A miscellaneous note on the equivalence of two poisson likelihoods

This note shows that the concept of an offset, frequently introduced in Poisson regression models to cope with ratetype data, can be simply treated with a regular Poisson regression model. Hence Poisson regression models requiring an offset can be fitted with ordinary Poisson regression models. Some illustrations are provided and it is discussed how this result came about

A randomised controlled trial of a digital intervention (Renewed) to support symptom management, wellbeing and quality of life in cancer survivors

Background: Many cancer survivors following primary treatment have prolonged poor quality of life.Aim: To determine the effectiveness of a bespoke digital intervention to support cancer survivors.Design: Pragmatic parallel open randomised trial.Setting: UK general practices.Methods: People having finished primary treatment (&lt;= 10 years previously) for colo-rectal, breast or prostate cancers, with European-Organization-for-Research-and-Treatment-of-Cancer QLQ-C30 score &lt;85, were randomised by online software to: 1) detailed ‘generic’ digital NHS support (‘LiveWell’;n=906), 2) a bespoke complex digital intervention (‘Renewed’;n=903) addressing symptom management, physical activity, diet, weight loss, distress, or 3) ‘Renewed-with-support’ (n=903): ‘Renewed’ with additional brief email and telephone support. Results: Mixed linear regression provided estimates of the differences between each intervention group and generic advice: at 6 months (primary time point: n’s respectively 806;749;705) all groups improved, with no significant between-group differences for EORTC QLQ-C30, but global health improved more in both intervention groups. By 12 months there were: small improvements in EORTC QLQ-C30 for Renewed-with-support (versus generic advice: 1.42, 95% CIs 0.33-2.51); both groups improved global health (12 months: renewed: 3.06, 1.39-4.74; renewed-with-support: 2.78, 1.08-4.48), dyspnoea, constipation, and enablement, and lower NHS costs (generic advice £265: in comparison respectively £141 (153-128) and £77 (90-65) lower); and for Renewed-with-support improvement in several other symptom subscales. No harms were identified.Conclusion: Cancer survivors quality of life improved with detailed generic online support. Robustly developed bespoke digital support provides limited additional short term benefit, but additional longer term improvement in global healthenablement and symptom management, with substantially lower NHS costs.<br/

A randomised controlled trial of a digital intervention (renewed) to support symptom management, wellbeing and quality of life in cancer survivors

Background: Many cancer survivors following primary treatment have prolonged poor quality of life. Aim: To determine the effectiveness of a bespoke digital intervention to support cancer survivors. Design: Pragmatic parallel open randomised trial. Setting: UK general practices. Methods: People having finished primary treatment (<= 10 years previously) for colo-rectal, breast or prostate cancers, with European-Organization-for-Research-and-Treatment-of-Cancer QLQ-C30 score <85, were randomised by online software to: 1)detailed ‘generic’ digital NHS support (‘LiveWell’;n=906), 2) a bespoke complex digital intervention (‘Renewed’;n=903) addressing symptom management, physical activity, diet, weight loss, distress, or 3) ‘Renewed-with-support’ (n=903): ‘Renewed’ with additional brief email and telephone support. Results: Mixed linear regression provided estimates of the differences between each intervention group and generic advice: at 6 months (primary time point: n’s respectively 806;749;705) all groups improved, with no significant between-group differences for EORTC QLQ-C30, but global health improved more in both intervention groups. By 12 months there were: small improvements in EORTC QLQ-C30 for Renewed-with-support (versus generic advice: 1.42, 95% CIs 0.33-2.51); both groups improved global health (12 months: renewed: 3.06, 1.39-4.74; renewed-with-support: 2.78, 1.08-4.48), dyspnoea, constipation, and enablement, and lower NHS costs (generic advice £265: in comparison respectively £141 (153-128) and £77 (90-65) lower); and for Renewed-with-support improvement in several other symptom subscales. No harms were identified. Conclusion: Cancer survivors quality of life improved with detailed generic online support. Robustly developed bespoke digital support provides limited additional short term benefit, but additional longer term improvement in global health enablement and symptom management, with substantially lower NHS costs

