A Multiple‐Absorbent Markov Process in Survival Studies: Application to Breast Cancer

A Markov process with several absorbent states is applied for analyzing a breast cancer dataset. The study examines the evolution of patients until death, and shows that two well‐differentiated ways can be considered in the evolution of patients towards the death state: those who relapse and those who not. The risk groups we have considered are determined by the application of treatments radiotherapy and chemotherapy, which are introduced as covariates. Four states are distinguished: no relapse, relapse, death after metastasis, and death without metastasis, the last two absorbent. We apply a methodology that uses algorithmic procedures, avoiding differential equations. The transition probability functions and the likelihood function in the model are calculated. For the dataset, the survival functions and the mean times in states for the different group of risks are determined. We show that the metastasis is the main cause of death in this cohort, but the number of deaths by relapse is not negligible.     

Application of discrete cosine transform to assess the effect of tumor motion variations on the definition of ITV in lung and liver SBRT

PurposeTo use Discrete Cosine Transform to include tumor motion variations on ITV definition of SBRT patients.MethodsData from 66 patients was collected. 2D planar fluoroscopy images (FI) were available for 54 patients. Daily CBCT projections (CBCTp) from 29 patients were employed to measure interfraction amplitude variability. Systematic amplitude variations were obtained from 17 patients with data from both FI and CBCTp.Tumor motion curves obtained from FI were characterized with a Cosine model (CM), based on cosine functions to the power of 2, 4 or 6, and DCT. Performance of both models was evaluated by means of R² coefficient and by comparing their results on Internal Target Volume (ITV) margins against those calculated from original tumor motion curves.Amplitude variations from CBCTp, as well as estimations of baseline shift variations were added to the DCT model to account for their effect on ITV margins.ResultsDCT replicated tumor motion curves with a mean R² values for all patients of 0.86, 0.91 and 0.96 for the lateral (LAT), anterior-posterior (AP) and cranio-caudal (CC) directions respectively. CM yielded worst results, with R² values of 0.64, 0.61 and 0.74 in the three directions.Interfraction amplitude variation increased ITV margins by a 9%, while baseline shift variability implied a 40% and 80–100% increase for normalized values of baseline shift of 0.2 and 0.4 respectively.ConclusionsProbability distribution functions of tumor positions can be successfully characterized with DCT. This permits to include tumor motion variablilities obtained from patient population into patient specific ITVs.     

New approaches to the simulation of heat-capacity curves and phase diagrams of pseudobinary phospholipid mixtures.

A simulation program using least-squares minimization was developed to calculate and fit heat capacity (cp) curves to experimental thermograms of dilute aqueous dispersions of phospholipid mixtures determined by high-sensitivity differential scanning calorimetry. We analyzed cp curves and phase diagrams of the pseudobinary aqueous lipid systems 1,2-dimyristoyl-sn-glycero-3-phosphatidylglycerol/ 1,2-dipalmitoyl-sn-glycero-3phosphatidylcholine (DMPG/DPPC) and 1,2-dimyristoyl-sn-glycero-3-phosphatidic acid/1, 2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DMPA/DPPC) at pH 7. The simulation of the cp curves is based on regular solution theory using two nonideality parameters rho g and rho l for symmetric nonideal mixing in the gel and the liquid-crystalline phases. The broadening of the cp curves owing to limited cooperativity is incorporated into the simulation by convolution of the cp curves calculated for infinite cooperativity with a broadening function derived from a simple two-state transition model with the cooperative unit size n = delta HVH/delta Hcal as an adjustable parameter. The nonideality parameters and the cooperative unit size turn out to be functions of composition. In a second step, phase diagrams were calculated and fitted to the experimental data by use of regular solution theory with four different model assumptions. The best fits were obtained with a four-parameter model based on nonsymmetric, nonideal mixing in both phases. The simulations of the phase diagrams show that the absolute values of the nonideality parameters can be changed in a certain range without large effects on the shape of the phase diagram as long as the difference of the nonideality parameters for rho g for the gel and rho l for the liquid-crystalline phase remains constant. The miscibility in DMPG/DPPC and DMPA/DPPC mixtures differs remarkably because, for DMPG/DPPC, delta rho = rho l -rho g is negative, whereas for DMPA/DPPC this difference is positive. For DMPA/DPPC, this difference is interpreted as being caused by a negative rho g value, indicating complex formation of unlike molecules in the gel phase.     

