Nonparametric estimation of the causal effect of a stochastic threshold-based intervention

Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. In view of this goal, we consider a covariate-adjusted threshold-based interventional estimand, which happens to equal the binary treatment–specific mean estimand from the causal inference literature obtained by dichotomizing the continuous biomarker or treatment as above or below a threshold. The unadjusted version of this estimand was considered in Donovan et al.. Expanding upon Stitelman et al., we show that this estimand, under conditions, identifies the expected outcome of a stochastic intervention that sets the treatment dose of all participants above the threshold. We propose a novel nonparametric efficient estimator for the covariate-adjusted threshold-response function for the case of informative outcome missingness, which utilizes machine learning and targeted minimum-loss estimation (TMLE). We prove the estimator is efficient and characterize its asymptotic distribution and robustness properties. Construction of simultaneous 95% confidence bands for the threshold-specific estimand across a set of thresholds is discussed. In the Supporting Information, we discuss how to adjust our estimator when the biomarker is missing at random, as occurs in clinical trials with biased sampling designs, using inverse probability weighting. Efficiency and bias reduction of the proposed estimator are assessed in simulations. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.     

Developmental outcomes in children exposed to Zika virus in utero from a Brazilian urban slum cohort study

BackgroundThe prevalence of developmental alterations associated with in-utero Zika virus (ZIKV) exposure in children is not well understood. Furthermore, estimation of the Population Attributable Fraction (PAF) of developmental alterations attributed to ZIKV has not been performed due to lack of population-based cohorts with data on symptomatic and asymptomatic ZIKV exposures and an appropriate control group. The aim of this study was to characterize neurodevelopmental outcomes of children at 11 to 32 months of age with intrauterine ZIKV exposure and estimate the PAF of alterations secondary to ZIKV exposure.Methodology/Principal findingsWe performed a cohort of biannual community-based prospective serosurveys in a slum community in Salvador, Brazil. We recruited women participating in our cohort, with a documented pregnancy from January 2015 to December 2016 and children born to those mothers. Children were classified as ZIKV exposed in utero (born from women with ZIKV seroconversion during pregnancy) or unexposed (born from women without ZIKV seroconversion or that seroconverted before/after pregnancy) by using an IgG monoclonal antibody blockade-of-binding (BoB). We interviewed mothers and performed anthropometric, audiometric, ophthalmological, neurologic, and neurodevelopmental evaluations of their children at 11 to 32 months of age. Among the 655 women participating in the cohort, 66 (10%) were pregnant during the study period. 46 (70%) of them completed follow-up, of whom ZIKV seroconversion occurred before, during, and after pregnancy in 25 (54%), 13 (28%), and 1 (2%), respectively. The rest of women, 7 (21.2%), did not present ZIKV seroconversion. At 11 to 32 months of life, the 13 ZIKV-exposed children had increased risk of mild cognitive delay (RR 5.1; 95%CI 1.1–24.4) compared with the 33 children unexposed, with a PAF of 53.5%. Exposed children also had increased risk of altered auditory behavior (RR 6.0; 95%CI 1.3–26.9), with a PAF of 59.5%.ConclusionsA significant proportion of children exposed in utero to ZIKV developed mild cognitive delay and auditory behavioral abnormalities even in the absence of gross birth defects such as microcephaly and other neurodevelopmental domains. Furthermore, our findings suggest that over half of these abnormalities could be attributed to intrauterine ZIKV exposure.     

Ultrasound-based subject-specific parameters improve fascicle behaviour estimation in Hill-type muscle model

The estimation of muscle fascicle behaviour is decisive in a Hill-type model as they are related to muscle force by the force–length–velocity relationship and the tendon force–strain relationship. This study was aimed at investigating the influence of subject-specific tendon force–strain relationship and initial fascicle geometry (IFG) on the estimation of muscle forces and fascicle behaviour during isometric contractions. Ultrasonography was used to estimate the in vivo muscle fascicle behaviour and compare the muscle fascicle length and pennation angle estimated from the Hill-type model. The calibration–prediction process of the electromyography-driven model was performed using generic or subject-specific tendon definition with or without IFG as constraint. The combination of subject-specific tendon definition and IFG led to muscle fascicle behaviour closer to ultrasound data and significant lower forces of the ankle dorsiflexor and plantarflexor muscles compared to the other conditions. Thus, subject-specific ultrasound measurements improve the accuracy of Hill-type models on muscle fascicle behaviour.     

