A general piecewise multi-state survival model: Application to breast cancer

Multi-state models are considered in the field of survival analysis for modelling illnesses that evolve through several stages over time. Multi-state models can be developed by applying several techniques, such as non-parametric, semi-parametric and stochastic processes, particularly Markov processes. When the development of an illness is being analysed, its progression is tracked periodically. Medical reviews take place at discrete times, and a panel data analysis can be formed. In this paper, a discrete-time piecewise non-homogeneous Markov process is constructed for modelling and analysing a multi-state illness with a general number of states. The model is built, and relevant measures, such as survival function, transition probabilities, mean total times spent in a group of states and the conditional probability of state change, are determined. A likelihood function is built to estimate the parameters and the general number of cut-points included in the model. Time-dependent covariates are introduced, the results are obtained in a matrix algebraic form and the algorithms are shown. The model is applied to analyse the behaviour of breast cancer. A study of the relapse and survival times of 300 breast cancer patients who have undergone mastectomy is developed. The results of this paper are implemented computationally with MATLAB and R.Ministerio de Economía y Competitividad FQM-307European Regional Development Fund (ERDF) MTM2017-88708-PUniversity of Milano-Bicocca 2014-ATE-022

Effects of Total Resources, Resource Ratios, and Species Richness on Algal Productivity and Evenness at Both Metacommunity and Local Scales

The study of the interrelationship between productivity and biodiversity is a major research field in ecology. Theory predicts that if essential resources are heterogeneously distributed across a metacommunity, single species may dominate productivity in individual metacommunity patches, but a mixture of species will maximize productivity across the whole metacommunity. It also predicts that a balanced supply of resources within local patches should favor species coexistence, whereas resource imbalance would favor the dominance of one species. We performed an experiment with five freshwater algal species to study the effects of total supply of resources, their ratios, and species richness on biovolume production and evenness at the scale of both local patches and metacommunities. Generally, algal biovolume increased, whereas algal resource use efficiency (RUE) and evenness decreased with increasing total supply of resources in mixed communities containing all five species. In contrast to predictions for biovolume production, the species mixtures did not outperform all monocultures at the scale of metacommunities. In other words, we observed no general transgressive overyielding. However, RUE was always higher in mixtures than predicted from monocultures, and analyses indicate that resource partitioning or facilitation in mixtures resulted in higher-than-expected productivity at high resource supply. Contrasting our predictions for the local scale, balanced supply of resources did not generally favor higher local evenness, however lowest evenness was confined to patches with the most imbalanced supply. Thus, our study provides mixed support for recent theoretical advancements to understand biodiversity-productivity relationships

A Key Marine Diazotroph in a Changing Ocean: The Interacting Effects of Temperature, CO2 and Light on the Growth of Trichodesmium erythraeum IMS101

Trichodesmium is a globally important marine diazotroph that accounts for approximately 60-80% of marine biological N2 fixation and as such plays a key role in marine N and C cycles. We undertook a comprehensive assessment of how the growth rate of Trichodesmium erythraeum IMS101 was directly affected by the combined interactions of temperature, pCO2 and light intensity. Our key findings were: low pCO2 affected the lower temperature tolerance limit (Tmin) but had no effect on the optimum temperature (Topt) at which growth was maximal or the maximum temperature tolerance limit (Tmax); low pCO2 had a greater effect on the thermal niche width than low-light; the effect of pCO2 on growth rate was more pronounced at suboptimal temperatures than at supraoptimal temperatures; temperature and light had a stronger effect on the photosynthetic efficiency (Fv/Fm) than did CO2; and at Topt, the maximum growth rate increased with increasing CO2, but the initial slope of the growth-irradiance curve was not affected by CO2. In the context of environmental change, our results suggest that the (i) nutrient replete growth rate of Trichodesmium IMS101 would have been severely limited by low pCO2 at the last glacial maximum (LGM), (ii) future increases in pCO2 will increase growth rates in areas where temperature ranges between Tmin to Topt, but will have negligible effect at temperatures between Topt and Tmax, (iii) areal increase of warm surface waters (> 18°C) has allowed the geographic range to increase significantly from the LGM to present and that the range will continue to expand to higher latitudes with continued warming, but (iv) continued global warming may exclude Trichodesmium spp. from some tropical regions by 2100 where temperature exceeds Topt

