Solutions for surrogacy validation with longitudinal outcomes for a gene therapy

Valid surrogate endpoints S can be used as a substitute for a true outcome of interest T to measure treatment efficacy in a clinical trial. We propose a causal inference approach to validate a surrogate by incorporating longitudinal measurements of the true outcomes using a mixed modeling approach, and we define models and quantities for validation that may vary across the study period using principal surrogacy criteria. We consider a surrogate-dependent treatment efficacy curve that allows us to validate the surrogate at different time points. We extend these methods to accommodate a delayed-start treatment design where all patients eventually receive the treatment. Not all parameters are identified in the general setting. We apply a Bayesian approach for estimation and inference, utilizing more informative prior distributions for selected parameters. We consider the sensitivity of these prior assumptions as well as assumptions of independence among certain counterfactual quantities conditional on pretreatment covariates to improve identifiability. We examine the frequentist properties (bias of point and variance estimates, credible interval coverage) of a Bayesian imputation method. Our work is motivated by a clinical trial of a gene therapy where the functional outcomes are measured repeatedly throughout the trial.     

Reparameterizing the pattern mixture model for sensitivity analyses under informative dropout

Pattern mixture models are frequently used to analyze longitudinal data where missingness is induced by dropout. For measured responses, it is typical to model the complete data as a mixture of multivariate normal distributions, where mixing is done over the dropout distribution. Fully parameterized pattern mixture models are not identified by incomplete data; Little (1993, Journal of the American Statistical Association 88, 125-134) has characterized several identifying restrictions that can be used for model fitting. We propose a reparameterization of the pattern mixture model that allows investigation of sensitivity to assumptions about nonidentified parameters in both the mean and variance, allows consideration of a wide range of nonignorable missing-data mechanisms, and has intuitive appeal for eliciting plausible missing-data mechanisms. The parameterization makes clear an advantage of pattern mixture models over parametric selection models, namely that the missing-data mechanism can be varied without affecting the marginal distribution of the observed data. To illustrate the utility of the new parameterization, we analyze data from a recent clinical trial of growth hormone for maintaining muscle strength in the elderly. Dropout occurs at a high rate and is potentially informative. We undertake a detailed sensitivity analysis to understand the impact of missing-data assumptions on the inference about the effects of growth hormone on muscle strength.     

Can we predict ectotherm responses to climate change using thermal performance curves and body temperatures?

Thermal performance curves (TPCs), which quantify how an ectotherm's body temperature (T_b) affects its performance or fitness, are often used in an attempt to predict organismal responses to climate change. Here, we examine the key – but often biologically unreasonable – assumptions underlying this approach; for example, that physiology and thermal regimes are invariant over ontogeny, space and time, and also that TPCs are independent of previously experienced T_b. We show how a critical consideration of these assumptions can lead to biologically useful hypotheses and experimental designs. For example, rather than assuming that TPCs are fixed during ontogeny, one can measure TPCs for each major life stage and incorporate these into stage‐specific ecological models to reveal the life stage most likely to be vulnerable to climate change. Our overall goal is to explicitly examine the assumptions underlying the integration of TPCs with T_b, to develop a framework within which empiricists can place their work within these limitations, and to facilitate the application of thermal physiology to understanding the biological implications of climate change.     

Determination of thermodynamic functions from scanning calorimetry data

We present a theoretical basis and new methods for the determination of thermodynamic functions from scanning calorimetry data. A thermodynamic state is defined here as an ensemble of microstates in the system, and it can be defined only through assumptions of its heat capacity function and the two integral constants. With these assumptions, scanning calorimetry data can be analyzed using the single or double (or multi-) deconvolution presented here. New equations to calculate the van't Hoff enthalpy function and the calorimetric enthalpy function are presented. We prove that the agreement of these two functions is a necessary and sufficient factor for the condition that the system can be described with the assumed two-state model.     