The antifungal protein PAF interferes with PKC/MPK and cAMP/PKA signalling of Aspergillus nidulans

The Penicillium chrysogenum antifungal protein PAF inhibits polar growth and induces apoptosis in Aspergillus nidulans. We report here that two signalling cascades are implicated in its antifungal activity. PAF activates the cAMP/protein kinase A (Pka) signalling cascade. A pkaA deletion mutant exhibited reduced sensitivity towards PAF. This was substantiated by the use of pharmacological modulators: PAF aggravated the effect of the activator 8‐Br‐cAMP and partially relieved the repressive activity of caffeine. Furthermore, the Pkc/mitogen‐activated protein kinase (Mpk) signalling cascade mediated basal resistance to PAF, which was independent of the small GTPase RhoA. Non‐functional mutations of both genes resulted in hypersensitivity towards PAF. PAF did not increase MpkA phosphorylation or induce enzymes involved in the remodelling of the cell wall, which normally occurs in response to activators of the cell wall integrity pathway. Notably, PAF exposure resulted in actin gene repression and a deregulation of the chitin deposition at hyphal tips of A. nidulans, which offers an explanation for the morphological effects evoked by PAF and which could be attributed to the interconnection of the two signalling pathways. Thus, PAF represents an excellent tool to study signalling pathways in this model organism and to define potential fungal targets to develop new antifungals.     

Subject-specific tendon-aponeurosis definition in hill-type model predicts higher muscle forces in dynamic tasks

Neuromusculoskeletal models are a common method to estimate muscle forces. Developing accurate neuromusculoskeletal models is a challenging task due to the complexity of the system and large inter-subject variability. The estimation of muscles force is based on the mechanical properties of tendon-aponeurosis complex. Most neuromusculoskeletal models use a generic definition of the tendon-aponeurosis complex based on in vitro test, perhaps limiting their validity. Ultrasonography allows subject-specific estimates of the tendon-aponeurosis complex's mechanical properties. The aim of this study was to investigate the influence of subject-specific mechanical properties of the tendon-aponeurosis complex on a neuromusculoskeletal model of the ankle joint. Seven subjects performed isometric contractions from which the tendon-aponeurosis force-strain relationship was estimated. Hopping and running tasks were performed and muscle forces were estimated using subject-specific tendon-aponeurosis and generic tendon properties. Two ultrasound probes positioned over the muscle-tendon junction and the mid-belly were combined with motion capture to estimate the in vivo tendon and aponeurosis strain of the medial head of gastrocnemius muscle. The tendon-aponeurosis force-strain relationship was scaled for the other ankle muscles based on tendon and aponeurosis length of each muscle measured by ultrasonography. The EMG-driven model was calibrated twice - using the generic tendon definition and a subject-specific tendon-aponeurosis force-strain definition. The use of subject-specific tendon-aponeurosis definition leads to a higher muscle force estimate for the soleus muscle and the plantar-flexor group, and to a better model prediction of the ankle joint moment compared to the model estimate which used a generic definition. Furthermore, the subject-specific tendon-aponeurosis definition leads to a decoupling behaviour between the muscle fibre and muscle-tendon unit in agreement with previous experiments using ultrasonography. These results indicate the use of subject-specific tendon-aponeurosis definitions in a neuromusculoskeletal model produce better agreement with measured external loads and more physiological model behaviour.     

Sensitivity analysis for principal stratum direct effects, with an application to a study of physical activity and coronary heart disease

Summary .  In many studies, the aim is to learn about the direct exposure effect, that is, the effect not mediated through an intermediate variable. For example, in circulation disease studies it may be of interest to assess whether a suitable level of physical activity can prevent disease, even if it fails to prevent obesity. It is well known that stratification on the intermediate may introduce a so-called posttreatment selection bias. To handle this problem, we use the framework of principal stratification ( Frangakis and Rubin, 2002 , Biometrics 58, 21–29) to define a causally relevant estimand—the principal stratum direct effect (PSDE). The PSDE is not identified in our setting. We propose a method of sensitivity analysis that yields a range of plausible values for the causal estimand. We compare our work to similar methods proposed in the literature for handling the related problem of "truncation by death."     

