A linear mixed model for predicting a binary event from longitudinal data under random effects misspecification

Predictions of machine learning with mixed-effects in analyzing longitudinal data under model misspecification

We consider predictions in longitudinal studies, and investigate the well known statistical mixed-effects model, piecewise linear mixed-effects model and six different popular machine learning approaches: decision trees, bagging, random forest, boosting, support-vector machine and neural network. In order to consider the correlated data in machine learning, the random effects is combined into the traditional tree methods and random forest. Our focus is the performance of statistical modelling and machine learning especially in the cases of the misspecification of the fixed effects and the random effects. Extensive simulation studies have been carried out to evaluate the performance using a number of criteria. Two real datasets from longitudinal studies are analysed to demonstrate our findings. The R code and dataset are freely available at https://github.com/shuwen92/MEML.

Bayesian semiparametric joint modeling of longitudinal explanatory variables of mixed types and a binary outcome

Many prospective biomedical studies collect longitudinal clinical and lifestyle data that are both continuous and discrete. In some studies, there is interest in the association between a binary outcome and the values of these longitudinal measurements at a specific time point. A common problem in these studies is inconsistency in timing of measurements and missing follow-ups which can lead to few measurements at the time of interest. Some methods have been developed to address this problem, but are only applicable to continuous measurements. To address this limitation, we propose a new class of joint models for a binary outcome and longitudinal explanatory variables of mixed types. The longitudinal model uses a latent normal random variable construction with regression splines to model time-dependent trends in mean with a Dirichlet Process prior assigned to random effects to relax distribution assumptions. We also standardize timing of the explanatory variables by relating the binary outcome to imputed longitudinal values at a set time point. The proposed model is evaluated through simulation studies and applied to data from a cancer survivor study of participants in the Women's Health Initiative.

Discriminatory Capacity of Prenatal Ultrasound Measures for Large-for-Gestational-Age Birth: A Bayesian Approach to ROC Analysis Using Placement Values

Predicting large fetuses at birth is of great interest to obstetricians. Using an NICHD Scandinavian Study that collected longitudinal ultrasound examination data during pregnancy, we estimate diagnostic accuracy parameters of estimated fetal weight (EFW) at various times during pregnancy in predicting large-for-gestational-age. We adopt a placement value based Bayesian regression model with random effects to estimate ROC curves. The use of placement values allows us to model covariate effects directly on the ROC curves and the adoption of a Bayesian approach accommodates the a priori constraint that an ROC curve of EFW near delivery should dominate another further away. The proposed methodology is shown to perform better than some alternative approaches in simulations and its application to the Scandinavian Study data suggests that diagnostic accuracy of EFW can improve about 65% from week 17 to 37 of gestation.

The effect of random-effects misspecification on classification accuracy

Mixed models are a useful way of analysing longitudinal data. Random effects terms allow modelling of patient specific deviations from the overall trend over time. Correlation between repeated measurements are captured by specifying a joint distribution for all random effects in a model. Typically, this joint distribution is assumed to be a multivariate normal distribution. For Gaussian outcomes misspecification of the random effects distribution usually has little impact. However, when the outcome is discrete (e.g. counts or binary outcomes) generalised linear mixed models (GLMMs) are used to analyse longitudinal trends. Opinion is divided about how robust GLMMs are to misspecification of the random effects. Previous work explored the impact of random effects misspecification on the bias of model parameters in single outcome GLMMs. Accepting that these model parameters may be biased, we investigate whether this affects our ability to classify patients into clinical groups using a longitudinal discriminant analysis. We also consider multiple outcomes, which can significantly increase the dimensions of the random effects distribution when modelled simultaneously. We show that when there is severe departure from normality, more flexible mixture distributions can give better classification accuracy. However, in many cases, wrongly assuming a single multivariate normal distribution has little impact on classification accuracy.

