Modeling longitudinal data with a random change point and no time-zero: applications to inference and prediction of the labor curve

A mixed effects changepoint quantile regression model for longitudinal data with application on COVID-19 data

Introduction

Longitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the follow-up period, with one or more unknown transition points (changepoints). The detection and estimation of these changepoints is crucial. Most of the proposed statistical methods for detecting and estimating changepoints in literature rely on distributional assumptions that may not hold. In this case, a good alternative is to use a robust approach; the quantile regression model. There are methods in the literature to deal with quantile regression models with a changepoint. These methods ignore the within-subject dependence of longitudinal data.

Methods

We propose a mixed effects quantile regression model with changepoints to account for dependence structure in the longitudinal data. Fixed effects parameters, in addition to the location of the changepoint, are estimated using the profile estimation method. The stochastic approximation EM algorithm is proposed to estimate the fixed effects parameters exploiting the link between an asymmetric Laplace distribution and the quantile regression. In addition, the location of the changepoint is estimated using the usual optimization methods.

Results and discussion

A simulation study shows that the proposed estimation and inferential procedures perform reasonably well in finite samples. The practical use of the proposed model is illustrated using COVID-19 data. The data focus on the effect of global economic and health factors on the monthly death rate due to COVID-19 from 1 April 2020 to 30th April 2021. the results show a positive effect on the monthly number of patients with COVID-19 in intensive care units (ICUs) for both 0.5th and 0.8th quantiles of new monthly deaths per million. The stringency index, hospital beds, and diabetes prevalence have no significant effect on both 0.5th and 0.8th quantiles of new monthly deaths per million.

Modeling repeated labor curves in consecutive pregnancies: Individualized prediction of labor progression from previous pregnancy data

The measurement of cervical dilation of a pregnant woman is used to monitor the progression of labor until 10 cm when pushing begins. There is anecdotal evidence that labor tracks across repeated pregnancies; moreover, no statistical methodology has been developed to address this important issue, which can help obstetricians make more informed clinical decisions about an individual woman's progression. Motivated by the NICHD Consecutive Pregnancies Study (CPS), we propose new methodology for analyzing labor curves across consecutive pregnancies. Our focus is both on studying the correlation between repeated labor curves on the same woman and on using the cervical dilation data from prior pregnancies to predict subsequent labor curves. We propose a hierarchical random effects model with a random change point that characterizes repeated labor curves within and between women to address these issues. We employ Bayesian methodology for parameter estimation and prediction. Model diagnostics to examine the appropriateness of the hierarchical random effects structure for characterizing the dependence structure across consecutive pregnancies are also proposed. The methodology was used in analyzing the CPS data and in developing a predictor for labor progression that can be used in clinical practice.

A Joint Model Approach for Longitudinal Data with no Time-Zero and Time-to-Event with Competing Risks

The joint modeling of longitudinal and time-to-event data is an active area in biostatistics research. The focus of this article is on developing a modeling framework for these joint models when the longitudinal and time-to-event data do not have a meaningful time-zero. The motivating example is the study of a longitudinal assessment of station during child labor and it's relationship to time-to-delivery. A good predictor of delivery type and timing would help obstetricians better manage the end of pregnancy and better facilitate delivery. One measure of labor progression is station, a measure of the position of the fetus' head in relation to the pelvis of the pregnant women, may be a good marker for delivery time and type. However, women enter the hospital, where their station is closely monitored, at arbitrary points in their labor process, resulting in no clear time zero. In addition, since delivery may be of various types, the competing risks due to type need to be accounted for. We develop a joint model of longitudinal and time-to-event data for this situation. The model is formulated through shared random effects between the survival and longitudinal processes, and parameter estimation is conducted through a Bayesian approach. The model is illustrated with longitudinal data on station where the relationship between station and event-time is studied and the model is used to assess the ability of longitudinal measures of station to predict the type and timing of pregnancy. We illustrate the methodology with longitudinal data taken during labor.

Estimating time to event characteristics via longitudinal threshold regression models - an application to cervical dilation progression

In longitudinal studies, it is sometimes of interest to estimate the distribution of the time a longitudinal process takes to traverse from one threshold to another. For example, the distribution of the time it takes a woman's cervical dilation to progress from 3 to 4 cm can aid the decision-making of obstetricians as to whether a stalled labor should be allowed to proceed or stopped in favor of other options. Often researchers treat this type of data structure as interval censored and employ traditional survival analysis methods. However, the traditional interval censoring approaches are inefficient in that they do not use all of the available data. In this paper, we propose utilizing a longitudinal threshold model to estimate the distribution of the elapsed time between two thresholds of the longitudinal process from repeated measurements. We extend this modeling framework to be used with multiple thresholds. A Wiener process under the first hitting time framework is used to represent survival distribution. We demonstrate our model through simulation studies and an analysis of data from the Consortium on Safe Labor study. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.