Platelet‐activating factor interaction with the human erythrocyte membrane

Platelet‐activating factor (PAF) is a soluble signal messenger present in blood at nanomolar concentration. PAF has a wide spectrum of biological activities and is produced by and effective in different cell types. Owing to its important physiological role, we wanted to characterize membrane intercalation and interaction of PAF‐16 (1‐O‐hexadecyl‐2‐acetyl‐sn‐glycero‐3‐phosphocholine) by studying its capacity to induce during short‐term incubations at high concentrations cell shape alterations, phosphatidylserine exposure, and hemolysis in human erythrocytes. Our results showed that PAF‐16 at micromolar concentrations rapidly (≤1 min) induces stable but wash‐sensitive echinocytosis and hemolysis, but no substantial phosphatidylserine exposure. In conclusion, our study characterizes PAF‐16 as a highly membrane partitioning non‐permeable molecule accumulating in the outer membrane leaflet. These membrane interacting properties of PAF should, also at physiological concentrations, be important part of its nature as a membrane affector molecule. © 2009 Wiley Periodicals, Inc. J Biochem Mol Toxicol 23:345–348, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jbt.20297     

化合物ADMET性质预测平台的构建

在药物研发早期阶段对化合物成药性和安全性进行评估,对于提高药物研发成功率、降低研发成本具有十分重要的意义。为了能够帮助药物研究工作者快速准确地判断候选化合物的成药性与安全性,开发了一个基于计算机方法的化合物ADMET性质预测平台。首先,通过文本挖掘的方法收集了化合物药代动力学性质和毒性(ADMET)的高质量实验数据。然后,根据原始文献复原了13个预测模型,同时采用支持向量机方法自建了15个具有较高预测能力的计算模型。最后,基于分布式架构,结合高性能计算集群优势,开发了化合物ADMET性质预测平台(http://www.vslead.com/?r=admet/index),用于预测28种重要的化合物ADMET性质。研究者可以使用这一平台快捷方便地对药物研究中比较重要的ADMET性质进行预测,在药物研发早期对候选化合物进行成药性评价和风险评估,有助于提高药物研的成功率,节省研发时间和经费的投入。     

Evaluating candidate principal surrogate endpoints

SUMMARY: Frangakis and Rubin (2002, Biometrics 58, 21-29) proposed a new definition of a surrogate endpoint (a "principal" surrogate) based on causal effects. We introduce an estimand for evaluating a principal surrogate, the causal effect predictiveness (CEP) surface, which quantifies how well causal treatment effects on the biomarker predict causal treatment effects on the clinical endpoint. Although the CEP surface is not identifiable due to missing potential outcomes, it can be identified by incorporating a baseline covariate(s) that predicts the biomarker. Given case-cohort sampling of such a baseline predictor and the biomarker in a large blinded randomized clinical trial, we develop an estimated likelihood method for estimating the CEP surface. This estimation assesses the "surrogate value" of the biomarker for reliably predicting clinical treatment effects for the same or similar setting as the trial. A CEP surface plot provides a way to compare the surrogate value of multiple biomarkers. The approach is illustrated by the problem of assessing an immune response to a vaccine as a surrogate endpoint for infection.     

Association between Air Pollutants and Asthma Emergency Room Visits and Hospital Admissions in Time Series Studies: A Systematic Review and Meta-Analysis

Background

Air pollution constitutes a significant stimulus of asthma exacerbations; however, the impacts of exposure to major air pollutants on asthma-related hospital admissions and emergency room visits (ERVs) have not been fully determined.

Objective

We sought to quantify the associations between short-term exposure to air pollutants [ozone (O₃), carbon monoxide (CO), nitrogen dioxide (NO₂), sulfur dioxide (SO₂), and particulate matter ≤10μm (PM₁₀) and PM_2.5] and the asthma-related emergency room visits (ERV) and hospitalizations.

Methods

Systematic computerized searches without language limitation were performed. Pooled relative risks (RRs) and 95% confidence intervals (95%CIs) were estimated using the random-effect models. Sensitivity analyses and subgroup analyses were also performed.