Exploratory assessment of treatment-dependent random-effects distribution using gradient functions

In analyzing repeated measurements from randomized controlled trials with mixed-effects models, it is important to carefully examine the conventional normality assumption regarding the random-effects distribution and its dependence on treatment allocation in order to avoid biased estimation and correctly interpret the estimated random-effects distribution. In this article, we propose the use of a gradient function method in modeling with the different random-effects distributions depending on the treatment allocation. This method can be effective for considering in advance whether a proper fit requires a model that allows dependence of the random-effects distribution on covariates, or for finding the subpopulations in the random effects.

Value of dynamic clinical and biomarker data for mortality risk prediction in COVID-19: a multicentre retrospective cohort study

OBJECTIVES

Being able to predict which patients with COVID-19 are going to deteriorate is important to help identify patients for clinical and research practice. Clinical prediction models play a critical role in this process, but current models are of limited value because they are typically restricted to baseline predictors and do not always use contemporary statistical methods. We sought to explore the benefits of incorporating dynamic changes in routinely measured biomarkers, non-linear effects and applying 'state-of-the-art' statistical methods in the development of a prognostic model to predict death in hospitalised patients with COVID-19.

DESIGN

The data were analysed from admissions with COVID-19 to three hospital sites. Exploratory data analysis included a graphical approach to partial correlations. Dynamic biomarkers were considered up to 5 days following admission rather than depending solely on baseline or single time-point data. Marked departures from linear effects of covariates were identified by employing smoothing splines within a generalised additive modelling framework.

SETTING

3 secondary and tertiary level centres in Greater Manchester, the UK.

PARTICIPANTS

392 hospitalised patients with a diagnosis of COVID-19.

RESULTS

392 patients with a COVID-19 diagnosis were identified. Area under the receiver operating characteristic curve increased from 0.73 using admission data alone to 0.75 when also considering results of baseline blood samples and to 0.83 when considering dynamic values of routinely collected markers. There was clear non-linearity in the association of age with patient outcome.

CONCLUSIONS

This study shows that clinical prediction models to predict death in hospitalised patients with COVID-19 can be improved by taking into account both non-linear effects in covariates such as age and dynamic changes in values of biomarkers.

Statistical approaches using longitudinal biomarkers for disease early detection: A comparison of methodologies

Early detection of clinical outcomes such as cancer may be predicted using longitudinal biomarker measurements. Tracking longitudinal biomarkers as a way to identify early disease onset may help to reduce mortality from diseases like ovarian cancer that are more treatable if detected early. Two disease risk prediction frameworks, the shared random effects model (SREM) and the pattern mixture model (PMM) could be used to assess longitudinal biomarkers on disease early detection. In this article, we studied the discrimination and calibration performances of SREM and PMM on disease early detection through an application to ovarian cancer, where early detection using the risk of ovarian cancer algorithm (ROCA) has been evaluated. Comparisons of the above three approaches were performed via analyses of the ovarian cancer data from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial. Discrimination was evaluated by the time-dependent receiver operating characteristic curve and its area, while calibration was assessed using calibration plot and the ratio of observed to expected number of diseased subjects. The out-of-sample performances were calculated via using leave-one-out cross-validation, aiming to minimize potential model overfitting. A careful analysis of using the biomarker cancer antigen 125 for ovarian cancer early detection showed significantly improved discrimination performance of PMM as compared with SREM and ROCA, nevertheless all approaches were generally well calibrated. Robustness of all approaches was further investigated in extensive simulation studies. The improved performance of PMM relative to ROCA is in part due to the fact that the biomarker measurements were taken at a yearly interval, which is not frequent enough to reliably estimate the changepoint or the slope after changepoint in cases under ROCA.