Multiple comparisons in the randomization analysis of designed experiments with growth curve responses

A randomization approach to multiple comparisons is developed for comparing several growth curves in randomized experiments. The exact Type I probability error rate for these comparisons may be prespecified, and a Type I error probability for each component test can be evaluated. These procedures are free of many of the standard assumptions for analyzing growth curves and for making multiple comparisons. An application of the procedure gives all pairwise comparisons among the mean growth curves associated with four treatments in an animal experiment using a Youden square design, where growth curves are obtained on monitoring hormone levels over time.     

The determination of sensitivity parameters for auxin-induced H+-efflux from Avena coleoptile segments

Abstract A method is described for the measurement of auxin-induced H⁺-efflux from small populations of Avena coleoptile segments. The method allows the simultaneous investigation of the kinetics of rapid auxin responses over a wide concentration range. IAA promoted linear rates of H⁺-efflux and the change in amplitude of response occurred mainly over a low, narrow concentration range (10–50 μmol m^-3). The sigmoidal curve of best-fit to each set of dose-response data was determined using non-linear regression techniques, allowing the objective determination of characteristic tissue sensitivity parameters (R_MIN, R_MAX, K_D and p). The sensitivity parameters for the auxin-type herbicide fluroxypyr are also presented as well as IAA parameters determined in the presence of abscisic acid and the ‘antiauxin’ PCIB. The interpretation of the parameter values and the potential use of sensitivity parameter analysis for the evaluation of theories concerning plant hormone action and interaction is discussed.     

high-performance liquid chromatography of amino acids, peptides and proteins : LXIII. Reversed-phase high-performance liquid chromatographic characterisation of several polypeptide and protein hormones

The chromatographic behaviour on alkylsilicas of a variety of hormonal proteins is described. Optimization of resolution and recovery of these protein hormones, which included porcine relaxins, human chorionic gonadotropin, human placental lactogen, pituitary derived growth hormone and adenohypophyseal glycoprotein hormones, was achieved by manipulation of both mobile and stationary phase parameters. With standard stainless-steel analytical columns (10–30 cm × 0.4 cm) packed with meso- or macro-porous n-alkylsilica supports these proteins can be readily fractionated at the semi-preparative level with separation times generally under 90 min using elution systems directly compatible with subsequent methods of primary structure determination or biological functional analysis. The effects of changes in several experimental parameters on peak symmetry, retention and recovery are described.     

Quantitative analysis of the control of physiological phenomena by plant hormones

We highlight the need to combine information about hormone concentrations and tissue sensitivity when assessing control of physiological phenomena by plant hormones. A quantitative approach to this problem is suggested and the method illustrated using data for stomatal closure induced by abscisic acid. The technique requires accurate estimates of hormone concentration at the putative site of action and information about the kinetics of responses in the form of dose-response curves obtained under relevant conditions. Extending this approach, hormonal control is seen as relative, in that it must be considered against a background of other controlling influences. Possible means of evaluating this 'control potential' from dose-response curves are discussed. Finally, we draw together the above in an analytical framework for assessing hormonal control. This involves (1) matching observed and predicted responses; (2) studying effects of manipulating hormone concentration or sensitivity; and (3) assessing the relative control potential of the compound of interest.     

Good modeling practice for PAT applications: Propagation of input uncertainty and sensitivity analysis

The uncertainty and sensitivity analysis are evaluated for their usefulness as part of the model‐building within Process Analytical Technology applications. A mechanistic model describing a batch cultivation of Streptomyces coelicolor for antibiotic production was used as case study. The input uncertainty resulting from assumptions of the model was propagated using the Monte Carlo procedure to estimate the output uncertainty. The results showed that significant uncertainty exists in the model outputs. Moreover the uncertainty in the biomass, glucose, ammonium and base‐consumption were found low compared to the large uncertainty observed in the antibiotic and off‐gas CO₂ predictions. The output uncertainty was observed to be lower during the exponential growth phase, while higher in the stationary and death phases ‐ meaning the model describes some periods better than others. To understand which input parameters are responsible for the output uncertainty, three sensitivity methods (Standardized Regression Coefficients, Morris and differential analysis) were evaluated and compared. The results from these methods were mostly in agreement with each other and revealed that only few parameters (about 10) out of a total 56 were mainly responsible for the output uncertainty. Among these significant parameters, one finds parameters related to fermentation characteristics such as biomass metabolism, chemical equilibria and mass‐transfer. Overall the uncertainty and sensitivity analysis are found promising for helping to build reliable mechanistic models and to interpret the model outputs properly. These tools make part of good modeling practice, which can contribute to successful PAT applications for increased process understanding, operation and control purposes. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Target theory and survival curves