Results

After screening of 246 studies, 87 were included in our analyses. Air pollutants were associated with significantly increased risks of asthma ERVs and hospitalizations [O₃: RR(95%CI), 1.009 (1.006, 1.011); I² = 87.8%, population-attributable fraction (PAF) (95%CI): 0.8 (0.6, 1.1); CO: RR(95%CI), 1.045 (1.029, 1.061); I² = 85.7%, PAF (95%CI): 4.3 (2.8, 5.7); NO₂: RR(95%CI), 1.018 (1.014, 1.022); I² = 87.6%, PAF (95%CI): 1.8 (1.4, 2.2); SO₂: RR(95%CI), 1.011 (1.007, 1.015); I² = 77.1%, PAF (95%CI): 1.1 (0.7, 1.5); PM₁₀: RR(95%CI), 1.010 (1.008, 1.013); I² = 69.1%, PAF (95%CI): 1.1 (0.8, 1.3); PM_2.5: RR(95%CI), 1.023 (1.015, 1.031); I² = 82.8%, PAF (95%CI): 2.3 (1.5, 3.1)]. Sensitivity analyses yielded compatible findings as compared with the overall analyses without publication bias. Stronger associations were found in hospitalized males, children and elderly patients in warm seasons with lag of 2 days or greater.

Conclusion

Short-term exposures to air pollutants account for increased risks of asthma-related ERVs and hospitalizations that constitute a considerable healthcare utilization and socioeconomic burden.     

Platelet-activating factor: an endogenous mediator for bowel necrosis in endotoxemia

We have developed a model of isochemic bowel necrosis in the rat by injecting platelet-activating factor (PAF) or PAF in combination with bacterial endotoxin. PAF causes profound hypotension, and it has been suggested that it is released during endotoxin shock. Because ischemic bowel necrosis is often associated with shock or infection, it is possible that PAF is the endogenous mediator that causes shock and bowel necrosis during sepsis. In this study, we have demonstrated that: 1) normal intestine contained a small amount of PAF; 2) necrotic lesions of the intestine could be induced by endotoxin injection; 3) PAF production in the bowel is markedly increased in animals treated with endotoxin; 4) pretreatment of the animal with PAF antagonists prevent endotoxin-induced necrosis; 5) isolated, buffer-perfused small intestine produced a small quantity of PAF in response to endotoxin injection. Therefore, we conclude that PAF is a likely endogenous mediator in endotoxemia, which causes bowel necrosis and shock.     

Estimation and prediction of cell cycle specific effects of anticancer drugs

A mathematical model is used to estimate the cell cycle phase specific action of a new anticancer drug, CI-921, based on results of a short term (8 hr) stathmokinetic (blocked divisions) study on Friend leukemia cells. The estimate obtained is in the form of a sequence of fractions of the cell flow blocked in successive subcompartments of the cell cycle. At specific drug concentrations, the information contained in this estimate is sufficient to correctly predict the results of long term (24 hr) continuous drug exposure. The result obtained seems to be of interest, since the ability to predict the cell cycle phase specific effects of anticancer drugs is crucial for any attempt to improve the existing chemotherapeutic treatment schedules for cancer. This study required developing new mathematical techniques, among them a nonparametric method for estimation of the distributions of cell residence times in the G₁ phase of the cell cycle (Appendix). The methods developed are general enough to be applicable, in principle, to any chemotherapeutic agent the action of which is distributed throughout the cell cycle.     

Involvement of leukotriene B4 receptor 1 signaling in platelet-activating factor-mediated neutrophil degranulation and chemotaxis

Platelet-activating factor (PAF) is a potent lipid mediator of inflammation that can act on human neutrophils. When neutrophils are stimulated with PAF at concentrations greater than 10 nM, a double peak of intracellular calcium mobilization is observed. The second calcium peak observed in PAF-treated neutrophils has already been suggested to come from the production of endogenous leukotriene B4 (LTB4). Here we demonstrate the involvement of endogenous LTB4 production and subsequent activation of the high affinity LTB4 receptor (BLT1) in this second calcium mobilization peak observed after stimulation with PAF. We also show that the second, but not the first peak, could be desensitized by prior exposure to LTB4. Moreover, when neutrophils were pre-treated with pharmacological inhibitors of LTB4 production or with the specific BLT1 antagonist, U75302, PAF-mediated neutrophil degranulation was inhibited by more than 50%. On the other hand, pre-treating neutrophils with the PAF receptor specific antagonist (WEB2086) did not prevent any LTB4-induced degranulation. Also, when human neutrophils were pre-treated with U75302, PAF-mediated chemotaxis was reduced by more than 60%. These data indicate the involvement of BLT1 signaling in PAF-mediated neutrophil activities.     

