Comparison of statistical methods for the analysis of limiting dilution assays

Summary This study reports the results of a critical comparison of five statistical methods for estimating the density of viable cells in a limiting dilution assay (LDA). Artificial data were generated using Monte Carlo simulation. The performance of each statistical method was examined with respect to the accuracy of its estimator and, most importantly, the accuracy of its associated estimated standard error (SE). The regression method was found to perform at a level that is unacceptable for scientific research, due primarily to gross underestimation of the SE. The maximum likelihood method exhibited the best overall performance. A corrected version of Taswell's weighted-mean method, which provides the best performance among all noniterative methods examined, is also presented.     

Power analysis of statistical methods for comparing treatment differences from limiting dilution assays

Summary Six different statistical methods for comparing limiting dilution assays were evaluated, using both real data and a power analysis of simulated data. Simulated data consisted of a series of 12 dilutions for two treatment groups with 24 cultures per dilution and 1,000 independent replications of each experiment. Data within each replication were generated by Monte Carlo simulation, based on a probability model of the experiment. Analyses of the simulated data revealed that the type I error rates for the six methods differed substantially, with only likelihood ratio and Taswell's weighted mean methods approximating the nominal 5% significance level. Of the six methods, likelihood ratio and Taswell's minimum Chi-square exhibited the best power (least probability of type II errors). Taswell's weighted mean test yielded acceptable type I and type II error rates, whereas the regression method was judged unacceptable for scientific work.     

Statistical analysis of data from limiting dilution cloning to assess monoclonality in generating manufacturing cell lines

Assurance of monoclonality of recombinant cell lines is a critical issue to gain regulatory approval in biological license application (BLA). Some of the requirements of regulatory agencies are the use of proper documentations and appropriate statistical analysis to demonstrate monoclonality. In some cases, one round may be sufficient to demonstrate monoclonality. In this article, we propose the use of confidence intervals for assessing monoclonality for limiting dilution cloning in the generation of recombinant manufacturing cell lines based on a single round. The use of confidence intervals instead of point estimates allow practitioners to account for the uncertainty present in the data when assessing whether an estimated level of monoclonality is consistent with regulatory requirements. In other cases, one round may not be sufficient and two consecutive rounds are required to assess monoclonality. When two consecutive subclonings are required, we improved the present methodology by reducing the infinite series proposed by Coller and Coller (Hybridoma 1983;2:91–96) to a simpler series. The proposed simpler series provides more accurate and reliable results. It also reduces the level of computation and can be easily implemented in any spreadsheet program like Microsoft Excel. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 32:1061–1068, 2016     

Quantifying the frequency of tumor-propagating cells using limiting dilution cell transplantation in syngeneic zebrafish

Self-renewing cancer cells are the only cell types within a tumor that have an unlimited ability to promote tumor growth, and are thus known as tumor-propagating cells, or tumor-initiating cells. It is thought that targeting these self-renewing cells for destruction will block tumor progression and stop relapse, greatly improving patient prognosis. The most common way to determine the frequency of self-renewing cells within a tumor is a limiting dilution cell transplantation assay, in which tumor cells are transplanted into recipient animals at increasing doses; the proportion of animals that develop tumors is used the calculate the number of self-renewing cells within the original tumor sample. Ideally, a large number of animals would be used in each limiting dilution experiment to accurately determine the frequency of tumor-propagating cells. However, large scale experiments involving mice are costly, and most limiting dilution assays use only 10-15 mice per experiment. Zebrafish have gained prominence as a cancer model, in large part due to their ease of genetic manipulation and the economy by which large scale experiments can be performed. Additionally, the cancer types modeled in zebrafish have been found to closely mimic their counterpart human disease. While it is possible to transplant tumor cells from one fish to another by sub-lethal irradiation of recipient animals, the regeneration of the immune system after 21 days often causes tumor regression. The recent creation of syngeneic zebrafish has greatly facilitated tumor transplantation studies. Because these animals are genetically identical, transplanted tumor cells engraft robustly into recipient fish, and tumor growth can be monitored over long periods of time. Syngeneic zebrafish are ideal for limiting dilution transplantation assays in that tumor cells do not have to adapt to growth in a foreign microenvironment, which may underestimate self-renewing cell frequency. Additionally, one-cell transplants have been successfully completed using syngeneic zebrafish and several hundred animals can be easily and economically transplanted at one time, both of which serve to provide a more accurate estimate of self-renewing cell frequency. Here, a method is presented for creating primary, fluorescently-labeled T-cell acute lymphoblastic leukemia (T-ALL) in syngeneic zebrafish, and transplanting these tumors at limiting dilution into adult fish to determine self-renewing cell frequency. While leukemia is provided as an example, this protocol is suitable to determine the frequency of tumor-propagating cells using any cancer model in the zebrafish.     