A novel risk signature that combines 10 long noncoding RNAs to predict neuroblastoma prognosis

Neuroblastoma (NBL) is the most frequently encountered extracranial solid neoplasm and impacts significantly on the survival of patients, especially in cases of advanced tumor stage or relapse. A long noncoding RNA (lncRNA) signature to predict the survival of patients with NBL is proposed in this paper. Differentially expressed lncRNA (DElncRNA) was selected using the Limma plus Voom package in R based on the RNA-sequencing data downloaded from the Therapeutically Applicable Research To Generate Effective Treatments database and Genotype-Tissue Expression database. Univariate cox regression analysis, least absolute shrinkage and selection operator regression analysis, and multivariate cox regression analysis were conducted to identify candidate DElncRNAs for the risk signature. Consequently, 10 DElncRNAs were designated as candidate DElncRNAs for the risk signature. Time-dependent receiver operating characteristic curves and Kapan–Meier survival curves confirmed the efficacy of the risk signature in predicting the survival of patients with NBL (area under the curve = 0.941; p ≤ .001). One of the DElncRNA constituent subparts (LINC01010) was significantly associated with the survival outcome of patients with NBL in GSE62564 (p = .004). Thus, a risk signature comprising 10 DElncRNAs was identified as effective for individual risk stratification and the survival prediction outcomes of patients with NBL.     

Cardiac excitation mechanisms, wavefront dynamics and strength-interval curves predicted by 3D orthotropic bidomain simulations

The assessment and understanding of cardiac excitation mechanisms is very important for the development and improvement of implantable cardiac devices, pacing protocols, and arrhythmia treatments. Previous bidomain simulation studies have investigated cathodal and anodal make/break mechanisms of cardiac excitation and strength-interval (S-I) curves in two-dimensional sheets or cylindrical domains, that by symmetry reduce to the two-dimensional case. In this work, cathodal and anodal S-I curves are studied by means of detailed bidomain simulations which include: (i) three-dimensional cardiac slabs; (ii) transmural fiber rotation; (iii) unequal orthotropic anisotropy of the conducting media; (iv) incorporation of funny and electroporation currents in the ventricular membrane model. The predicted shape of cathodal and anodal S-I curves exhibit the same features of the S-I curves observed experimentally and the break/make transition coincides with the final descending phase of the S-I curves. Away from the break/make transition, only the break or make excitation mechanism is observed independently of the stimulus strength, whereas within an interval at the break/make transition, new paradoxical excitation behaviors are observed that depend on the stimulus strength.     

A model of microbial survival curves in water treated with a volatile disinfectant

AIM: To develop a method to calculate microbial survival parameters in water treated with a dissipating disinfectant and predict the inactivation patterns under different agent concentrations and decay rate regimes. METHODS AND RESULTS: It has been assumed that the survival curves of the organism, under (hypothetical) constant agent concentration conditions, follow the power law model log [N(t)/N0] = -btn with a concentration independent exponent, n. The concentration dependence of the 'rate parameter', b, has been assumed to obey a log logistic relationship. Under changing disinfectant concentration, the survival curve is constructed so that its local slope, i.e. momentary logarithmic inactivation rate of the organism, is the slope of the momentary 'constant concentration' curve at the momentary agent concentration, at the time which corresponds to the momentary survival ratio. The resulting differential equation was used to retrieve the survival parameters by numerical minimization procedures. Once these are calculated, the equation is solved numerically to produce the survival curve for almost any conceivable agent concentration history. The predictive ability of the method is demonstrated by using the survival parameters, calculated from published data obtained under one concentration profile, to predict survival curves under very different decay patterns. CONCLUSIONS: It is possible to calculate microbial survival parameters from data obtained in treatments where the unstable or volatile disinfectant progressively dissipates and use them to predict the outcome of different treatments. SIGNIFICANCE AND IMPACT OF THE STUDY: The proposed mathematical method will enable the prediction of microbial inactivation patterns in water treated with unstable and/or volatile chemical agents.     