基于Google Earth Engine与机器学习的大尺度30m分辨率沙地灌木覆盖度估算

相较于降雨充沛的南方,中国北方沙地植被呈现覆盖整体偏低、空间异质性强的特点。灌木作为该区域的优势植被,对于风沙固定、食品/木材供给起着极为重要的作用。针对当前大尺度、中高分辨率干旱地区灌木覆盖度遥感产品缺失的现状,研究提出了一套通过Collect Earth样本收集器进行样本采集、利用Google Earth Engine遥感云平台的数据与计算优势开展大尺度灌木覆盖度估算的方法,并选取中国北方四大沙地之一的毛乌素沙地开展了示范应用。研究结果表明:(1)Collect Earth样本收集器可以有效地获取地面灌木覆盖度样本数据集,可以将灌木与高大乔木与草本植被进行有效区分,为灌木覆盖度估算样本集的建立打下了基础;(2)利用Landsat数据与其他辅助数据,机器学习算法可以较好地实现灌木覆盖度的估算,CART模型确定性系数R~2为0.73,均方根误差(Root Mean Square Error, RMSE)为13.66%,预测精度(Estimated Accuracy, EA)为61.8%,SVM模型R~2为0.72,RMSE为13.73%,EA为61.6%;(3)提出的基于GEE的灌木覆盖度估算体系可为我国乃至全球尺度干旱地区沙地灌木覆盖度信息提取提供有效支撑,具有较大的应用潜力。     

Modeling and observer design for recombinant Escherichia coli strain

A mathematical model for recombinant bacteria which includes foreign protein production is developed. The experimental system consists of an Escherichia Coli strain and plasmid pIT34 containing genes for bioluminescence and production of a protein, β-galactosidase. This recombinant strain is constructed to facilitate on-line estimation and control in a complex bioprocess. Several batch experiments are designed and performed to validate the developed model. The design of a model structure, the identification of the model parameters and the estimation problem are three parts of a joint design problem. A nonlinear observer is designed and an experimental evaluation is performed on a batch fermentation process to estimate the substrate consumption.     

Hypoxia primes endotoxin-induced tissue factor expression in human monocytes and endothelial cells by a PAF-dependent mechanism

Tissue factor (TF) is a glycoprotein which acts as a trigger of the coagulation cascade. TF expression may be induced at the surface of monocytes and endothelial cells by several stimuli including bacterial endotoxin (LPS) and cytokines (IL1β, TNFα) and there is a large body of evidence for the involvement of hypoxia as a primaring factor in the process leading to thrombosis. To define the molecular basis underlying this phenomenon, we evaluated the relative role of platelet activating factor (PAF). PAF primed human monocytes and human umbilical vein endothelial cells (HUVEC) for TF expression following exposure to E. coli LPS but was unable to enhance the induction of TF expression by IL1β. The priming effect of PAF with regard to LPS occurred in a time-and dose-dependent manner and was inhibited by the PAF receptor antagonist SR 27417. When HUVEC or monocytes were exposed to an hypoxic environment, a significant rise in LPS-induced TF expression was observed. Hypoxia had no effect on IL1-induced TF expression. The enhanced LPS-induced TF expression in both cell types was mediated by PAF as indicated by the inhibition obtained with SR 27417, added during hypoxia. Although the importance of hypoxia in the etiology of venous thrombosis has been acknowledged for a long time, evaluation of the relative importance of PAF in the process leading to thrombus formation is still lacking. Stasis-induced thrombosis performed in the rabbit jugular vein was enhanced in a dose-dependent manner by the prior i.v. administration of LPS (0.05 to 100 μg/kg, i.v.). SR 27417 administered simultaneously with LPS prevented thrombus formation with an ED50 value of 0.1 ± 0.04 mg/kg. These results therefore show that hypoxia promotes LPS-induced TF expression in HUVEC and human monocytes through a PAF-dependent mechanism in vitro and in vivo. © 1996 Wiley-Liss, Inc.     

