Statistical methods for estimating doubling time in in vitro cell growth

Summary Doubling time has been widely used to represent the growth pattern of cells. A traditional method for finding the doubling time is to apply gray-scaled cells, where the logarithmic transformed scale is used. As an alternative statistical method, the log-linear model was recently proposed, for which actual cell numbers are used instead of the transformed gray-scaled cells. In this paper, I extend the log-linear model and propose the extended log-linear model. This model is designed for extra-Poisson variation, where the log-linear model produces the less appropriate estimate of the doubling time. Moreover, I compare statistical properties of the gray-scaled method, the log-linear model, and the extended log-linear model. For this purpose, I perform a Monte Carlo simulation study with three data-generating models: the additive error model, the multiplicative error model, and the overdispersed Poisson model. From the simulation study, I found that the gray-scaled method highly depends on the normality assumption of the gray-scaled cells; hence, this method is appropriate when the error model is multiplicative with the log-normally distributed errors. However, it is less efficient for other types of error distributions, especially when the error model is additive or the errors follow the Poisson distribution. The estimated standard error for the doubling time is not accurate in this case. The log-linear model was found to be efficient when the errors follow the Poisson distribution or nearly Poisson distribution. The efficiency of the log-linear model was decreased accordingly as the overdispersion increased, compared to the extended log-linear model. When the error model is additive or multiplicative with Gamma-distributed errors, the log-linear model is more efficient than the gray-scaled method. The extended log-linear model performs well overall for all three data-generating models. The loss of efficiency of the extended log-linear model is observed only when the error model is multiplicative with log-normally distributed errors, where the gray-scaled method is appropriate. However, the extended log-linear model is more efficient than the log-linear model in this case.     

Reliability Analysis of the Groundwater Conceptual Model

The hydrologic model is the foundation of water resource management and planning. Conceptual model is the essential component of groundwater model. Due to limited understanding of natural hydrogeological conditions, the conceptual model is always constructed incompletely. Therefore, the uncertainty in the model's output is evitable when natural groundwater field is simulated by a single groundwater model. A synthetic groundwater model is built and regarded as the true model, and three alternative conceptual models are constructed by considering incomplete hydrogeological conditions. The outputs (groundwater budget terms from boundary conditions) of these groundwater models are analyzed statistically. The results show that when the conceptual model is closer to the true hydrogeological conditions, the distributions of outputs of the groundwater model are more concentrated on the true outputs. Therefore, the more reliable the structure of the conceptual model is, the more reliable the output of the groundwater model is. Moreover, the uncertainty caused by the conceptual model cannot be compensated by parameter uncertainty.     

Multiple limit cycles in the chemostat with variable yield

The global asymptotic behavior of solutions of the variable yield model is determined. The model generalizes the classical Monod model and it assumes that the yield is an increasing function of the nutrient concentration. In contrast to the Monod model, it is demonstrated that the variable yield model exhibits sustained oscillations. Moreover, it is shown that the variable yield model may undergo a subcritical Hopf bifurcation and feature at least two distinct limit cycles. Implications for the coexistence of competing populations are discussed.     

More Parsimonious Linar-By-Linear Associatin Model in the Analysis of Cross-Classifications Having Ordered Categories

For the analysis of cross-classifications having ordered categories, this paper proposes a model which is more parsimonious than the linear-by-linear association (LL) model (that is, which can be described in terms of fewer parameters than the LL model). In a special case, this model is more parsimonious than the uniform association (U) model. Under this model, the expected frequency on a log scale is a linear function of row and column variables for fixed column and row variables, respectively. For the well-known operation and dumping severity data, the parsimonious U model proposed here fits well, and new interpretations are added.     

Patient-derived orthotopic xenograft (PDOX) mouse model of adult rhabdomyosarcoma invades and recurs after resection in contrast to the subcutaneous ectopic model

Rhabdomyosarcoma (RMS) is a rare mesenchymal tumor. The aim of the present study was to develop a patient-derived orthotopic xenograft (PDOX) mouse model of RMS and compare the PDOX model to a subcutaneous (s.c.)-transplant model. A patient RMS from a striated muscle was grown orthotopically in the right biceps femoris muscle and right quadriceps muscle of nude mice to establish a PDOX model, as well as under the skin to establish an s.c. model. PDOX tumors grew at a statistically-significant faster rate compared to the s.c. tumors. Recurrence after surgical resection occurred only in PDOX tumors, not in the s.c. model. Histologically, only the PDOX model was shown to be invasive. In conclusion, these results indicate that the PDOX model of adult RMS is malignant and the subcutaneous model is benign. These results emphasize that a proper tumor microenvironment is necessary for patient-like behavior of a tumor in a mouse model.     

