SUMMARY Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp { fl(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function /3(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher (1987), Harrell (1986), Lin (1991), Moreau, O'Quigley & Mesbah (1985), Nagelkerke, Oosting & Hart (1984), O'Quigley & Pessione (1989), Schoenfeld (1980) and Wei (1984) are related to time-weighted score tests of the proportional hazards hypothesis, and can be visualized as a weighted least-squares line fitted to the residual plot.

Proportional hazards tests and diagnostics based on weighted residuals

Scale development and validation are critical to much of the work in the health, social, and behavioral sciences. However, the constellation of techniques required for scale development and evaluation can be onerous, jargon-filled, unfamiliar, and resource-intensive. Further, it is often not a part of graduate training. Therefore, our goal was to concisely review the process of scale development in as straightforward a manner as possible, both to facilitate the development of new, valid, and reliable scales, and to help improve existing ones. To do this, we have created a primer for best practices for scale development in measuring complex phenomena. This is not a systematic review, but rather the amalgamation of technical literature and lessons learned from our experiences spent creating or adapting a number of scales over the past several decades. We identified three phases that span nine steps. In the first phase, items are generated and the validity of their content is assessed. In the second phase, the scale is constructed. Steps in scale construction include pre-testing the questions, administering the survey, reducing the number of items, and understanding how many factors the scale captures. In the third phase, scale evaluation, the number of dimensions is tested, reliability is tested, and validity is assessed. We have also added examples of best practices to each step. In sum, this primer will equip both scientists and practitioners to understand the ontology and methodology of scale development and validation, thereby facilitating the advancement of our understanding of a range of health, social, and behavioral outcomes.

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Best Practices for Developing and Validating Scales for Health, Social, and Behavioral Research: A Primer.

4. Modelling Survival Data in Medical Research

Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.

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Verification and Validation in Scientific Computing

Symmetry and limb dominance in able-bodied gait: a review.

Applying the Rasch Model

Preface Contributors List of Tables List of Figures ---------------------- Part I. History and Fundamentals Karl Pearson and the Chi-Squared Test / D.R. Cox Karl Pearson Chi-Square Test-The Dawn of Statistical Inference / C.R. Rao Approximate Models / P.J. Huber -------------------- Part II. Chi-Squared Test Partitioning the Pearson-Fisher Chi-Squared Goodness-of-Fit Statistic / G.D. Rayner Statistical Tests for Normal Family in Presence of Outlying Observations / A. Zerbet Chi-Squared Test for the Law of Annual Death Rates: Case with Censure for Life Insurance Files / L. Gerville-Reache ------------------------ Part III. Goodness-of-Fit Tests for Parametric Distributions Shapiro-Wilk Type Goodness-of-Fit Tests for Normality: Asymptotics Revisited / P. Kumar A Test for Exponentiality Based on Spacings for Progressively Type II Censored Data / N. Balakrishnan, H.K.T. Ng, and N. Kannan Goodness-of- Fit Statistics for the Exponential Distribution When the Data are Grouped / S. Gulati and J. Neus Characterization Theorems and Goodness-of-Fit Tests / C.E. Marchetti and G.S. Mudholkar Goodness-of-Fit Tests Based on Record Data and Generalized Ranked Set Data / B.C. Arnold, R.J. Beaver, E. Castillo, and J.M. Sarabia ------------------------------- Part IV. Regression and Goodness-of-Fit Tests Gibbs Regression and a Test of Goodness-of-Fit / L. Seymour A CLT for the L_2 Norm of the Regression Estimators Under alpha-Mixing: Application to G-O-F Tests / C.A.T. Diack Testing theGoodness-of-Fit of a Linear Model in Nonparametric Regression / Z. Mohdeb and A. Mokkadem A New Test of Linear Hypothesis in Regression / Y. Baraud, S. Huet, and B. Laurent ------------------------------------- Part V. Goodness-of-Fit Tests in Survival Analysis and Reliability Inference in Extensions of the Cox Model for Heterogeneous Populations / O. Pons Assumptions of a Latent Survival Model / M.-L. Ting Lee and G.A. Whitmore Goodness-of-Fit Testing of the Cox Proportional Hazards Model / K. Devarajan and N. Ebrahimi A New Family of Multivariate Distributions for Survival Data / S.T. Gross and C. Huber-Carol Discrimination Index, the Area Under to ROC Curve / B.-H. Nam and R. B. D'Agostino Goodness-of-Fit Tests for Accelerated Life Models / V. Bagdonavicius and M.S. Nikulin ------------------------------ Part VI. Graphic Methods and General Goodness-of-Fit Tests Two Nonstandard Examples of the Classical Stratification Approach to Graphically Assessing Proportionality of Hazards / N. Keiding Association in Contingency Tables, Correspondence Analysis, and (Modified) Andrews Plots / R. Khattree and D.N. Naik Orthogonal Expansions and Distinction Between Logistic and Normal / C.M. Cuadras and D. Cuadras Functional Tests of Fit / D. Bosq Quasi Most Powerful Invariant Tests of Goodness-of-Fit --------------------------------- Part VII. Model Validity in Quality of Life Test of Monotonicity for the Rasch Model J. Bretagnolle Validation of Model Assumptions in Quality of Life Measurements / A. Hamon, J.F. Dupuy, and M. Mesbah &nbsp

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Goodness-of-fit tests and model validity

Rasch Models in Health

SUMMARY A simple alternative to the proportional hazards model is considered, whereby the regression coefficients can vary with time. It leads to a statistic which can be used for checking the assumption of proportional hazards. In the two-sample problem, this statistic is the same as Schoenfeld's (1980); a conservative version, computationally simple, is proposed in this case.

Mounir Mesbah

Papers

Applying the Rasch Model

Goodness-of-fit tests and model validity

Rasch Models in Health

A Global Goodness‐Of‐Fit Statistic for the Proportional Hazards Model

Winter air pollution and infant bronchiolitis in Paris