Simulation of swallowing dysfunction and mechanical ventilation after a Montgomery T-tube insertion

The Montgomery T-tube is used as a combined tracheal stent and airway after laryngotracheoplasty, to keep the lumen open and prevent mucosal laceration from scarring. It is valuable in the management of upper and mid-tracheal lesions, while invaluable in long and multisegmental stenting lesions. Numerical simulations based on real-patient-tracheal geometry, experimental tissue characterization, and previous numerical estimation of the physiological swallowing force are performed to estimate the consequences of Montgomery T-tube implantation on swallowing and assisted ventilation: structural analysis of swallowing is performed to evaluate patient swallowing capacity, and computational fluid dynamics simulation is carried out to analyze related mechanical ventilation. With an inserted Montgomery T-tube, vertical displacement (Z-axis) reaches 8.01 mm, whereas in the Y-axis, it reaches 6.63 mm. The maximal principal stress obtained during swallowing was 1.6 MPa surrounding the hole and in the upper contact with the tracheal wall. Fluid flow simulation of the mechanical ventilation revealed positive pressure for both inhalation and exhalation, being higher for inspiration. The muscular deflections, considerable during normal breathing, are nonphysiological, and this aspect results in a constant overload of the tracheal muscle. During swallowing, the trachea ascends producing a nonhomogeneous elongation. This movement can be compromised when prosthesis is inserted, which explains the high incidence of glottis close inefficiency. Fluid simulations showed that nonphysiological pressure is established inside the trachea due to mechanical ventilation. This may lead to an overload of the tracheal muscle, explaining several related problems as muscle thinning or decrease in contractile function.     

Mechanism and regulation of neutrophil priming by platelet-activating factor

Although a weak direct stimulus of superoxide anion (O₂^?) production, platelet-activating factor (PAF) markedly enhances responses to chemotactic peptides (such as n-formyl-met-leu-phe, FMLP) and phorbol esters (such as phorbol myristate acetate, PMA) in human neutrophils. The mechanism of priming was explored first through inhibition of steps in the signal transduction pathway at and following PAF receptor occupation. Priming was not altered by pertussis toxin or intracellular calcium chelation, but the PAF receptor antagonist WEB 2086 and the protein kinase C (PKC) inhibitors sphinganine and staurosporine significantly inhibited the primed response. In order to study the regulation of PAF priming, the effect of PAF alone was desensitized by exposure to escalating doses of PAF prior to exposure to the secondary stimuli. The priming effect of PAF was not desensitized under these conditions. The role of PKC in desensitization was also studied. Prior exposure to PAF also desensitized the increase in membrane PKC activity evoked by a single concentration of PAF. However, when the PAF response was desensitized, PKC priming of the response to FMLP or PMA still occurred, suggesting that PKC activity may play a role in the maintenance of the primed state despite PAF desensitization. These data suggest that: (1) PAF priming is receptor- and PKC-mediated but is independent of pertussis toxin-inhibitable G-proteins or intracellular calcium, (2) during migration in vivo, neutrophils may be desensitized to the direct effects of PAF but maintain the capacity for enhanced responses to other stimuli, (3) desensitization of PAF-induced particulate PKC activity also occurs, but PAF primes PKC activity despite PAF desensitization, and (4) distinct mechanisms govern the direct and priming effects of PAF on oxidative metabolism. © 1993 Wiley-Liss, Inc.     

Evaluation of statistical precision and design of efficient sampling for the population estimation based on frequency of occurrence

The binomial sampling to estimate population density of an organism based simply upon the frequency of its occurrence among sampled quadrats is a labour-saving technique which is potentially useful for small animals like insects and has actually been applied occasionally to studies of their populations. The present study provides a theoretical basis for this convenient technique, which makes it statistically reliable and tolerable for consistent use in intensive as well as preliminary population censuses. Firs, the magnitude of sampling error in relation to sample size is formulated mathematically for the estimate to be obtained by this indirect method of census, using either of the two popular models relating frequency of occurrence (p) to mean density (m), i.e. the negative binomial model, p=1−(1+m/k)^−k, and the empirical model, p=1−exp(−am^b). Then, the equations to calculate sample size and census cost that are necessary to attain a given desired level of precision in the estimation are derived for both models. A notable feature of the relationship of necessary sample size (or census cost) to mean density in the frequency method, in constrast to that in the ordinary census, is that it shows a concave curve which tends to rise sharply not only towards lower but also towards higher levels of density. These theoretical results make it also possible to design sequential estimation procedures based on this convenient census technique, which may enable us with the least necessary cost to get a series of population estimates with the desired precision level. Examples are presented to explain how to apply these programs to acutal censuses in the field.