Comparative Studies on the Estimation of Genetic Variances by Several Variance Components Estimation Method

Using a quantitative genetic model, this paper compares four different methods for estimating genetic variance components. Given various genetic parameters, data were generated and estimates computed. The number of negative estimates, the sample mean, the sample variance, and the sample mean squared error were computed for each method. It is shown that, if the genetic values are not very small, the traditional MATHER -JINKS method is at least as good as any other method. The ML method might be preferable only if the genetic values are very small and the number of loci large.     

Small Sample Properties of the Likelihood Estimator in Proportional Hazard Regression Models with Omitted Variables

The paper deals with the effects of incorrectly omitted regressor variables in a parametric proportional hazard regression model. By studying conditions for equality between the estimators of correct and incorrect models it is demonstrated analytically that such cases are not to be expected in practise. A small sample Monte Carlo experiment indicates severe negative effects on the retained parameters both in terms of bias and mean square error.     

The effect of dielectric polarization of the electrode on anomalous temperature effects in the electrical double layer

Monte Carlo simulations and a modified Poisson–Boltzmann (MPB) theory are used to investigate the temperature dependence of the capacitance (around the potential of zero charge) of an electric double layer in the presence of surface polarization due to a dielectric boundary. Within the context of the restricted primitive model planar double layer, whose solvent dielectric constant is ε₂, the cases when the electrode is an insulator (ε₁ = 1), when the electrode and the electrolyte have the same permittivity (ε₁ = ε₂, no polarization), and when the electrode is a conductor (ε₁ → ∞) are studied for the case where the electrolyte concentration is 0.1 M. The simulations reveal a capacitance anomaly, that is, a positive temperature dependence of the capacitance at low temperatures for the former two situations. The MPB theory also shows this effect for these two situations and is in qualitative or better agreement with the simulation data. In these two cases, both the simulations and theory show a dramatic increase of the diffuse layer potential in the temperature regime where capacitance anomaly occurs. However, in the latter situation, where the electrode is metallic, the capacitance always has a negative temperature derivative for the MPB theory and probably also for the simulation data.     

Analysis of foraging behavior of the whitefly parasitoidEncarsia formosa (Hymenoptera: Aphelinidae) in an experimental arena: A simulation study

Foraging ofEncarsia formosa was analyzed using a stochastic simulation model of the parasitoid's behavior. Parasitoids were allowed to search during a fixed time in an experimental arena with immatures of the greenhouse whitefly,Trialeurodes vaporariorum. The model simulates host searching, selection, and handling behavior and the physiological state (egg load) of the parasitoid. The simulated number of hosts encountered, parasitized, or killed by host feeding agreed well with observations on leaf disks. The hypothesis of random host encounter seems to be correct. The number of ovipositions on the leaf at low host densities was strongly affected by the parasitoid's walking speed and walking activity, the probability of oviposition after encountering a host, and the initial egg load. At high densities, the initial and maximum egg load were most important. A strong temperature effect was found at 18°C or below. The number of encounters, ovipositions, and host feedings increased with host density to a maximum of 25, 6.5, and 1.5, respectively, during 2 h at 25°C. The shape of the curves resembled a Holling Type II, which may be the result of the experimental procedure, where a parasitoid was confined to a patch during a fixed time.     

Hemocyanin gene family evolution in spiders (Araneae), with implications for phylogenetic relationships and divergence times in the infraorder Mygalomorphae

Hemocyanins are multimeric copper-containing hemolymph proteins involved in oxygen binding and transport in all major arthropod lineages. Most arachnids have seven primary subunits (encoded by paralogous genes a–g), which combine to form a 24-mer (4 × 6) quaternary structure. Within some spider lineages, however, hemocyanin evolution has been a dynamic process with extensive paralog duplication and loss. We have obtained hemocyanin gene sequences from numerous representatives of the spider infraorders Mygalomorphae and Araneomorphae in order to infer the evolution of the hemocyanin gene family and estimate spider relationships using these conserved loci. Our hemocyanin gene tree is largely consistent with the previous hypotheses of paralog relationships based on immunological studies, but reveals some discrepancies in which paralog types have been lost or duplicated in specific spider lineages. Analyses of concatenated hemocyanin sequences resolved deep nodes in the spider phylogeny and recovered a number of clades that are supported by other molecular studies, particularly for mygalomorph taxa. The concatenated data set is also used to estimate dates of higher-level spider divergences and suggests that the diversification of extant mygalomorphs preceded that of extant araneomorphs. Spiders are diverse in behavior and respiratory morphology, and our results are beneficial for comparative analyses of spider respiration. Lastly, the conserved hemocyanin sequences allow for the inference of spider relationships and ancient divergence dates.