samples required to determine whether the economic threshold had been reached to different levels of certainty and accuracy. Significant relationships were detected between all the relative sampling techniques and the absolute, suggesting that all could be used to estimate field populations. However, due to the high variance and therefore increased sample sizes required, or the length of time taken to collect samples, only beat-cloth sampling appeared to offer a realistic method for farmers in the field. The results also suggest that the current best practice of sampling six locations per crop provides an adequate assessment of the field populations at the currently accepted threshold level of 6 larvae m⁻². However, if the economic spray was reduced, the number of samples required to determine an accurate population estimate would increase dramatically.     

The digging‐in effect on ant studies with pitfall traps: influence of type of habitat and sampling time

Pitfall traps are among the most common sampling methods used for the study of ants. There are many types of traps and many possible ways of using them. The various methodologies may introduce biases in sampling. One possible bias may be caused by the digging‐in effect (DE), resulting in higher catches of ants immediately after traps are set in the ground which subsequently decline. In this study, we performed two experiments to verify the consequences of the DE for ants in a Mediterranean ecosystem. In the first experiment we distinguished between two types of habitats: closed and open (i.e., with or without shrub or tree cover). The second experiment was carried out in a homogeneous pasture where the time of prevalence of the DE was verified, investigating the duration of the effect. The results indicate differences between communities in the first 24 h after setting of the traps, which had disappeared after 48 h. This does not dismiss the possibility of certain species being affected either positively (increase in captures) or negatively (decrease). Changes in species composition, determining whether the DE was manifested or not, differed among habitat types.