The Cochrane Handbook for Systematic Reviews of Interventions is the official document that describes in detail the process of preparing and maintaining Cochrane systematic reviews on the effects of healthcare interventions.

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Cochrane Handbook for Systematic Reviews of Interventions

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

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Experimental Design and Data Analysis for Biologists

https://www.thelancet.com/pdfs/journals/lancet/PIIS0140-6736(06)69283-0.pdf

Worldwide time trends in the prevalence of symptoms of asthma, allergic rhinoconjunctivitis, and eczema in childhood: ISAAC Phases One and Three repeat multicountry cross-sectional surveys

We consider statistical inference for regression when data are grouped into clus- ters, with regression model errors independent across clusters but correlated within clusters. Examples include data on individuals with clustering on village or region or other category such as industry, and state-year dierences-in-dierences studies with clustering on state. In such settings default standard errors can greatly overstate es- timator precision. Instead, if the number of clusters is large, statistical inference after OLS should be based on cluster-robust standard errors. We outline the basic method as well as many complications that can arise in practice. These include cluster-specic �xed eects, few clusters, multi-way clustering, and estimators other than OLS.

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A Practitioner’s Guide to Cluster-Robust Inference

We study rare events data, binary dependent variables with dozens to thousands of times fewer ones (events, such as wars, vetoes, cases of political activism, or epidemiological infections) than zeros ("nonevents"). In many literatures, these variables have proven difficult to explain and predict, a problem that seems to have at least two sources. First, popular statistical procedures, such as logistic regression, can sharply underestimate the probability of rare events. We recommend corrections that outperform existing methods and change the estimates of absolute and relative risks by as much as some estimated effects reported in the literature. Second, commonly used data collection strategies are grossly inefficient for rare events data. The fear of collecting data with too few events has led to data collections with huge numbers of observations but relatively few, and poorly measured, explanatory variables, such as in international conflict data with more than a quarter-million dyads, only a few of which are at war. As it turns out, more efficient sampling designs exist for making valid inferences, such as sampling all variable events (e.g., wars) and a tiny fraction of nonevents (peace). This enables scholars to save as much as 99% of their (nonfixed) data collection costs or to collect much more meaningful explanatory variables. We provide methods that link these two results, enabling both types of corrections to work simultaneously, and software that implements the methods developed.

Logistic Regression in Rare Events Data

The impact of survey design on standard multinomial-based methods for a multiway contingency table is studied, under nested loglinear models. The asymptotic null distribution of the Pearson chi-squared test statistic, $X^2$ (or the likelihood ratio test statistic, $G^2$) is obtained as a weighted sum of independent $\chi^2_1$ random variables, and the weights are then related to the familiar design effects (deffs) used by survey samplers. A simple correction to $X^2$ (or $G^2$) is also obtained which requires the knowledge of only the cell deffs and the deffs for collapsed tables (marginals), whenever the model admits a direct solution of likelihood equations under multinomial sampling. Finally, an example on the relative performance of $X^2$ and some corrected $X^2$ statistics in a three-way table is given, using some data from the Canada Health Survey, 1978-1979.

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On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data

The effect of stratification and clustering on the asymptotic distributions of standard Pearson chi-squared test statistics for goodness of fit (simple hypothesis) and independence in a two-way contingency table, denoted as X 2 and XI 2, respectively, is investigated It is shown that both X 2 and XI 2 are asymptotically distributed as weighted sums of independent χ1 2 random variables The weights are then related to the familiar design effects (deffs) used by survey samplers A simple correction to X 2, which requires only the knowledge of variance estimates (or deffs) for individual cells in the goodness-of-fit problem, is proposed and empirical results on the performance of corrected X 2 provided Empirical work on XI 2 indicated that the distortion of nominal significance level is substantially smaller with XI 2 than with X 2 Some results under simple models for clustering are also given

https://www.jstor.org/stable/pdfplus/2287815.pdf

The Analysis of Categorical Data from Complex Sample Surveys: Chi-Squared Tests for Goodness of Fit and Independence in Two-Way Tables

A simple method for comparing independent groups of clustered binary data with group-specific covariates is proposed It is based on the concepts of design effect and effective sample size widely used in sample surveys, and assumes no specific models for the intracluster correlations It can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing The method is applied to a variety of problems involving clustered binary data: testing homogeneity of proportions, estimating dose-response models and testing for trend in proportions, and performing the Mantel-Haenszel chi-squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance Illustrative applications of the method are also presented

https://www.jstor.org/stable/pdfplus/2532311.pdf

A simple method for the analysis of clustered binary data.

Aim To assess the occurrence and impact of adverse events in New Zealand public hospitals. Methods Two-stage retrospective review of 6579 medical records, selected by systematic list sample from admissions for 1998 in 13 generalist hospitals providing acute care. After initial screening, medical records were reviewed by trained medical practitioners using a standardised protocol. Results Except for hospital stay, the sample appeared to be closely representative of New Zealand public hospital admissions for 1998 on key demographic and clinical criteria. The proportion of hospital admissions associated with an adverse event was 12.9% (incidence rate, 11.2%), of which nearly one fifth had occurred outside a public hospital (mainly doctor s rooms, patient s home, rest home, or private hospital). Most adverse events had minor patient impact, with less than 15% associated with permanent disability or death. Hospital workload was strongly affected, however, with adverse events adding an average of over nine days (median 4 days) to the expected hospital stay. There was limited evidence of patterning by diagnostic category. The elderly were disproportionately affected. Conclusions The study provides representative base parameters that can contribute to the wider understanding, and potential improvement, of patient safety and the quality of care in New Zealand public hospitals.

Adverse events in New Zealand public hospitals I: occurrence and impact.

For testing the goodness-of-fit of a $\log$-linear model to a multi-way contingency table with cell proportions estimated from survey data, Rao and Scott (1984) derived a first-order correction, $\delta\ldot$, to Pearson chi-square statistic, $X^2$ (or the likelihood ratio statistic, $G^2$) that takes account of the survey design. It was also shown that $\delta\ldot$ requires the knowledge of only the cell design effects (deffs) and the marginal deffs provided the model admits direct solution to likelihood equations under multinomial sampling. Simple upper bounds on $\delta\ldot$ are obtained here for models not admitting direct solutions, also requiring only cell deffs and marginal deffs or some generalized deffs not depending on any hypothesis. Applicability of an $F$-statistic used in GLIM to test a nested hypothesis is also investigated. In the case of a logit model involving a binary response variable, simple upper bounds on $\delta\ldot$ are obtained in terms of deffs of response proportions for each factor combination or some generalized deffs not depending on any hypothesis. Applicability of the GLIM $F$-statistic for nested hypotheses is also studied.

https://projecteuclid.org/download/pdf_1/euclid.aos/1176350273

Alastair Scott

Papers

On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data

The Analysis of Categorical Data from Complex Sample Surveys: Chi-Squared Tests for Goodness of Fit and Independence in Two-Way Tables

A simple method for the analysis of clustered binary data.

Adverse events in New Zealand public hospitals I: occurrence and impact.

On Simple Adjustments to Chi-Square Tests with Sample Survey Data