Image Analysis: Basic Procedures for Description of Plant Structures

This chapter gives examples of basic procedures of quantification of plant structures with use of image analysis, which are commonly employed to describe differences among experimental treatments or phenotypes of plant material. Tasks are demonstrated with the use of ImageJ, a widely used public domain Java image processing program. Principles of sampling design based on systematic uniform random sampling for quantitative studies of anatomical parameters are given to obtain their unbiased estimations and simplified "rules of thumb" are presented. The basic procedures mentioned in the text are: (1) sampling, (2) calibration, (3) manual length measurement, (4) leaf surface area measurement, (5) estimation of particle density demonstrated on an example of stomatal density, and (6) analysis of epidermal cell shape.

On point estimation of the abnormality of a Mahalanobis index

Mahalanobis distance may be used as a measure of the disparity between an individual’s profile of scores and the average profile of a population of controls. The degree to which the individual’s profile is unusual can then be equated to the proportion of the population who would have a larger Mahalanobis distance than the individual. Several estimators of this proportion are examined. These include plug-in maximum likelihood estimators, medians, the posterior mean from a Bayesian probability matching prior, an estimator derived from a Taylor expansion, and two forms of polynomial approximation, one based on Bernstein polynomial and one on a quadrature method. Simulations show that some estimators, including the commonly-used plug-in maximum likelihood estimators, can have substantial bias for small or moderate sample sizes. The polynomial approximations yield estimators that have low bias, with the quadrature method marginally to be preferred over Bernstein polynomials. However, the polynomial estimators sometimes yield infeasible estimates that are outside the 0–1 range. While none of the estimators are perfectly unbiased, the median estimators match their definition; in simulations their estimates of the proportion have a median error close to zero. The standard median estimator can give unrealistically small estimates (including 0) and an adjustment is proposed that ensures estimates are always credible. This latter estimator has much to recommend it when unbiasedness is not of paramount importance, while the quadrature method is recommended when bias is the dominant issue.

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We seek an estimate of the population proportion with extreme Mahalanobis index.

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Nine point estimates are examined in an extensive simulation study.

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Maximum likelihood estimates have substantial bias.

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Methods based on polynomial approximations give low bias, but can be out-of-range.

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An adapted median estimator that always gives sensible estimates is proposed.

Comparison of unbiased estimation of neuronal number in the rat hippocampus with different staining methods

BACKGROUND

NeuN and Nissl staining (toluidine blue, cresyl violet staining) are routinely used methods in unbiased stereological estimation of the total number of hippocampal neurons.

NEW METHOD

In the present study, we stained serial frozen coronal sections from 5 normal adult male Sprague-Dawley rat brains with different methods, measured the deformation of hippocampal area in brain sections and estimated the total number of hippocampal neurons using the optical fractionator.

RESULTS

The deformation in x, y-axis was not obviously different with different staining protocols, but shrinkage in z-axis was significant after staining (p < 0.001). NeuN staining produced significant higher estimate number than cresyl violet staining by 24% (p = 0.002), however, NeuN and Cresyl Violet staining showed a high degree of correlation in quantification of total neuronal numbers and both methods are suitable for unbiased stereological estimation.

COMPARISON WITH EXISTING METHOD (S)

NeuN is more reliable but if time is limited or the number of animals used in experiments is high, cresyl violet staining may be a feasible method.

CONCLUSIONS

Compared with previous estimates of the neurons number in rat hippocampus, our present data is reliable and the stereological analysis based on our system is a cost-effective unbiased method for estimation of neuron number.

Estimation of treatment effects in all-comers randomized clinical trials with a predictive marker

Recent advances in genomics and biotechnologies have accelerated the development of molecularly targeted treatments and accompanying markers to predict treatment responsiveness. However, it is common at the initiation of a definitive phase III clinical trial that there is no compelling biological basis or early trial data for a candidate marker regarding its capability in predicting treatment effects. In this case, it is reasonable to include all patients as eligible for randomization, but to plan for prospective subgroup analysis based on the marker. One analysis plan in such all-comers designs is the so-called fallback approach that first tests for overall treatment efficacy and then proceeds to testing in a biomarker-positive subgroup if the first test is not significant. In this approach, owing to the adaptive nature of the analysis and a correlation between the two tests, a bias will arise in estimating the treatment effect in the biomarker-positive subgroup after a non-significant first overall test. In this article, we formulate the bias function and show a difficulty in obtaining unbiased estimators for a whole range of an associated parameter. To address this issue, we propose bias-corrected estimation methods, including those based on an approximation of the bias function under a bounded range of the parameter using polynomials. We also provide an interval estimation method based on a bivariate doubly truncated normal distribution. Simulation experiments demonstrated a success in bias reduction. Application to a phase III trial for lung cancer is provided.