Parameterization of Multivariate Random Effects Models for Categorical Data

Alternative parameterizations and problems of identification and estimation of multivariate random effects models for categorical responses are investigated. The issues are illustrated in the context of the multivariate binomial logit-normal (BLN) model introduced by Coull and Agresti (2000, Biometrics 56, 73-80). We demonstrate that the BLN model is poorly identified unless proper restrictions are imposed on the parameters. Moreover, estimation of BLN models is unduly computationally complex. In the first application considered by Coull and Agresti, an identification problem results in highly unstable, highly correlated parameter estimates and large standard errors. A probit-normal version of the specified BLN model is demonstrated to be underidentified, whereas the BLN model is empirically underidentified. Identification can be achieved by constraining one of the parameters. We show that a one-factor probit model is equivalent to the probit version of the specified BLN model and that a one-factor logit model is empirically equivalent to the BLN model. Estimation is greatly simplified by using a factor model.     

A Novel Optimal Load Distribution Algorithm for Divisible Loads

A new model for divisible load problem is introduced. Its characteristics are analyzed. Optimal load distribution algorithms on the new model are presented for the tree-network and linear network. Applications that fit our model are briefly described. We show that our model outperforms the existing model such as Cheng–Robertazzi model. We show that the linear model is equivalent to a single-level tree network if the intermediate processors do not follow the store-and-forward communication model, but they follow the store-and-bypass model. This paper introduces the concept of store-and-bypass for divisible load theory.     

Spatial mixture multiscale modeling for aggregated health data

One of the main goals in spatial epidemiology is to study the geographical pattern of disease risks. For such purpose, the convolution model composed of correlated and uncorrelated components is often used. However, one of the two components could be predominant in some regions. To investigate the predominance of the correlated or uncorrelated component for multiple scale data, we propose four different spatial mixture multiscale models by mixing spatially varying probability weights of correlated (CH) and uncorrelated heterogeneities (UH). The first model assumes that there is no linkage between the different scales and, hence, we consider independent mixture convolution models at each scale. The second model introduces linkage between finer and coarser scales via a shared uncorrelated component of the mixture convolution model. The third model is similar to the second model but the linkage between the scales is introduced through the correlated component. Finally, the fourth model accommodates for a scale effect by sharing both CH and UH simultaneously. We applied these models to real and simulated data, and found that the fourth model is the best model followed by the second model.     

Doubly robust estimation in missing data and causal inference models

The goal of this article is to construct doubly robust (DR) estimators in ignorable missing data and causal inference models. In a missing data model, an estimator is DR if it remains consistent when either (but not necessarily both) a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified. Because with observational data one can never be sure that either a missingness model or a complete data model is correct, perhaps the best that can be hoped for is to find a DR estimator. DR estimators, in contrast to standard likelihood-based or (nonaugmented) inverse probability-weighted estimators, give the analyst two chances, instead of only one, to make a valid inference. In a causal inference model, an estimator is DR if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified. Because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct, inference based on DR estimators should improve upon previous approaches. Indeed, we present the results of simulation studies which demonstrate that the finite sample performance of DR estimators is as impressive as theory would predict. The proposed method is applied to a cardiovascular clinical trial.     

Interactions of small nonpolar molecules with biological membranes: an exactly solvable model

An exactly solvable model of the interaction of small nonpolar molecules with biological membranes is developed. This model, which is based upon a “decorated dimer model” extension of Nagle's membrane model, is demonstrated to qualitatively reproduce many of the changes in the order-disorder phase transition seen when biological membranes are exposed to anesthetic gases. The decorated dimer model is itself interesting because it provides an example of an exactly solvable monomer-dimer model in which phase transitions can occur in the presence of monomers.     

A modified mathematical model of the anatomy of the cardiac left ventricle

A modification of the mathematical model of the shape and fiber direction field of the left cardiac ventricle is presented. The model was developed based on the idea of nested spiral surfaces. The ventricle is composed of surfaces that model myocardial layers. Each layer is filled with curves corresponding to myocardial fibers. The tangents to these curves form the myofiber direction field. A modified spherical coordinate system is linked with the model left ventricle, where the ventricular boundaries are coordinate surfaces. The model is based on echocardiographic, computed-tomography, or magnetic-resonance-imaging data. For this purpose, four-chamber and two-chamber echocardiography views or sections along the long axis of the left ventricle from these tomographic data in several positions are approximated with a model profile. To construct a 3D model, we then interpolate model parameters by periodic cubic splines and the vector field of the tangents to the model fibers is calculated. For verification of the model, we used diffusion-tensor magneticresonance-imaging data of the human heart.     

The SMM model as a boundary value problem using the discrete diffusion equation

A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.     

Development of a constructed subsurface-flow wetland simulation model

This paper presents a mechanistic, compartmental simulation model of subsurface-flow constructed wetlands. The model consists of six submodels, including the nitrogen and carbon cycles, both autotrophic and heterotrophic bacteria growth and metabolism, and water and oxygen balances. Data from an existing constructed wetland in Maryland were used to calibrate the model. Model results reproduced seasonal trends well. Interactions between the carbon, nitrogen, and oxygen cycles were evident in model output. In general, effluent biochemical oxygen demand, organic nitrogen, ammonium and nitrate concentrations were predicted well. Because little is known about rootzone aeration by wetland plants, oxygen predictions were fair. The model is generally insensitive to changes in individual parameters. This is due to the complexity of the ecosystem and the model, as well as the numerous feedback mechanisms. The model is most sensitive to changes in parameters that affect microbial growth and substrate use directly. This dynamic, compartmental, simulation model is an effective tool for evaluating the performance of subsurface-flow constructed wetlands. The model provided insights into treatment problems at an existing constructed wetland. With further evaluation and refinement, the model will be a useful design tool for subsurface-flow constructed wetlands.     