The covariate-adjusted frequency plot for the Rasch Poisson Counts model

The Rasch Poisson Counts model is an appropriate item response theory (IRT) model for analyzing many kinds of count data in educational and psychological testing. The evaluation of a fitted Rasch Poisson model by means of a graphical display or graphical device is difficult and, hence, very much an open problem, since the observations come from different distributions. Hence methods, potentially straightforward in the univariate case, cannot be applied for this model. However, it is possible to use a method, called the covariate–adjusted frequency plot, which incorporates covariate information into a marginal frequency plot. We utilize this idea here to construct a covariate-adjusted frequency plot for the Rasch Poisson Counts model. This graphical method is useful in illustrating goodness-of-fit of the model as well as identifying potential areas (items) with problematic fit. A case study using typical data from a frequently used intelligence test illustrates the method which is easy to us

Power series mixtures and the ratio plot with applications to zero-truncated count distribution modelling

The purpose of this note is to contribute some general points on how mixtures of power series distributions relate to their ratios of neighboring probabilities and how the associated graph, the ratio plot, can be used as diagnostic device as suggested in Böhning (J Comput Graph Stat 22:133–155, 2013). This work is continued here and extensively used to explore the aptness of the negative-binomial and beta-binomial model as capture-recapture zero-truncated count models. It is concluded that these models are less suitable for capture-recapture modelling as frequently readily assumed. This is mainly due to an inherent boundary problem that is elaborated here and illustrated at hand of some case studies

Chao’s lower bound estimator and the size of the Pleiades

In this note we would like to point out that the lower bound estimator of the frequency of hidden units in a target population, developed by Chao in ecology, was developed independently in astro-physics and has been used to estimate the size of flare stars in the Pleiades

Meta-analysis and meta-modelling for diagnostic problems

BackgroundA proportional hazards measure is suggested in the context of analyzing SROC curves that arise in the meta–analysis of diagnostic studies. The measure can be motivated as a special model: the Lehmann model for ROC curves. The Lehmann model involves study–specific sensitivities and specificities and a diagnostic accuracy parameter which connects the two.MethodsA study–specific model is estimated for each study, and the resulting study-specific estimate of diagnostic accuracy is taken as an outcome measure for a mixed model with a random study effect and other study-level covariates as fixed effects. The variance component model becomes estimable by deriving within-study variances, depending on the outcome measure of choice. In contrast to existing approaches – usually of bivariate nature for the outcome measures – the suggested approach is univariate and, hence, allows easily the application of conventional mixed modelling.ResultsSome simple modifications in the SAS procedure proc mixed allow the fitting of mixed models for meta-analytic data from diagnostic studies. The methodology is illustrated with several meta–analytic diagnostic data sets, including a meta–analysis of the Mini–Mental State Examination as a diagnostic device for dementia and mild cognitive impairment.ConclusionsThe proposed methodology allows us to embed the meta-analysis of diagnostic studies into the well–developed area of mixed modelling. Different outcome measures, specifically from the perspective of whether a local or a global measure of diagnostic accuracy should be applied, are discussed as well. In particular, variation in cut-off value is discussed together with recommendations on choosing the best cut-off value. We also show how this problem can be addressed with the proposed methodology

Population size estimation based upon zero-truncated, one-inflated and sparse count data: Estimating the number of dice snakes in Graz and flare stars in the Pleiades

Estimating the size of a hard-to-count population is a challenging matter. In particular, when only few observations of the population to be estimated are available. The matter gets even more complex when one-inflation occurs. This situation is illustrated with the help of two examples: the size of a dice snake population in Graz (Austria) and the number of flare stars in the Pleiades. The paper discusses how one-inflation can be easily handled in likelihood approaches and also discusses how variances and confidence intervals can be obtained by means of a semi-parametric bootstrap. A Bayesian approach is mentioned as well and all approaches result in similar estimates of the hidden size of the population. Finally, a simulation study is provided which shows that the unconditional likelihood approach as well as the Bayesian approach using Jeffreys’ prior perform favorable.</p