Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

Predictors of local recurrence after treatment of ductal carcinoma in situ - A meta-analysis

lBACKGROUND. Management of patients with ductal carcinoma in situ (DCIS) is a dilemma, as mastectomy provides nearly a 100% cure rate but at the expense of physical and psychologic morbidity. It would be helpful if we could predict which patients with DCIS are at sufficiently high risk of local recurrence after conservative surgery (CS) alone to warrant postoperative radiotherapy (RT) and which patients are at sufficient risk of local recurrence after CS + RT to warrant mastectomy. The authors reviewed the published studies and identified the factors that may be predictive of local recurrence after management by mastectomy, CS alone, or CS + RT. METHODS. The authors examined patient, tumor, and treatment factors as potential predictors for local recurrence and estimated the risks of recurrence based on a review of published studies. They examined the effects of patient factors (age at diagnosis and family history), tumor factors (sub-type of DCIS, grade, tumor size, necrosis, and margins), and treatment (mastectomy, CS alone, and CS + RT). The 95% confidence intervals (CI) of the recurrence rates for each of the studies were calculated for subtype, grade, and necrosis, using the exact binomial; the summary recurrence rate and 95% CI for each treatment category were calculated by quantitative meta-analysis using the fixed and random effects models applied to proportions. RESULTS, Meta-analysis yielded a summary recurrence rate of 22.5% (95% CI = 16.9-28.2) for studies employing CS alone, 8.9% (95% CI = 6.8-11.0) for CS + RT, and 1.4% (95% CI = 0.7-2.1) for studies involving mastectomy alone. These summary figures indicate a clear and statistically significant separation, and therefore outcome, between the recurrence rates of each treatment category, despite the likelihood that the patients who underwent CS alone were likely to have had smaller, possibly low grade lesions with clear margins. The patients with risk factors of presence of necrosis, high grade cytologic features, or comedo subtype were found to derive the greatest improvement in local control with the addition of RT to CS. Local recurrence among patients treated by CS alone is approximately 20%, and one-half of the recurrences are invasive cancers. For most patients, RT reduces the risk of recurrence after CS alone by at least 50%. The differences in local recurrence between CS alone and CS + RT are most apparent for those patients with high grade tumors or DCIS with necrosis, or of the comedo subtype, or DCIS with close or positive surgical margins. CONCLUSIONS, The authors recommend that radiation be added to CS if patients with DCIS who also have the risk factors for local recurrence choose breast conservation over mastectomy. The patients who may be suitable for CS alone outside of a clinical trial may be those who have low grade lesions with little or no necrosis, and with clear surgical margins. Use of the summary statistics when discussing outcomes with patients may help the patient make treatment decisions. Cancer 1999;85:616-28. (C) 1999 American Cancer Society.

Anthropometric measures in relation to Basal Cell Carcinoma: a longitudinal study

Background: The relationship between anthropometric indices and risk of basal cell carcinoma ( BCC) is largely unknown. We aimed to examine the association between anthropometric measures and development of BCC and to demonstrate whether adherence to World Health Organisation guidelines for body mass index, waist circumference, and waist/ hip ratio was associated with risk of BCC, independent of sun exposure. Methods: Study participants were participants in a community- based skin cancer prevention trial in Nambour, a town in southeast Queensland ( latitude 26 degrees S). In 1992, height, weight, and waist and hip circumferences were measured for all 1621 participants and weight was remeasured at the end of the trial in 1996. Prevalence proportion ratios were calculated using a log- binomial model to estimate the risk of BCC prior to or prevalent in 1992, while Poisson regression with robust error variances was used to estimate the relative risk of BCC during the follow- up period. Results: At baseline, 94 participants had a current BCC, and 202 had a history of BCC. During the 5- year follow- up period, 179 participants developed one or more new BCCs. We found no significant association between any of the anthropometric measures or indices and risk of BCC after controlling for potential confounding factors including sun exposure. There was a suggestion that short- term weight gain may increase the risk of developing BCC for women only. Conclusion: Adherence to World Health Organisation guidelines for body mass index, waist circumference and waist/ hip ratio is not significantly associated with occurrence of basal cell carcinomas of the skin.