A general theoretical treatment of cellular radiation damage is presented. The basic assumptions are: (1) the initial damage (“hit”) is not harmful per se, but may be either developed into a biologically significant “lesion” or repaired; (2) each lesion has a certain probability to be lethal, this probability does not depend on the number of lesions per cell; (3) the initial “hits” follow Poisson's distribution. It is shown that under these assumptions the shape of survival curves can be explained. The classical “single-hit” and “multi-hit” curves are obtained as limiting cases.     

Calculating thermodynamic data for transitions of any molecularity from equilibrium melting curves

In this paper, we derive the general forms of the equations required to extract thermodynamic data from equilibrium transition curves on oligomeric and polymeric nucleic acids of any molecularity. Significantly, since the equations and protocols are general, they also can be used to characterize thermodynamically equilibrium processes in systems other than nucleic acids. We briefly review how the reduced forms of the general equations have been used by many investigators to evaluate mono- and bimolecular transitions, and then explain how these equations can be generalized to calculate thermodynamic parameters from common experimental observables for transitions of higher molecularities. We emphasize the strengths and weaknesses of each method of data analysis so that investigators can select the approach most appropriate for their experimental circumstances. We also describe how to analyze calorimetric heat capacity curves and noncalorimetric differentiated melting curves so as to extract both model-independent and model-dependent thermodynamic data for transitions of any molecularity. The general equations and methods of analysis described in this paper should be of particular interest to laboratories that currently are investigating association and dissociation processes in nucleic acids that exhibit molecularities greater than two.     

Temporally patterned pulse trains affect directional sensitivity of inferior collicular neurons of the big brown bat, Eptesicus fuscus

The directional sensitivity of inferior collicular neurons of the big brown bat, Eptesicus fuscus, was studied under free field stimulation conditions with 3 temporally patterned trains of sound pulses which differed in pulse repetition rate and duration. The directional sensitivity curves of 92 neurons studied can be described as hemifield, directionally-selective, or non-directional according to the variation in the number of impulses with pulse train direction. When these neurons were stimulated with all 3 pulse trains, the directional sensitivity curves of 50 neurons was unchanged but that of the other 42 neurons changed from one type into another. When these pulse trains were delivered at high pulse repetition rate and short pulse duration, they significantly sharpened the directional sensitivity of two thirds of the neurons examined by reducing the angular range and increasing the slope of their impulse directional sensitivity curves. These pulse trains also sharpened the slope of the threshold directional sensitivity curves of 25 neurons studied. However, when directional sensitivity of collicular neurons was determined with pulse trains that differed only in pulse repetition rate or in pulse duration, significant sharpening of directional sensitivity was rarely observed in all experimental conditions tested. Possible mechanisms underlying these findings are discussed.     

Compartment analysis of plant cells by means of turgor pressure relaxation: I. Theoretical considerations

Summary Turgor pressure relaxation curves for individual plant cells represent an important source of information for the plant physiologist. However, the accurate interpretation of these curves is strongly dependent on the model chosen to describe the plant cell. If the compartmentation of the cell into vacuole and cytoplasm is taken into account, a theoretical analysis shows that pressure relaxation curves can be represented by the sum of two exponential functions. Givena priori assumptions about the exchange area of the tonoplast and its reflection coefficient, the hydraulic conductivities of the plasmalemma and tonoplast can be determined and the proportion of the total cell volume occupied by the cytoplasm is also obtained. Numerical solutions to the flow equations have shown that the biphasic nature of pressure relaxations is maintained even when a permeable tonoplast is assumed. Depending on the magnitude of the reflection coefficient and the permeability of the vacuolar membrane, large errors can arise in the determination of the hydraulic conductivity of the tonoplast. However, under certain conditions, even a highly permeable tonoplast may behave like a nonpermeable membrane during pressure relaxation.     