Volumetric properties of the formation of double stranded DNA: a nearest-neighbor analysis

The kinetics of the helix-coil transition have been studied by performing UV-monitored melting and reannealing curves of DNA and analyzing the resultant hysteresis between these curves. The analysis assumes a single-step bimolecular transition with duplex formation defined as the forward reaction. Volume parameters of the helix-coil transition were obtained by measuring the pressure dependence of the rate constants from 5-200 MPa. The data were interpreted in terms of several possible nearest-neighbor models, ranging from one to eleven parameters. Twenty-four oligonucleotide duplexes 22 base pairs in length were used to solve for individual nearest-neighbor activation volumes and transition volumes. Statistically, the most valid fit of the volumetric data was obtained with a six-parameter model in which the directionality of the dinucleotide steps is not considered, for example, 5'AG/CT is the same as 5'GA/TC. The resultant transition volumes at 48 degrees C ranged from -7.1 +/- 0.8 mL/mol (GC/CG) to +2.9 +/- 0.3 mL/mol (AA/TT). The success of the six-parameter model suggests that the relative size of the nearest-neighbor dinucleotides is the most important factor determining the magnitude of the volumetric parameters. The finding that the magnitude of the volumetric parameters correlates with the change in the solvent accessible surface area of the bases during the helix-coil transition corroborates this hypothesis.     

Frequency responses of cat rapidly adapting mechanoreceptive fibers

The frequency responses of 11 rapidly adapting (RA) fibers in cat were studied by representing the average firing rate as a function of sinusoidal stimulus amplitude and stimulus frequency. Specifically, rate-intensity functions at different stimulation frequencies were fitted by four-parameter (a0, a1, a2, a3), piece-wise linear functions using nonlinear regression (n = 59; R2 > 0.877). Rate-intensity functions at intermediate frequencies were found by linear interpolation. The result of this analysis is rate-amplitude-frequency functions plotted as two-dimensional surfaces. The surfaces consist of five regions separated and sufficiently defined by four space curves. At 14 different frequencies, the statistical distribution of each rate-intensity-function parameter could be approximated by a particular lognormal distribution (n = 56; R2 > 0.796). The Kolmogorov-Smirnov test fails to reject this hypothesis for each combination of frequency and parameter (56 tests; p > 0.39). Therefore, at a given frequency, the variation of the parameters can be represented by lognormal distributions with specific means and standard deviations. Responses of six RA fibers, which are different from the data-set used for modeling, were compared with the stochastic model at different frequencies. The parameters of those fibers were tested against the null hypotheses that they were sampled from the particular parameter distributions dictated by the model. The Kolmogorov-Smirnov test fails to reject all the hypotheses at the alpha = 0.05 level (44 tests). At the alpha = 0.10 level, only a few test parameters were found to be departing from the model (a0 and a1 at 5 Hz; a2 at 20 Hz; a2 and a3 at 50 Hz). The remaining test parameters could be accurately described by the model. Having confirmed the validity of the model, the logarithmic means and the logarithmic standard deviations of the lognormally distributed rate-intensity-function parameters were estimated in the frequency range of 4-200 Hz. The rate-amplitude-frequency surfaces sampled from the established stochastic model completely characterize the rate responses of RA fibers to sinusoidal stimuli and are superior to tuning curves which require selecting criterion responses. The current rate-response model is promising for future computational work, especially on population modeling.     

Thermal perturbation differential spectra of ribonucleic acids. II. Nearest neighbour interactions.

Dinucleoside monophosphates are used here as models for studying sequence dependence of the hypochromic effect correlated with base stacking. It was shown that once the contribution due to the temperature dependent hydration change of the bases is substracted from the thermal perturbation difference spectra of dinucleoside monophosphates, the absorbance change of the dimer only due to unstacking of the bases could be obtained. In order to be able to use these corrected thermal perturbation difference spectra as models for studying nearest neighbour interactions in nucleic acids, it was necessary to normalize them to 100% unstacking of the bases. To perform this normalization, apparent thermodynamic parameters were extracted from the corrected transition curves by means of the two-state model.     

