Non-parametric estimation of reference adjusted, standardised probabilities of all-cause death and death due to cancer for population group comparisons

Background Ensuring fair comparisons of cancer survival statistics across population groups requires careful consideration of differential competing mortality due to other causes, and adjusting for imbalances over groups in other prognostic covariates (e.g. age). This has typically been achieved using comparisons of age-standardised net survival, with age standardisation addressing covariate imbalance, and the net estimates removing differences in competing mortality from other causes. However, these estimates lack ease of interpretability. In this paper, we motivate an alternative non-parametric approach that uses a common rate of other cause mortality across groups to give reference-adjusted estimates of the all-cause and cause-specific crude probability of death in contrast to solely reporting net survival estimates. Methods We develop the methodology for a non-parametric equivalent of standardised and reference adjusted crude probabilities of death, building on the estimation of non-parametric crude probabilities of death. We illustrate the approach using regional comparisons of survival following a diagnosis of rectal cancer for men in England. We standardise to the covariate distribution and other cause mortality of England as a whole to offer comparability, but with close approximation to the observed all-cause region-specific mortality. Results The approach gives comparable estimates to observed crude probabilities of death, but allows direct comparison across population groups with different covariate profiles and competing mortality patterns. In our illustrative example, we show that regional variations in survival following a diagnosis of rectal cancer persist even after accounting for the variation in deprivation, age at diagnosis and other cause mortality. Conclusions The methodological approach of using standardised and reference adjusted metrics offers an appealing approach for future cancer survival comparison studies and routinely published cancer statistics. Our non-parametric estimation approach through the use of weighting offers the ability to estimate comparable survival estimates without the need for statistical modelling.

Development of an estimation-experimental method for estimating the preservation indicators of single-use articles

To manage the operation of modern single-use products, it is necessary to evaluate their preservation indicators as uncontrolled, non-repairable, and maintenance-free objects. Data for assessing its parameters are considered as one-time censored samples with continuous monitoring, which does not correspond to the mode of storage of products during operation. Under the conditions of limited volumes of censored samples, it is problematic to identify the parametric model of persistence. To solve this problem, a non-parametric estimation-experimental method has been devised, which is a set of models for data generation, estimation of the function of the distribution of the preservation period and preservation indicators. The data generation model is represented by a scheme of operational tests and analytical relationships between the quantities of tested and failed articles. The model of estimating the distribution function describes the process of its construction on the generated data. Models for estimating preservation indicators are represented by ratios for their point and interval estimates, as functionals from the restored distribution function. Unlike the well-known ones, the developed method implements the assessment of indicators under the conditions of combined censorship. The method can be used to assess the preservation indicators of single-use articles with an error of at least 7 %. At the same time, their lower confidence limits are estimated at 0.9 with an error not worse than 14 % with a censorship degree of not more than 0.23. The restored distribution function agrees well (reliability 0.9, error 0.1) with the actual persistence of articles with censorship degrees of not more than 0.73, which is acceptable for solving the problems of managing their operation.

A Review of Shannon and Differential Entropy Rate Estimation

In this paper, we present a review of Shannon and differential entropy rate estimation techniques. Entropy rate, which measures the average information gain from a stochastic process, is a measure of uncertainty and complexity of a stochastic process. We discuss the estimation of entropy rate from empirical data, and review both parametric and non-parametric techniques. We look at many different assumptions on properties of the processes for parametric processes, in particular focussing on Markov and Gaussian assumptions. Non-parametric estimation relies on limit theorems which involve the entropy rate from observations, and to discuss these, we introduce some theory and the practical implementations of estimators of this type.

Disparity Analysis for Single Variable Interventions

A recent literature in sociology and epidemiology introduces the `targeted disparity': the extent to which socio-demographic inequalities would persist under an intervention to equalize some intervening variable on the path from the demographic marker to an outcome. In this paper, I propose a unified framework with which to understand targeted interventions. This framework helps researchers map a graphical claim about an intervention in terms of blocking causal and non-causal pathways from a demographic marker to an outcome onto mathematical claims which involve defining an intervention in terms of a probability function. Further, I propose a new type of targeted disparity which intervenes on one of two intermediate variables, and generalize this to describe an intervention that intervenes with respect to an arbitrary `intervention set'. Each of the interventions I describe can be understood as mapping onto a particular set of policy interventions, but can additionally be shown to decompose the total disparity between socio-demographic groups into cumulative pathways through a mediator. Finally, I propose a series of parametric and non–parametric estimation strategies that can be combined with machine-learning methods to estimate the disparities of interest.