Sex allocation in the sexually monomorphic fairy martin

Offspring sex ratios were examined at the population and family level in the sexually monomorphic, socially monogamous fairy martin Petrochelidon ariel at five colony sites over a 4-year period (1993 1996). The sex of 465 nestlings from 169 broods % as determined using sex-specific PCR at the CHD locus. In accordance with predicted sex allocation patterns, population sex ratios at hatching and fledging did not differ from parity in an), year and the variance in brood sex ratios did not deviate from the binomial distribution, Further, brood sex ratio did not vary with hatching date during the season, brood number, brood size or colony size, The sex ratio or broods with extra-pair young did not differ from those without, while the sex ratio of broods fathered by males that gained extra-pair fertilizations did not differ from broods fathered by other males. Extra-pair chicks were as likely to be male as female. Neither the total number of feeding visits to the brood nor the relative feeding contribution by the sexes varied significantly with brood sex ratio. Brood sex ratios were also unrelated to paternal size, condition and breeding experience or maternal condition and breeding experience, However, contrary to our prediction, brood sex ratio was negatively correlated with maternal size. Generally, these results were consistent with our expectations that brood sex ratios would not vary with environmental factors or parental characteristics, and would not influence the level of parental provisioning. However, the finding that females with longer tarsi produced an excess of daughters is difficult to reconcile with our current understanding or fairy martin life history and breeding ecology.

Indirect evidence of density-dependent population regulation in Aponomma hydrosauri (Acari : Ixodidae), an ectoparasite of reptiles

The extent to which density-dependent processes regulate natural populations is the subject of an ongoing debate. We contribute evidence to this debate showing that density-dependent processes influence the population dynamics of the ectoparasite Aponomma hydrosauri (Acari: Ixodidae), a tick species that infests reptiles in Australia. The first piece of evidence comes from an unusually long-term dataset on the distribution of ticks among individual hosts. If density-dependent processes are influencing either host mortality or vital rates of the parasite population, and those distributions can be approximated with negative binomial distributions, then general host-parasite models predict that the aggregation coefficient of the parasite distribution will increase with the average intensity of infections. We fit negative binomial distributions to the frequency distributions of ticks on hosts, and find that the estimated aggregation coefficient k increases with increasing average tick density. This pattern indirectly implies that one or more vital rates of the tick population must be changing with increasing tick density, because mortality rates of the tick's main host, the sleepy lizard, Tiliqua rugosa, are unaffected by changes in tick burdens. Our second piece of evidence is a re-analysis of experimental data on the attachment success of individual ticks to lizard hosts using generalized linear modelling. The probability of successful engorgement decreases with increasing numbers of ticks attached to a host. This is direct evidence of a density-dependent process that could lead to an increase in the aggregation coefficient of tick distributions described earlier. The population-scale increase in the aggregation coefficient is indirect evidence of a density-dependent process or processes sufficiently strong to produce a population-wide pattern, and thus also likely to influence population regulation. The direct observation of a density-dependent process is evidence of at least part of the responsible mechanism.

Functional analysis of neurotransmission at β2-laminin deficient terminals

beta2-Laminin is important for the formation of neuromuscular junctions in vertebrates. Previously, we have inactivated the gene that encodes for beta2-laminin in mice and observed predominantly prejunctional structural defects. In this study, we have used both intra- and extracellular recording methods to investigate evoked neurotransmission in beta2-laminin-deficient mice, from postnatal day 8 (P8) through to day 18(P18). Our results confirmed that there was a decrease in the frequency of spontaneous release, but no change in the postjunctional response to such release. Analysis of evoked neurotransmission showed an increase in the frequency of stimuli that failed to elicit an evoked postjunctional response in the mutants compared to litter mate controls, resulting in a 50% reduction in mean quantal content at mutant terminals. Compared to littermate controls, beta2-laminin-deficient terminals showed greater synaptic depression when subjected to high frequency stimulation. Furthermore, the paired pulse ratio of the first two stimuli was significantly lower in beta2-laminin mutant terminals. Statistical analysis of the binomial parameters of release showed that the decrease in quantal content was due to a decrease in the number of release sites without any significant change in the average probability of release. This suggestion was supported by the observation of fewer synaptic vesicle protein 2 (SV2)-positive varicosities in beta2-laminin-deficient terminals and by ultrastructural observations showing smaller terminal profiles and increased Schwann cell invasion in beta2-laminin mutants; the differences between beta2-laminin mutants and wild-type mice were the same at both P8 and P18. From these results we conclude that beta2-laminin plays a role in the early structural development of the neuromuscular junction. We also suggest that transmitter release activity may act as a deterrent to Schwarm cell invasion in the absence of beta2-laminin.