The ROC curve for regularly measured longitudinal biomarkers

The receiver operating characteristic (ROC) curve is a commonly used graphical summary of the discriminative capacity of a thresholded continuous scoring system for a binary outcome. Estimation and inference procedures for the ROC curve are well-studied in the cross-sectional setting. However, there is a paucity of research when both biomarker measurements and disease status are observed longitudinally. In a motivating example, we are interested in characterizing the value of longitudinally measured CD4 counts for predicting the presence or absence of a transient spike in HIV viral load, also time-dependent. The existing method neither appropriately characterizes the diagnostic value of observed CD4 counts nor efficiently uses status history in predicting the current spike status. We propose to jointly model the binary status as a Markov chain and the biomarkers levels, conditional on the binary status, as an autoregressive process, yielding a dynamic scoring procedure for predicting the occurrence of a spike. Based on the resulting prediction rule, we propose several natural extensions of the ROC curve to the longitudinal setting and describe procedures for statistical inference. Lastly, extensive simulations have been conducted to examine the small sample operational characteristics of the proposed methods.

Likelihood contrasts: a machine learning algorithm for binary classification of longitudinal data

Machine learning methods have gained increased popularity in biomedical research during the recent years. However, very few of them support the analysis of longitudinal data, where several samples are collected from an individual over time. Additionally, most of the available longitudinal machine learning methods assume that the measurements are aligned in time, which is often not the case in real data. Here, we introduce a robust longitudinal machine learning method, named likelihood contrasts (LC), which supports study designs with unaligned time points. Our LC method is a binary classifier, which uses linear mixed models for modelling and log-likelihood for decision making. To demonstrate the benefits of our approach, we compared it with existing methods in four simulated and three real data sets. In each simulated data set, LC was the most accurate method, while the real data sets further supported the robust performance of the method. LC is also computationally efficient and easy to use.

Harnessing repeated measurements of predictor variables for clinical risk prediction: a review of existing methods

BACKGROUND

Clinical prediction models (CPMs) predict the risk of health outcomes for individual patients. The majority of existing CPMs only harness cross-sectional patient information. Incorporating repeated measurements, such as those stored in electronic health records, into CPMs may provide an opportunity to enhance their performance. However, the number and complexity of methodological approaches available could make it difficult for researchers to explore this opportunity. Our objective was to review the literature and summarise existing approaches for harnessing repeated measurements of predictor variables in CPMs, primarily to make this field more accessible for applied researchers.

METHODS

MEDLINE, Embase and Web of Science were searched for articles reporting the development of a multivariable CPM for individual-level prediction of future binary or time-to-event outcomes and modelling repeated measurements of at least one predictor. Information was extracted on the following: the methodology used, its specific aim, reported advantages and limitations, and software available to apply the method.

RESULTS

The search revealed 217 relevant articles. Seven methodological frameworks were identified: time-dependent covariate modelling, generalised estimating equations, landmark analysis, two-stage modelling, joint-modelling, trajectory classification and machine learning. Each of these frameworks satisfies at least one of three aims: to better represent the predictor-outcome relationship over time, to infer a covariate value at a pre-specified time and to account for the effect of covariate change.

CONCLUSIONS

The applicability of identified methods depends on the motivation for including longitudinal information and the method's compatibility with the clinical context and available patient data, for both model development and risk estimation in practice.

Accounting for random observation time in risk prediction with longitudinal markers: An imputation approach

Longitudinally measured biomarkers are useful to predict the risk of clinical endpoints, since subject-specific marker trajectory contains additional information on pathology and critical windows. The work is motivated by the Scandinavian Fetal Growth Study, aiming at predicting pregnancy outcomes with repeated ultrasound measurements during pregnancy. While the observation time of markers often varies across individuals, it is not well understood how the variations affect risk prediction. Existing methods of longitudinal risk prediction, such as shared random effects model and pattern mixture model, construct a prediction implicitly as a function of the biomarkers and their observation time. Methods that ignore the longitudinal structure, such as sufficient dimension reduction and logistic regression, have better interpretability regarding how a biomarker measured at specific time window contributes to the disease risk, but often have reduced accuracy because of ignoring the observation time information. We propose a novel imputation approach to handle the random observation time, while preserving the direct interpretation. Through extensive simulation studies and analyses of the Scandinavian Fetal Growth Study data, we systematically compared the discrimination and calibration performance of different risk prediction methods, and found that the imputation method has comparable performance to longitudinal methods with an advantage of better interpretability.

