RPEM: Randomized Monte Carlo parametric expectation maximization algorithm.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis-Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi-Random Parametric Expectation Maximization (QRPEM) for a realistic two-compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log-normal cases.

Global, region and national trends and age-period-cohort effects in colorectal cancer burden from 1990 to 2019, with predictions to 2039.

Nowadays, colorectal cancer (CRC) is the second leading cause of cancer deaths and contributes to a gradually increasing disease burden. We aimed to estimate the secular trends of global CRC burden, the effect of age, period, and birth cohort, and project the global burden over time. Based on the epidemiological CRC data from 1990 to 2019 in 204 countries and territories from GBD 2019, the estimated annual percentage change (EAPC), was calculated from a linear model and joinpoint regression model. We utilized an age-period-cohort model to reckon age, period, and birth cohort effects on CRC age-standardized rate. The burden of CRC was projected by conducting the BAPC model. Globally, there was a slight decline in the age-standardized DALY rate, which was more apparent in females, with high SDI regions and in Australia and Western Europe areas. Meanwhile, our model predicts a weaker increase in morbidity (EAPC of 0.37) and a speedier reduction in mortality (EAPC of -0.66) by the next 20 years. The relative risk of period for high SDI regions decreased from 1.08 (95%UI: 1.06-1.1) in 1990-1994 to 0.85 (95%UI:0.83-0.88) in 2015-2019, but worsens in low and middle SDI regions. The local drifts were more than 1 in the 30-34 and 35-39 age groups, indicating the rising tide of early-onset CRC. Given the gender and region-specific CRC, targeted efforts to reduce the prevalence of risk factors, improve screening coverage rates, and strengthen foundational medical facilities are necessary.

Nonlinear stochastic Markov processes and modeling uncertainty in populations.

We consider an alternative approach to the use of nonlinear stochastic Markov processes (which have a Fokker-Planck or Forward Kolmogorov representation for density) in modeling uncertainty in populations. These alternate formulations, which involve imposing probabilistic structures on a family of deterministic dynamical systems, are shown to yield pointwise equivalent population densities. Moreover, these alternate formulations lead to fast efficient calculations in inverse problems as well as in forward simulations. Here we derive a class of stochastic formulations for which such an alternate representation is readily found.