结合自噬相关基因表达谱和临床因素的肺腺癌预后预测模型

对肺腺癌自噬相关基因进行生物信息学分析,结合多基因预后标志和临床参数构建能够预测肺腺癌患者预后的模型。首先,对TCGA肺腺癌数据中的938个自噬相关基因进行差异分析,获得了82个差异自噬相关基因,使用单因素Cox比例风险回归模型从差异自噬相关基因中筛选出候选基因,通过 lasso回归进一步筛选出预后相关基因,分别是ARNTL2、NAPSA、ATG9B、CAPN12、MAP1LC3C和KRT81。通过多因素Cox回归分析以构建风险评分模型,根据最优cutoff值将患者分为高低风险组,生存曲线显示高低风险组之间生存差异显著,ROC曲线显示风险评分的预测能力良好,并在内、外验证集中得到验证。同时对传统的临床因素进行单因素和多因素Cox回归分析,结果显示Stage、复发和风险评分能够独立预测预后,结合这三个独立的预后参数以构建列线图模型,使用一致性指数、校准曲线评估列线图的预测能力,结果显示预测结果与实际结果之间具有良好的一致性。通过与Stage和风险评分的比较发现,列线图的预测能力表现最佳。基于肺腺癌相关的自噬基因和临床参数构建了一个列线图模型来预测肺腺癌患者的预后生存,这可能为临床医生提供了一种可靠的预后评估工具。     

Modeling survival of experimentally virus-infected laboratory animals

Although survival analysis is a well-established mathematical discipline, there seem to be almost no attempts in survival modeling for experimentally virus-infected laboratory animals. We have taken up a stochastic approach originally developed by Shortley in the sixties and have applied it to three different types of experimental data: to virus titer determination, to the dose dependence of the mean survival time and to single survival curves. Experience concerning parameter estimation is reported and new ways of working with the model parameters are proposed. A standard mean survival time is defined and suggested as a new quantitative measure of virulence. Moreover, for the comparison of two experiments for which the amount of virions inoculated is kept fixed, but for which other parameters may vary, a new scheme of systematizing survival data from experimentally virus-infected laboratory animals is proposed. It is very likely that the model can be also applied to cancer survival data or any other infectious pathogen.     

Estimating microbial inactivation parameters from survival curves obtained under varying conditions--the linear case

When the isothermal semi-logarithmic survival curves of heat inactivated microbial cells or spores are known to be linear it is possible to calculate their survival parameters from curves obtained under nonisothermal conditions, provided that the temperature history (’profile’) satisfies certain simple mathematical requirements. These requirements have been identified. The concept was tested by retrieving the survival parameters of a Listeria-like organism from generated survival curves for linear and nonlinear heating profiles on which noise had been superimposed. The availability of such a procedure eliminates the need to determine the survival parameters under perfect isothermal conditions, which are difficult to create for technical reasons. It will also enable determination of the survival parameters in the actual medium of interest, which may contain particles or may be too viscous to be treated in a capillary or narrow tube as is currently done. The method can also be used to assess survival parameters in nonthermal inactivation. A treatment with a dissipating chemical agent or anti-microbial is an example. In principle, the concept can be extended to the more general situation where the isothermal or iso-concentration semi-logarithmic survival curves are clearly nonlinear, but this will require a modification of the model and a different numerical calculation procedure.     

Effects of Continuous Low Dose-Rate Irradiation: Computer Simulations

Abstract. The effects of continuous low dose-rate irradiation are studied with a computer model that incorporates cell kinetics and the accumulation and repair of radiation damage. This theoretical approach independently explores the effects on survival curves of a phase block, inherited damage and proliferation by dying cells. the computer model is a Monte Carlo simulation which follows the evolution in time of the family trees of a growing cell population under continuous irradiation. the model uses as input the measured phase-specific survival curves for acute exposures and the cell kinetic parameters to generate survival curves for continous low dose-rate irradiations. Cell survival curves for Chinese hamster lung cells (V79) for dose rates ranging from 15 to 500 cGy/h have been generated using various model assumptions. the model shows that for these cells a G₂ block will maximize cell killing for an optimum dose rate near 75 cGy/h. the effect on survival curves of inherited damage, as well as that of the proliferation by dying cells, is shown to increase monotonically with decreasing dose rates, and to be quite large at low dose rates.     