Shared random parameter models: A legacy of the biostatistics program at the National Heart, Lung, and Blood Institute

Shared random parameter models (SRPMs) were first introduced by researchers at the National Heart Lung and Blood Institute (NHLBI) Biostatistics Branch for analyzing longitudinal data with informative dropout (Wu and Carroll, 1987; Wu and Bailey, 1988; Follmann and Wu, 1995; Albert and Follmann, 2000; Albert et al, 2002). This work was all focused on characterizing the longitudinal data process in the presence of an informative missing data mechanism that is treated as a nuisance. Shared random parameter modeling approaches have also been developed from the perspective of characterizing the relationship between longitudinal data and a subsequent outcome that may be an event time, a dichotomous measurement, or another longitudinal outcome. This article will review the early contributions of the NHLBI biostatisticians on SRPMs for analyzing longitudinal data with dropout and demonstrate how these ideas have, more recently, been applied in these other areas of biostatistics. Rather than focus on technical details or specific analyses, this article presents a conceptual framework for SRPMs within a historical context.

Prediction complements explanation in understanding the developing brain

A central aim of human neuroscience is understanding the neurobiology of cognition and behavior. Although we have made significant progress towards this goal, reliance on group-level studies of the developed adult brain has limited our ability to explain population variability and developmental changes in neural circuitry and behavior. In this review, we suggest that predictive modeling, a method for predicting individual differences in behavior from brain features, can complement descriptive approaches and provide new ways to account for this variability. Highlighting the outsized scientific and clinical benefits of prediction in developmental populations including adolescence, we show that predictive brain-based models are already providing new insights on adolescent-specific risk-related behaviors. Together with large-scale developmental neuroimaging datasets and complementary analytic approaches, predictive modeling affords us the opportunity and obligation to identify novel treatment targets and individually tailor the course of interventions for developmental psychopathologies that impact so many young people today.

Fetal growth velocity and body proportion in the assessment of growth

Fetal growth restriction implies failure of a fetus to meet its growth potential and is associated with increased perinatal mortality and morbidity. Therefore, antenatal detection of fetal growth restriction is of major importance in an attempt to deliver improved clinical outcomes. The most commonly used approach towards screening for fetal growth restriction is by means of sonographic fetal weight estimation, to detect fetuses small for gestational age, defined by an estimated fetal weight <10th percentile for gestational age. However, the predictive accuracy of this approach is limited both by suboptimal detection rate (as it may overlook non-small-for-gestational-age growth-restricted fetuses) and by a high false-positive rate (as most small-for-gestational-age fetuses are not growth restricted). Here, we review 2 strategies that may improve the diagnostic accuracy of sonographic fetal biometry for fetal growth restriction. The first strategy involves serial ultrasound evaluations of fetal biometry. The information obtained through these serial assessments can be interpreted using several different approaches including fetal growth velocity, conditional percentiles, projection-based methods, and individualized growth assessment that can be viewed as mathematical techniques to quantify any decrease in estimated fetal weight percentile, a phenomenon that many care providers assess and monitor routinely in a qualitative manner. This strategy appears promising in high-risk pregnancies where it seems to improve the detection of growth-restricted fetuses at increased risk of adverse perinatal outcomes and, at the same time, decrease the risk of falsely diagnosing healthy constitutionally small-for-gestational-age fetuses as growth restricted. Further studies are needed to determine the utility of this strategy in low-risk pregnancies as well as to optimize its performance by determining the optimal timing and interval between exams. The second strategy refers to the use of fetal body proportions to classify fetuses as either symmetric or asymmetric using 1 of several ratios; these include the head circumference to abdominal circumference ratio, transverse cerebellar diameter to abdominal circumference ratio, and femur length to abdominal circumference ratio. Although these ratios are associated with small for gestational age at birth and with adverse perinatal outcomes, their predictive accuracy is too low for clinical practice. Furthermore, these associations become questionable when other, potentially more specific measures such as umbilical artery Doppler are being used. Furthermore, these ratios are of limited use in determining the etiology underlying fetal smallness. It is possible that the use of the 2 gestational-age-independent ratios (transverse cerebellar diameter to abdominal circumference and femur length to abdominal circumference) may have a role in the detection of mild-moderate fetal growth restriction in pregnancies without adequate dating. In addition, despite their limited predictive accuracy, these ratios may become abnormal early in the course of fetal growth restriction and may therefore identify pregnancies that may benefit from closer monitoring of fetal growth.