枯落物分解研究方法和模型讨论

由于研究目的、尺度范围和要求精度的不同,枯落物分解的研究方法各异：野外分解袋法是最直接和最准确的方法,但是耗时太长;室内分解培养法与野外分解袋法相似,但具有灵活设计试验方案的优越性;现量估算法方法简捷,但是只对进入稳定发展和动态平衡阶段的生态系统可以获得较好的精度;综合平衡法能反映整个生长历史时期的枯落物分解速率平均水平,但其准确性取决于对历年凋落物量预测的精度。在枯落物分解模型中,分解率概算模型只适合于林地枯落物积累达到动态平衡时的情况,所以作者提出了另外的枯落物动态平衡模型予以修正;时间衰减模型以Olson指数模型为典型代表,但由于在应用过程中存在一些问题,也提出了相应的修正办法;影响因子关系模型包括基质质量因子关系模型、非生物环境因子关系模型和生物因子关系模型等类型。作者提出构建过程模型将是未来枯落物分解模型研究的方向。     

Analysis of several biomechanical models for the simulation of lamb liver behaviour using similarity coefficients from medical image

In this study, six biomechanical models for simulating lamb liver behaviour are presented. They are validated using similarity coefficients from Medical Image on reconstructed volumes from computerised tomography images. In particular, the Jaccard and Hausdorff coefficients are used. Loads of 20 and 40 g are applied to the livers and their deformation is simulated by means of the finite element method. The models used are a linear elastic model, a neo-Hookean model, a Mooney–Rivlin model, an Ogden model, a linear viscoelastic model and a viscohyperelastic model. The model that provided a behaviour that is closest to reality was the viscohyperelastic model, where the hyperelastic part was modelled with an Ogden model.     

Application of CT images in the diagnosis of lung cancer based on finite mixed model

ObjectiveInvestigating the application of CT images when diagnosing lung cancer based on finite mixture model is the objective. Method: 120 clean healthy rats were taken as the research objects to establish lung cancer rat model and carry out lung CT image examination. After the successful CT image data preprocessing, the image is segmented by different methods, which include lung nodule segmentation on the basis of Adaptive Particle Swarm Optimization – Gaussian mixture model (APSO-GMM), lung nodule segmentation on the basis of Adaptive Particle Swarm Optimization – gamma mixture model (APSO-GaMM), lung nodule segmentation based on statistical information and self-selected mixed distribution model, and lung nodule segmentation based on neighborhood information and self-selected mixed distribution model. The segmentation effect is evaluated. Results: Compared with the results of lung nodule segmentation based on statistical information and self-selected mixed distribution model, the Dice coefficient of lung nodule segmentation based on neighborhood information and self-selected mixed distribution model is higher, the relative final measurement accuracy is smaller, the segmentation is more accurate, but the running time is longer. Compared with APSO-GMM and APSO-GaMM, the dice value of self-selected mixed distribution model segmentation method is larger, and the final measurement accuracy is smaller. Conclusion: Among the five methods, the dice value of the self-selected mixed distribution model based on neighborhood information is the largest, and the relative accuracy of the final measurement is the smallest, indicating that the segmentation effect of the self-selected mixed distribution model based on neighborhood information is the best.     

Bayesian informative dropout model for longitudinal binary data with random effects using conditional and joint modeling approaches

Dropouts are common in longitudinal study. If the dropout probability depends on the missing observations at or after dropout, this type of dropout is called informative (or nonignorable) dropout (ID). Failure to accommodate such dropout mechanism into the model will bias the parameter estimates. We propose a conditional autoregressive model for longitudinal binary data with an ID model such that the probabilities of positive outcomes as well as the drop‐out indicator in each occasion are logit linear in some covariates and outcomes. This model adopting a marginal model for outcomes and a conditional model for dropouts is called a selection model. To allow for the heterogeneity and clustering effects, the outcome model is extended to incorporate mixture and random effects. Lastly, the model is further extended to a novel model that models the outcome and dropout jointly such that their dependency is formulated through an odds ratio function. Parameters are estimated by a Bayesian approach implemented using the user‐friendly Bayesian software WinBUGS. A methadone clinic dataset is analyzed to illustrate the proposed models. Result shows that the treatment time effect is still significant but weaker after allowing for an ID process in the data. Finally the effect of drop‐out on parameter estimates is evaluated through simulation studies.     

Computation of a Stabilizing Set of Feedback Matrices bf a Large-scale Nonlinear Musculoskeletal Dynamic Model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/ output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.