Improving precision and reducing bias in biological surveys: estimating false-negative error rates

The use of presence/absence data in wildlife management and biological surveys is widespread. There is a growing interest in quantifying the sources of error associated with these data. We show that false-negative errors (failure to record a species when in fact it is present) can have a significant impact on statistical estimation of habitat models using simulated data. Then we introduce an extension of logistic modeling, the zero-inflated binomial (ZIB) model that permits the estimation of the rate of false-negative errors and the correction of estimates of the probability of occurrence for false-negative errors by using repeated. visits to the same site. Our simulations show that even relatively low rates of false negatives bias statistical estimates of habitat effects. The method with three repeated visits eliminates the bias, but estimates are relatively imprecise. Six repeated visits improve precision of estimates to levels comparable to that achieved with conventional statistics in the absence of false-negative errors In general, when error rates are less than or equal to50% greater efficiency is gained by adding more sites, whereas when error rates are >50% it is better to increase the number of repeated visits. We highlight the flexibility of the method with three case studies, clearly demonstrating the effect of false-negative errors for a range of commonly used survey methods.

Transmission dynamics of the Echinococcus granulosus sheep-dog strain (G1 genotype) in camels in Tunisia

Cystic echinococcosis, caused by Echinococcus grantilosus, is highly endemic in North Africa and the Middle East. This paper examines the abundance and prevalence of infection of E. granulosus in camels in Tunisia. No cysts were found in 103 camels from Kebili, whilst 19 of 188 camels from Benguerden (10.1%) were infected. Of the cysts found 95% were considered fertile with the presence of protoscolices and 80% of protoscolices were considered viable by their ability to exclude aqueous eosin. Molecular techniques were used on cyst material from camels and this demonstrated that the study animals were infected with the G1 sheep strain of E. granulosus. Observed data were fitted to a mathematical model by maximum likelihood techniques to define the parameters and their confidence limits and the negative binomial distribution was used to define the error variance in the observed data. The infection pressure to camels was somewhat lower in comparison to sheep reported in an earlier study. However, because camels are much longer-lived animals, the results of the model fit suggested that older camels have a relatively high prevalence rate, reaching a most likely value of 32% at age 15 years. This could represent an important source of transmission to dogs and hence indirectly to man of this zonotic strain. In common with similar studies on other species, there was no evidence of parasite-induced immunity in camels. (C) 2004 Elsevier B.V. All rights reserved.

Single patient (n-of-1) trials with binary treatment preference

The use of a fully parametric Bayesian method for analysing single patient trials based on the notion of treatment 'preference' is described. This Bayesian hierarchical modelling approach allows for full parameter uncertainty, use of prior information and the modelling of individual and patient sub-group structures. It provides updated probabilistic results for individual patients, and groups of patients with the same medical condition, as they are sequentially enrolled into individualized trials using the same medication alternatives. Two clinically interpretable criteria for determining a patient's response are detailed and illustrated using data from a previously published paper under two different prior information scenarios. Copyright (C) 2005 John Wiley & Sons, Ltd.