A Two-Step Approach for Analysis of Nonignorable Missing Outcomes in Longitudinal Regression: an Application to Upstate KIDS Study

BACKGROUND

Imperfect follow-up in longitudinal studies commonly leads to missing outcome data that can potentially bias the inference when the missingness is nonignorable; that is, the propensity of missingness depends on missing values in the data. In the Upstate KIDS Study, we seek to determine if the missingness of child development outcomes is nonignorable, and how a simple model assuming ignorable missingness would compare with more complicated models for a nonignorable mechanism.

METHODS

To correct for nonignorable missingness, the shared random effects model (SREM) jointly models the outcome and the missing mechanism. However, the computational complexity and lack of software packages has limited its practical applications. This paper proposes a novel two-step approach to handle nonignorable missing outcomes in generalized linear mixed models. We first analyse the missing mechanism with a generalized linear mixed model and predict values of the random effects; then, the outcome model is fitted adjusting for the predicted random effects to account for heterogeneity in the missingness propensity.

RESULTS

Extensive simulation studies suggest that the proposed method is a reliable approximation to SREM, with a much faster computation. The nonignorability of missing data in the Upstate KIDS Study is estimated to be mild to moderate, and the analyses using the two-step approach or SREM are similar to the model assuming ignorable missingness.

CONCLUSIONS

The two-step approach is a computationally straightforward method that can be conducted as sensitivity analyses in longitudinal studies to examine violations to the ignorable missingness assumption and the implications relative to health outcomes.

Modeling the Relationships Among Late-Life Body Mass Index, Cerebrovascular Disease, and Alzheimer's Disease Neuropathology in an Autopsy Sample of 1,421 Subjects from the National Alzheimer's Coordinating Center Data Set

The relationship between late-life body mass index (BMI) and Alzheimer's disease (AD) is poorly understood due to the lack of research in samples with autopsy-confirmed AD neuropathology (ADNP). The role of cerebrovascular disease (CVD) in the interplay between late-life BMI and ADNP is unclear. We conducted a retrospective longitudinal investigation and used joint modeling of linear mixed effects to investigate causal relationships among repeated antemortem BMI measurements, CVD (quantified neuropathologically), and ADNP in an autopsy sample of subjects across the AD clinical continuum. The sample included 1,421 subjects from the National Alzheimer's Coordinating Center's Uniform Data Set and Neuropathology Data Set with diagnoses of normal cognition (NC; n = 234), mild cognitive impairment (MCI; n = 201), or AD dementia (n = 986). ADNP was defined as moderate to frequent neuritic plaques and Braak stageIII-VI. Ischemic Injury Scale (IIS) operationalized CVD. Joint modeling examined relationships among BMI, IIS, and ADNP in the overall sample and stratified by initial visit Clinical Dementia Rating score. Subject-specific random intercept for BMI was the predictor for ADNP due to minimal BMI change (p = 0.3028). Analyses controlling for demographic variables and APOE ɛ4 showed lower late-life BMI predicted increased odds of ADNP in the overall sample (p < 0.001), and in subjects with CDR of 0 (p = 0.0021) and 0.5 (p = 0.0012), but not ≥1.0 (p = 0.2012). Although higher IIS predicted greater odds of ADNP (p < 0.0001), BMI did not predict IIS (p = 0.2814). The current findings confirm lower late-life BMI confers increased odds for ADNP. Lower late-life BMI may be a preclinical indicator of underlying ADNP.

