Non-homogeneous continuous-time Markov chain with covariates: Applications to ambulatory hypertension monitoring

Hypertension significantly increases the risk for many health conditions including heart disease and stroke. Hypertensive patients often have continuous measurements of their blood pressure to better understand how it fluctuates over the day. The continuous-time Markov chain (CTMC) is commonly used to study repeated measurements with categorical outcomes. However, the standard CTMC may be restrictive, because the rates of transitions between states are assumed to be constant through time, while the transition rates for describing the dynamics of hypertension are likely to be changing over time. In addition, the applications of CTMC rarely account for the effects of other covariates on state transitions. In this article, we considered a non-homogeneous continuous-time Markov chain with two states to analyze changes in hypertension while accounting for multiple covariates. The explicit formulas for the transition probability matrix as well as the corresponding likelihood function were derived. In addition, we proposed a maximum likelihood estimation algorithm for estimating the parameters in the time-dependent rate function. Lastly, the model performance was demonstrated through both a simulation study and application to ambulatory blood pressure data.

Maximum Likelihood Estimation for Semiparametric Regression Models With Panel Count Data

Panel count data, in which the observation for each study subject consists of the number of recurrent events between successive examinations, are commonly encountered in industrial reliability testing, medical research, and various other scientific investigations. We formulate the effects of potentially time-dependent covariates on one or more types of recurrent events through non-homogeneous Poisson processes with random effects. We adopt nonparametric maximum likelihood estimation under arbitrary examination schemes and develop a simple and stable EM algorithm. We show that the resulting estimators of the regression parameters are consistent and asymptotically normal, with a covariance matrix that achieves the semiparametric efficiency bound and can be estimated through profile likelihood. We evaluate the performance of the proposed methods through extensive simulation studies and present a skin cancer clinical trial.

Joint modeling of time-varying HIV exposure and infection for estimation of per-act efficacy in HIV prevention trials

Objectives

Using the MTN-020/ASPIRE HIV prevention trial as a motivating example, our objective is to construct a joint model for the HIV exposure process through vaginal intercourse and the time to HIV infection in a population of sexually active women. By modeling participants' HIV infection in terms of exposures, rather than time exposed, our aim is to obtain a valid estimate of the per-act efficacy of a preventive intervention.

Methods

Within the context of HIV prevention trials, in which the frequency of sex acts is self-reported periodically by the participants, we model the exposure process of the trial participants with a non-homogeneous Poisson process. This approach allows for variability in the rate of sexual contacts between participants as well as variability in the rate of sexual contacts over time. The time to HIV infection for each participant is modeled as the time to the exposure that results in HIV infection, based on the modeled sexual contact rate. We propose an empirical Bayes approach for estimation.

Results

We report the results of a simulation study where we evaluate the performance of our proposed approachandcompareittothetraditionalapproachofestimatingtheoverallreductioninHIVincidenceusing a Proportional Hazards Cox model. The proposed approach is also illustrated with data from the MTN-020/ASPIRE trial.

Conclusions

The proposed joint modeling, along with the proposed empirical Bayes estimation approach, can provide valid estimation of the per-exposure efficacy of a preventive intervention.

Random forests for homogeneous and non-homogeneous Poisson processes with excess zeros

We propose a general hurdle methodology to model a response from a homogeneous or a non-homogeneous Poisson process with excess zeros, based on two forests. The first forest in the two parts model is used to estimate the probability of having a zero. The second forest is used to estimate the Poisson parameter(s), using only the observations with at least one event. To build the trees in the second forest, we propose specialized splitting criteria derived from the zero truncated homogeneous and non-homogeneous Poisson likelihood. The particular case of a homogeneous process is investigated in details to stress out the advantages of the proposed method over the existing ones. Simulation studies show that the proposed methods perform well in hurdle (zero-altered) and zero-inflated settings, for both homogeneous and non-homogeneous processes. We illustrate the use of the new method with real data on the demand for medical care by the elderly.

Bias and estimation under misspecification of the risk period in self-controlled case series studies

The self-controlled case series (SCCS) method is useful for estimating the relative incidence (RI) of acute events, such as adverse events (AEs) during a specified risk period following an exposure (e.g., 6-week period after vaccinations or 30-day period after infection-related hospitalizations). In practice, the "optimal" risk period is unknown and must be specified. To date, two approaches are available to guide the specification of the risk period. Both methods do not fully utilize the nature of the bias due to misspecification, which to date has not been characterized. Thus, we elucidate the bias of SCCS estimate of the RI when the risk period is misspecified. We then propose a novel method that more effectively estimates the optimal risk period and the associated RI of AEs. The new method incorporates information on the functional form of the bias. Efficacy of the proposed approach is illustrated with substantial reduction in bias and variance in simulation studies. The proposed method is illustrated with two SCCS studies to determine the (1) risk of idiopathic thrombocytopenic purpura after measles-mumps-rubella vaccination in children and (2) risk of cardiovascular events after infection-related hospitalizations in older patients on dialysis.