Linearisation of RGB Camera Responses for Quantitative Image Analysis of Visible and UV Photography: A Comparison of Two Techniques

Linear camera responses are required for recovering the total amount of incident irradiance, quantitative image analysis, spectral reconstruction from camera responses and characterisation of spectral sensitivity curves. Two commercially-available digital cameras equipped with Bayer filter arrays and sensitive to visible and near-UV radiation were characterised using biexponential and Bézier curves. Both methods successfully fitted the entire characteristic curve of the tested devices, allowing for an accurate recovery of linear camera responses, particularly those corresponding to the middle of the exposure range. Nevertheless the two methods differ in the nature of the required input parameters and the uncertainty associated with the recovered linear camera responses obtained at the extreme ends of the exposure range. Here we demonstrate the use of both methods for retrieving information about scene irradiance, describing and quantifying the uncertainty involved in the estimation of linear camera responses.     

Can Occupancy–Abundance Models Be Used to Monitor Wolf Abundance?

Estimating the abundance of wild carnivores is of foremost importance for conservation and management. However, given their elusive habits, direct observations of these animals are difficult to obtain, so abundance is more commonly estimated from sign surveys or radio-marked individuals. These methods can be costly and difficult, particularly in large areas with heavy forest cover. As an alternative, recent research has suggested that wolf abundance can be estimated from occupancy–abundance curves derived from “virtual” surveys of simulated wolf track networks. Although potentially more cost-effective, the utility of this approach hinges on its robustness to violations of its assumptions. We assessed the sensitivity of the occupancy–abundance approach to four assumptions: variation in wolf movement rates, changes in pack cohesion, presence of lone wolves, and size of survey units. Our simulations showed that occupancy rates and wolf pack abundances were biased high if track surveys were conducted when wolves made long compared to short movements, wolf packs were moving as multiple hunting units as opposed to a cohesive pack, and lone wolves were moving throughout the surveyed landscape. We also found that larger survey units (400 and 576 km²) were more robust to changes in these factors than smaller survey units (36 and 144 km²). However, occupancy rates derived from large survey units rapidly reached an asymptote at 100% occupancy, suggesting that these large units are inappropriate for areas with moderate to high wolf densities (>15 wolves/1,000 km²). Virtually-derived occupancy–abundance relationships can be a useful method for monitoring wolves and other elusive wildlife if applied within certain constraints, in particular biological knowledge of the surveyed species needs to be incorporated into the design of the occupancy surveys. Further, we suggest that the applicability of this method could be extended by directly incorporating some of its assumptions into the modelling framework.     

Action spectra for light-induced germination in dormant lettuce seeds

Fluence response curves for red light-induced germination of thermodormant (TD) seeds of Lactuca sativa L. show two regions that differ in their light sensitivity. In the region of high sensitivity, the germination responses differ between seed batches and can be altered by dark storage or far red irradiation. Induction of germination in far red dormant (FRD) seeds requires far higher fluences. Action spectra for induction to 60% germination were determined for these various response types. Spectra for the regions of low sensitivity response are similar for TD and FRD seeds. In comparison, the action spectrum for the highly sensitive response in TD seeds is significantly shifted to longer wavelengths. Analogous differences exist in the action spectra for far red reversal of the red induced germination responses. Germination induction in the low sensitivity region shows repeated red-far red reversibility. Far red reversal of red induction in the high sensitivity region does not saturate even at the highest far red fluences available and requires increased red fluences for subsequent reinduction. A model quantitatively accounting for these observations is presented. It is pointed out that action spectra of processes involving photoreversible pigments with partly overlapping absorption spectra in general are not identical with the absorption spectra of the partners. They should depend upon the degree of phototransformation required to elicit a given physiological response. In the case of induction of lettuce seed germination the observed action spectra can be interpreted as reflecting different requirements for P _fr of the various response types. Our results do not necessitate the assumption of spectroscopically different forms of phytochrome in these seeds.Abbreviations TD thermodormant - FRD far red dormant - P phytochrome - P _r red absorbing form of P - P _fr far red absorbing form of P     