Polymorphisms in glutathione S-transferases and non-melanoma skin cancer risk in Australian renal transplant recipients

Caucasian renal transplant recipients from Queensland, Australia have the highest non-melanoma skin cancer (NMSC) risk worldwide. Although ultraviolet light (UVR) exposure is critical, genetic factors also appear important. We and others have shown that polymorphism in the glutathione S-transferases (GST) is associated with NMSC in UK recipients. However, the effect of high UVR exposure and differences in immunosuppressive regimen on these associations is unknown. In this study, we examined allelism in GSTM1, GSTM3, GSTT1 and GSTP1 in 361 Queensland renal transplant recipients. Data on squamous (SCC) and basal cell carcinoma (BCC), UVR/tobacco exposure and genotype were obtained. Associations with both NMSC risk and numbers were examined using logistic and negative binomial regression, respectively. In the total group, GSTM1 AB [P = 0.049, rate ratio (RR) = 0.23] and GSTM3 AA (P = 0.015, RR = 0.50) were associated with fewer SCC. Recipients were then stratified by prednisolone dose (less than or equal to7 versus >7 mg/day). In the low-dose group, GSTT1 null (P = 0.006, RR = 0.20) and GSTP1 Val/Val (P = 0.021, RR = 0.20) were associated with SCC numbers. In contrast, in the high-dose group, GSTM1 AB (P = 0.009, RR = 0.05), GSTM3 AB (P = 0.042, RR = 2.29) and BB (P = 0.014, RR = 5.31) and GSTP1 Val/Val (P = 0.036, RR = 2.98) were associated with SCC numbers. GSTM1 AB (P = 0.016) and GSTP1 Val/Val (P = 0.046) were also associated with fewer BCC in this group. GSTP1 associations were strongest in recipients with lower UVR/tobacco exposure. The data confirm our UK findings, suggesting that protection against UVR-induced oxidative stress is important in NMSC development in recipients, but that this effect depends on the immunosuppressant regimen.

Food intake and risk of squamous cell carcinoma of the skin in a community: The Nambour skin cancer cohort study

There is some evidence that dietary factors may modify the risk of squamous cell carcinoma (SCC) of the skin, but the association between food intake and SCC has not been evaluated prospectively. We examined the association between food intake and SCC incidence among 1,056 randomly selected adults living in an Australian sub-tropical community. Measurement-error corrected estimates of intake in 15 food groups were defined from a validated food frequency questionnaire in 1992. Associations with SCC risk were assessed using Poisson and negative binomial regression to the persons affected and tumour counts, respectively, based on incident, histologically confirmed tumours occurring between 1992 and 2002. After multivariable adjustment, none of the food groups was significantly associated with SCC risk. Stratified analysis in participants with a past history of skin cancer showed a decreased risk of SCC tumours for high intakes of green leafy vegetables (RR = 0.45, 95% CI = 0.22-0.91; p for trend = 0.02) and an increased risk for high intake of unmodified dairy products (RR = 2.53, 95% CI: 1.15-5.54; p for trend = 0.03). Food intake was not associated with SCC risk in persons who had no past history of skin cancer. These findings suggest that consumption of green leafy vegetables may help prevent development of subsequent SCCs of the skin among people with previous skin cancer and that consumption of unmodified dairy products, such as whole milk, cheese and yoghurt, may increase SCC risk in susceptible persons.

Planar electromagnetic bandgap structures

This article presents various novel and conventional planar electromagnetic bandgap (EBG)-assisted transmission lines. Both microstrip lines and coplanar waveguides (CPWs) are designed with circular, rectangular, annular, plus-sign and fractal-patterned EBGs and dumbbell-shaped defected ground structure (DGS). The dispersion characteristics and the slow-wave factors of the design are investigated. (c) 2006 Wiley Periodicals, Inc.

Stochastic modelling of the invasion process of nematodes in fly larvae

Stochastic models based on Markov birth processes are constructed to describe the process of invasion of a fly larva by entomopathogenic nematodes. Various forms for the birth (invasion) rates are proposed. These models are then fitted to data sets describing the observed numbers of nematodes that have invaded a fly larval after a fixed period of time. Non-linear birthrates are required to achieve good fits to these data, with their precise form leading to different patterns of invasion being identified for three populations of nematodes considered. One of these (Nemasys) showed the greatest propensity for invasion. This form of modelling may be useful more generally for analysing data that show variation which is different from that expected from a binomial distribution.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.