Effects of continuous low dose-rate irradiation: computer simulations

The effects of continuous low dose-rate irradiation are studied with a computer model that incorporates cell kinetics and the accumulation and repair of radiation damage. This theoretical approach independently explores the effects on survival curves of a phase block, inherited damage and proliferation by dying cells. The computer model is a Monte Carlo simulation which follows the evolution in time of the family trees of a growing cell population under continuous irradiation. The model uses as input the measured phase-specific survival curves for acute exposures and the cell kinetic parameters to generate survival curves for continuous low dose-rate irradiations. Cell survival curves for Chinese hamster lung cells (V79) for dose rates ranging from 15 to 500 cGy/h have been generated using various model assumptions. The model shows that for these cells a G2 block will maximize cell killing for an optimum dose rate near 75 cGy/h. The effect on survival curves of inherited damage, as well as that of the proliferation by dying cells, is shown to increase monotonically with decreasing dose rates, and to be quite large at low dose rates.     

Maximum likelihood inference and bootstrap methods for plant organ growth via multi-phase kinetic models and their application to maize

* BACKGROUND AND AIMS: Fitting the parameters of models of plant organ growth is a means to investigate how environmental conditions affect plant architecture. The aim of this article is to evaluate some non-linear methods for fitting the parameters of multi-phase models of the kinetics of extension of plant organs such as laminae, sheaths and internodes. * METHODS: A set of computational procedures was developed allowing parameter-fitting of multi-phase models, using the maximum likelihood criterion, in which phases are identified with reference to ontogenic processes. Two bootstrap methods were compared to assess the precision of the estimates of fitted parameters, and of functions of these parameters such as the final leaf length, and the duration and rate of the rapid extension phase. Methods were applied to an experimental dataset, representing the kinetics of laminae, sheaths and internodes along the maize shoot, for two contrasting densities. * KEY RESULTS: A set of multi-phase models was proposed to describe the extension of laminae, sheaths and internodes along the shoot. The distinguishable phases differed between laminae, sheaths and internodes. For sheaths and laminae, but not for internodes, the same model could be fitted to all phytomers along the shoot. The variation of parameters along the shoot and between density treatments, as well as derived functions such as the durations of the phases of extension, are presented for laminae. It was the duration of the fast extension period, rather than its rate, which determined the difference in final length between treatments. * CONCLUSIONS: Such methods permit a large degree of objectivity and facilitate the analysis of such rather complicated but co-ordinated datasets. The work also illustrates some natural limitations of maximum likelihood methods, and viable ways of overcoming them by including a priori knowledge in the model fitting method are discussed.     

Using cross-validation to evaluate predictive accuracy of survival risk classifiers based on high-dimensional data

Developments in whole genome biotechnology have stimulated statistical focus on prediction methods. We review here methodology for classifying patients into survival risk groups and for using cross-validation to evaluate such classifications. Measures of discrimination for survival risk models include separation of survival curves, time-dependent ROC curves and Harrell's concordance index. For high-dimensional data applications, however, computing these measures as re-substitution statistics on the same data used for model development results in highly biased estimates. Most developments in methodology for survival risk modeling with high-dimensional data have utilized separate test data sets for model evaluation. Cross-validation has sometimes been used for optimization of tuning parameters. In many applications, however, the data available are too limited for effective division into training and test sets and consequently authors have often either reported re-substitution statistics or analyzed their data using binary classification methods in order to utilize familiar cross-validation. In this article we have tried to indicate how to utilize cross-validation for the evaluation of survival risk models; specifically how to compute cross-validated estimates of survival distributions for predicted risk groups and how to compute cross-validated time-dependent ROC curves. We have also discussed evaluation of the statistical significance of a survival risk model and evaluation of whether high-dimensional genomic data adds predictive accuracy to a model based on standard covariates alone.     