Bayesian methods for comparing species physiological and ecological response curves

Many ecological questions require information on species' optimal conditions or critical limits along environmental gradients. These attributes can be compared to answer questions on niche partitioning, species coexistence and niche conservatism. However, these comparisons are unconvincing when existing methods do not quantify the uncertainty in the attributes or rely on assumptions about the shape of species' responses to the environmental gradient. The aim of this study was to develop a model to quantify the uncertainty in the attributes of species response curves and allow them to be tested for substantive differences without making assumptions about the shape of the responses. We developed a model that used Bayesian penalised splines to produce and compare response curves for any two given species. These splines allow the data to determine the shape of the response curves rather than making a priori assumptions. The models were implemented using the R2OpenBUGS package for R, which uses Markov Chain Monte Carlo simulation to repetitively fit alternative response curves to the data. As each iteration produces a different curve that varies in optima, niche breadth and limits, the model estimates the uncertainty in each of these attributes and the probability that the two curves are different. The models were tested using two datasets of mosses from Antarctica. Both datasets had a high degree of scatter, which is typical of ecological research. This noise resulted in considerable uncertainty in the optima and limits of species response curves, but substantive differences were found. Schistidium antarctici was found to inhabit wetter habitats than Ceratodon purpureus, and Polytrichastrum alpinum had a lower optimal temperature for photosynthesis than Chorisodontium aciphyllum under high light conditions. Our study highlights the importance of considering uncertainty in physiological optima and other attributes of species response curves. We found that apparent differences in optima of 7.5 °C were not necessarily substantive when dealing with noisy ecological data, and it is necessary to consider the uncertainty in attributes when comparing the curves for different species. The model introduced here could increase the robustness of research on niche partitioning, species coexistence and niche conservatism.     

Progress Curves Analysis as an Alternative for Exploration of Activation-inhibition Phenomena in Cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

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.     

Stomatal response to humidity in a sugarcane field: simultaneous porometric and micrometeorological measurements*

Abstract. Gas exchange data obtained with wellventilated leaf cuvettes provide clear evidence of a stomatal response to leaf-air vapour pressure difference (V). In contrast, remotely sensed leaf temperatures with specific assumptions regarding canopy boundary layer characteristics, have been interpreted to mean that stomata do not respond to V. We address this apparent discrepancy in a sugarcane field by simultaneous application of a single-leaf, porometric technique and a whole-canopy, Bowen ratioenergy balance technique. These methods indicated significant stomatal response to V in well-irrigated sugarcane. Stomatal responses to V in the field were obscured by strong covariance of major environmental parameters so that opening responses to light and closing responses to V tended to offset each other. Low boundary layer conductance significantly uncoupled V at the leaf surface (V_s) from V determined in the bulk atmosphere (V_a). This reduced the range of the stimulus, V_s, thereby reducing the range of the stomatal response, without indicating low stomatal sensitivity to V. Stomatal responses to V_a may be smaller than expected from V response curves in cuvettes, since V_s rather than the conventionally measured V_a is analogous to V in a well-stirred cuvette. Recently published conclusions that remotely sensed canopy temperatures are inconsistent with stomatal response to V may be based on erroneous estimates of canopy boundary layer conductance and thus of V_s, use of air saturation deficit rather than V to express evaporative demand, and investigation at higher levels of evaporative demand than those eliciting maximal stomatal response.