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More reliable inference for the dissimilarity index of segregation.

ABSTRACT: The most widely used measure of segregation is the so-called dissimilarity index. It is now well understood that this measure also reflects randomness in the allocation of individuals to units (i.e. it measures deviations from evenness, not deviations from randomness). This leads to potentially large values of the segregation index when unit sizes and/or minority proportions are small, even if there is no underlying systematic segregation. Our response to this is to produce adjustments to the index, based on an underlying statistical model. We specify the assignment problem in a very general way, with differences in conditional assignment probabilities underlying the resulting segregation. From this, we derive a likelihood ratio test for the presence of any systematic segregation, and bias adjustments to the dissimilarity index. We further develop the asymptotic distribution theory for testing hypotheses concerning the magnitude of the segregation index and show that the use of bootstrap methods can improve the size and power properties of test procedures considerably. We illustrate these methods by comparing dissimilarity indices across school districts in England to measure social segregation.

SUBMITTER: Allen R

PROVIDER: S-EPMC5054828 | biostudies-other | 2015 Feb

REPOSITORIES: biostudies-other

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More reliable inference for the dissimilarity index of segregation.

Allen Rebecca R Burgess Simon S Davidson Russell R Windmeijer Frank F

The econometrics journal 20150201 1

The most widely used measure of segregation is the so-called dissimilarity index. It is now well understood that this measure also reflects randomness in the allocation of individuals to units (i.e. it measures deviations from evenness, not deviations from randomness). This leads to potentially large values of the segregation index when unit sizes and/or minority proportions are small, even if there is no underlying systematic segregation. Our response to this is to produce adjustments to the in ...[more]

PMID: 27774035

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Project description:Background Accurately estimating the true richness of a target community is still a statistical challenge, particularly in highly diverse communities. Due to sampling limitations or limited resources, undetected species are present in many surveys and observed richness is an underestimate of true richness. In the literature, methods for estimating the undetected richness of a sample are generally divided into two categories: parametric and nonparametric estimators. Imposing no assumptions on species detection rates, nonparametric methods demonstrate robust statistical performance and are widely used in ecological studies. However, nonparametric estimators may seriously underestimate richness when species composition has a high degree of heterogeneity. Parametric approaches, which reduce the number of parameters by assuming that species-specific detection probabilities follow a given statistical distribution, use traditional statistical inference to calculate species richness estimates. When species detection rates meet the model assumption, the parametric approach could supply a nearly unbiased estimator. However, the infeasibility and inefficiency of solving maximum likelihood functions limit the application of parametric methods in ecological studies when the model assumption is violated, or the collected data is sparse. Method To overcome these estimating challenges associated with parametric methods, an estimator employing the moment estimation method instead of the maximum likelihood estimation method is proposed to estimate parameters based on a Gamma-Poisson mixture model. Drawing on the concept of the Good-Turing frequency formula, the proposed estimator only uses the number of singletons, doubletons, and tripletons in a sample for undetected richness estimation. Results The statistical behavior of the new estimator was evaluated by using real and simulated data sets from various species abundance models. Simulation results indicated that the new estimator reduces the bias presented in traditional nonparametric estimators, presents more robust statistical behavior compared to other parametric estimators, and provides confidence intervals with better coverage among the discussed estimators, especially in assemblages with high species composition heterogeneity.

Project description:BACKGROUND: A breast cancer prognostic tool should ideally be applicable to all types of invasive breast lesions. A number of studies have shown histopathological grade to be an independent prognostic factor in breast cancer, adding prognostic power to nodal stage and tumour size. The Nottingham Prognostic Index has been shown to accurately predict patient outcome in stratified groups with a follow-up period of 15 years after primary diagnosis of breast cancer. Clinically, breast tumours that lack the expression of Oestrogen Receptor, Progesterone Receptor and Human Epidermal growth factor Receptor 2 (HER2) are identified as presenting a "triple-negative" phenotype or as triple-negative breast cancers. These poor outcome tumours represent an easily recognisable prognostic group of breast cancer with aggressive behaviour that currently lack the benefit of available systemic therapy. There are conflicting results on the prevalence of lymph node metastasis at the time of diagnosis in triple-negative breast cancer patients but it is currently accepted that triple-negative breast cancer does not metastasize to axillary nodes and bones as frequently as the non-triple-negative carcinomas, favouring instead, a preferentially haematogenous spread. Hypothetically, this particular tumour dissemination pattern would impair the reliability of using Nottingham Prognostic Index as a tool for triple-negative breast cancer prognostication. METHODS: The present study tested the effectiveness of the Nottingham Prognostic Index in stratifying breast cancer patients of different subtypes with special emphasis in a triple-negative breast cancer patient subset versus non- triple-negative breast cancer. RESULTS: We demonstrated that besides the fact that TNBC disseminate to axillary lymph nodes as frequently as luminal or HER2 tumours, we also showed that TNBC are larger in size compared with other subtypes and almost all grade 3. Additionally, survival curves demonstrated that these prognostic factors are equally important to stratify different survival outcomes in non-TNBC as in TNBC. We also showed that the NPI retains the ability to stratify and predict survival of TNBC patients. CONCLUSION: The importance of this study relies on the need of prognostication improvements on TNBC, showing, at a clinical standpoint, that Nottingham Prognostic Index is as a truthful prognostic tool in TNBC.

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More reliable inference for the dissimilarity index of segregation.

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More reliable inference for the dissimilarity index of segregation.

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