A 23-gene prognostic classifier for prediction of recurrence and survival for Asian breast cancer patients

We report a 23- gene-classifier profiled from Asian women, with the primary purpose of assessing its clinical utility towards improved risk stratification for relapse for breast cancer patients from Asian cohorts within 10 years’ following mastectomy. Four hundred and twenty-two breast cancer patients underwent mastectomy and were used to train the classifier on a logistic regression model. A subset of 197 patients were chosen to be entered into the follow-up studies post mastectomy who were examined to determine the patterns of recurrence and survival analysis based on gene expression of the gene classifier, age at diagnosis, tumor stage and lymph node status, over a 5 and 10 years follow-up period. Metastasis to lymph node (N2-N3) with N0 as the reference (N2 vs. N0 hazard ratio: 2.02 (1.05–8.70), N3 vs. N0 hazard ratio: 4.32 (1.41–13.22) for 5 years) and gene expression of the 23-gene panel (P=0.06, 5 years and 0.02, 10 years, log-rank test) were found to have significant discriminatory effects on the risk of relapse (HR (95%CI):2.50 (0.95–6.50)). Furthermore, survival curves for subgroup analysis with N0-N1 and T1-T2 predicted patients with higher risk scores. The study provides robust evidence of the effectiveness of the 23-gene-classifier and could be used to determine the risk of relapse event (locoregional and distant recurrence) in Asian patients, leading to a meaningful reduction in chemotherapy recommendations.     

On translocation through a membrane channel via an internal binding site: kinetics and voltage dependence

Here we present a model for maltodextrin translocation through maltoporin channels. In a first step, our theoretical analysis does consider the case of a single binding site for a given substrate in a structurally unaffected channel with a possibly different entrance barrier on either side. It is shown how by means of conventional electrical conductance measurements (including current noise analysis) the basic equilibrium and rate constants can be determined as functions of the applied voltage. Then also the net translocation rate of the substrate becomes accessible quantitatively. This most simple model mechanism has been extended to include a voltage-dependent fast conformational change of the channel that prevents the binding process. The so developed approach has been tested with experimental data for a single maltoporin trimer being reconstituted in black lipid membranes when studied in the presence of maltohexaose as the substrate. The experimental results turned out to be clearly incompatible with binding alone. They are, however, very satisfactorily fitted by pertinent theoretical curves if also inhibition of binding by a conformational transition is taken into account. Accordingly, quantitative evaluations of the underlying parameters and eventually of the translocation rate have been carried out successfully. Our analysis reveals a set of parameters necessary for an optimal translocation that nicely corresponds to natural conditions.     

A penalized likelihood approach for an illness-death model with interval-censored data: application to age-specific incidence of dementia

We consider the problem of estimating the intensity functions for a continuous time 'illness-death' model with intermittently observed data. In such a case, it may happen that a subject becomes diseased between two visits and dies without being observed. Consequently, there is an uncertainty about the precise number of transitions. Estimating the intensity of transition from health to illness by survival analysis (treating death as censoring) is biased downwards. Furthermore, the dates of transitions between states are not known exactly. We propose to estimate the intensity functions by maximizing a penalized likelihood. The method yields smooth estimates without parametric assumptions. This is illustrated using data from a large cohort study on cerebral ageing. The age-specific incidence of dementia is estimated using an illness-death approach and a survival approach.     

The influence of local environment on the aging and mortality ofAedes aegypti (L.): Case study in Fortaleza‐CE,Brazil

It is generally assumed that the daily probability of survival of mosquitoes is independent of age. To test this assumption we have conducted a three‐year experimental fieldwork study (2005–2007) at Fortaleza‐CE in Brazil, determining daily survival rates of the dengue vector Aedes aegypti (L.). Survival rates of adult Ae. aegypti may be age‐dependent and the statistical analysis is a sensitive approach for comparing patterns of mosquito survival. The mosquito survival data were better fit by a Weibull survival function than by the more traditionally used Gompertz or logistic survival functions. Gompertz, Weibull, or logistic survival functions often fit the survival, and the tails of the survival curves usually appear to fall between the values predicted by the three functions. We corroborate that the mortality of Ae. aegypti in semi‐natural conditions may no more be considered as a constant phenomenon during the life of adult mosquitoes but varies according to the age and environmental conditions under a tropical climate. This study estimates the variability in the survival rate of Ae. aegypti and environmental factors that are related to such variability. The statistical analysis shows that the fitting ability, concerning the hazard function, was in decreasing order: Seasonal Cox, the three‐parameter Gompertz, and the three‐parameter Weibull, that was similar to the three‐parameter logistic. The advantage of using the Cox model is that it is convenient for exploring the relationship between survival and several explanatory variables. The Cox model has the advantage of preserving the variable in its original quantitative form and of using a maximum of information. The survival analyses indicate that mosquito mortality is both age‐ and environment‐dependent.