Individualised variable-interval risk-based screening for sight-threatening diabetic retinopathy: the Liverpool Risk Calculation Engine

Aims/hypothesis Individualised variable-interval risk-based screening offers better targeting and improved cost-effectiveness in screening for diabetic retinopathy. We developed a generalisable risk calculation engine (RCE) to assign personalised intervals linked to local population characteristics, and explored differences in assignment compared with current practice. Methods Data from 5 years of photographic screening and primary care for people with diabetes, screen negative at the first of > 1 episode, were combined in a purpose-built near-real-time warehouse. Covariates were selected from a dataset created using mixed qualitative/quantitative methods. Markov modelling predicted progression to screen-positive (referable diabetic retinopathy) against the local cohort history. Retinopathy grade informed baseline risk and multiple imputation dealt with missing data. Acceptable intervals (6, 12, 24 months) and risk threshold (2.5%) were established with patients and professional end users. Results Data were from 11,806 people with diabetes (46,525 episodes, 388 screen-positive). Covariates with sufficient predictive value were: duration of known disease, HbA1c, age, systolic BP and total cholesterol. Corrected AUC (95% CIs) were: 6 months 0.88 (0.83, 0.93), 12 months 0.90 (0.87, 0.93) and 24 months 0.91 (0.87, 0.94). Sensitivities/specificities for a 2.5% risk were: 6 months 0.61, 0.93, 12 months 0.67, 0.90 and 24 months 0.82, 0.81. Implementing individualised RCE-based intervals would reduce the proportion of people becoming screen-positive before the allocated screening date by > 50% and the number of episodes by 30%. Conclusions/interpretation The Liverpool RCE shows sufficient performance for a local introduction into practice before wider implementation, subject to external validation. This approach offers potential enhancements of screening in improved local applicability, targeting and cost-effectiveness

Computation of the asymptotic null distribution of goodness-of-fit tests for multi-state models.

We develop an improved approximation to the asymptotic null distribution of the goodness-of-fit tests for panel observed multi-state Markov models (Aguirre-Hernandez and Farewell, Stat Med 21:1899-1911, 2002) and hidden Markov models (Titman and Sharples, Stat Med 27:2177-2195, 2008). By considering the joint distribution of the grouped observed transition counts and the maximum likelihood estimate of the parameter vector it is shown that the distribution can be expressed as a weighted sum of independent X^2_1 random variables, where the weights are dependent on the true parameters. The performance of this approximation for finite sample sizes and where the weights are calculated using the maximum likelihood estimates of the parameters is considered through simulation. In the scenarios considered, the approximation performs well and is a substantial improvement over the simple X^2_1 approximation

Recurrent events modelling of haemophilia bleeding events

Abstract A pharmacokinetic–pharmacodynamic (PK-PD) approach is developed for modelling the recurrent bleeding events in patients with severe haemophilia to investigate the relationship between factor VIII plasma activity level and the instantaneous risk of a bleed. The model incorporates patient-level pharmacokinetic (PK) information obtained through measurements taken prior to the study which are used to fit a non-linear mixed-effects two-compartment PK model. Dosing times within the study are combined with the PK model to provide the estimated factor VIII plasma level for all patients, which is used as a time-dependent covariate within the recurrent events model. Methods are developed to correct the attenuation in covariate effects that would otherwise arise due to the discrepancy between estimated and true factor VIII. In contrast to existing methods proposed for such data, such as count data regression or time-to-event analysis, the new method allows all the bleeding times to be used to investigate the relationship between current factor VIII and risk of a bleed. The performance of the proposed estimators are assessed via simulation and found to outperform the naive estimator, which treats the estimated factor VIII levels as if they were measured without error, both in terms of bias and mean squared error.</jats:p

Goodness-of-fit tests for parametric nonhomogeneous Markov processes

Tests for parametric nonhomogeneous and homogeneous Markov processes are given. Asymptotic distribution of test statistics is investigated. Tests for various well-known models are discussed as examples