Clinical, ultrasound and molecular biomarkers for early prediction of large for gestational age infants in nulliparous women: An international prospective cohort study

Objective

To develop a prediction model for term infants born large for gestational age (LGA) by customised birthweight centiles.

Methods

International prospective cohort of nulliparous women with singleton pregnancy recruited to the Screening for Pregnancy Endpoints (SCOPE) study. LGA was defined as birthweight above the 90^th customised centile, including adjustment for parity, ethnicity, maternal height and weight, fetal gender and gestational age. Clinical risk factors, ultrasound parameters and biomarkers at 14–16 or 19–21 weeks were combined into a prediction model for LGA infants at term using stepwise logistic regression in a training dataset. Prediction performance was assessed in a validation dataset using area under the Receiver Operating Characteristics curve (AUC) and detection rate at fixed false positive rates.

Results

The prevalence of LGA at term was 8.8% (n = 491/5628). Clinical and ultrasound factors selected in the prediction model for LGA infants were maternal birthweight, gestational weight gain between 14–16 and 19–21 weeks, and fetal abdominal circumference, head circumference and uterine artery Doppler resistance index at 19–21 weeks (AUC 0.67; 95%CI 0.63–0.71). Sensitivity of this model was 24% and 49% for a fixed false positive rate of 10% and 25%, respectively. The addition of biomarkers resulted in selection of random glucose, LDL-cholesterol, vascular endothelial growth factor receptor-1 (VEGFR1) and neutrophil gelatinase-associated lipocalin (NGAL), but with minimal improvement in model performance (AUC 0.69; 95%CI 0.65–0.73). Sensitivity of the full model was 26% and 50% for a fixed false positive rate of 10% and 25%, respectively.

Conclusion

Prediction of LGA infants at term has limited diagnostic performance before 22 weeks but may have a role in contingency screening in later pregnancy.

Longitudinal hemodynamics in acute phase of treatment with labetalol in hypertensive pregnant women to predict need for vasodilatory therapy

OBJECTIVE

Hypertensive pregnant women who do not respond to treatment with labetalol to control blood pressure (BP), but require vasodilatory therapy, progress rapidly to severe hypertension. This could be delayed by early recognition and individualized treatment. In this study, we sought to create prediction models from data at presentation and at 1 h and 24 h after commencement of treatment to identify patients who will not have a sustained response to labetalol and therefore need vasodilatory therapy.

METHODS

The study population comprised 134 women presenting with hypertension at a UK hospital. Treatment with oral labetalol was administered when BP was > 150/100 mmHg or > 140/90 mmHg with systemic disease. BP and hemodynamic parameters were recorded at presentation and at 1 h and 24 h after commencement of treatment. Labetalol doses were titrated to maintain BP around 135/85 mmHg. Women with unresponsive BP, despite labetalol dose maximization (2400 mg/day), received additional vasodilatory therapy with nifedipine. Binary logistic and longitudinal (mixed-model) data analyses were performed to create prediction models anticipating the likelihood of hypertensive women needing vasodilatory therapy. The prediction models were created from data at presentation and at 1 h and 24 h after treatment, to assess the value of central hemodynamics relative to the predictive power of BP, heart rate and demographic variables at these intervals.

RESULTS

Twenty-two percent of our cohort required additional vasodilatory therapy antenatally. These women had higher rates of severe hypertension and delivered smaller babies at earlier gestational ages. The unresponsive women were more likely to be of black ethnicity, had higher BP and peripheral vascular resistance (PVR), and lower heart rate and cardiac output (CO) at presentation. Those who needed vasodilatory therapy showed an initial decrease in BP and PVR, which rebounded at 24 h, whereas BP and PVR in those who responded to labetalol showed a sustained decrease at 1 h and 24 h. Stroke volume and CO did not decrease during the acute phase of treatment in either group. The best model for prediction of the need for vasodilators was provided at 24 h by combining ethnicity and longitudinal BP and heart rate changes. The model achieved a detection rate of 100% for a false-positive rate of 20% and an area under the receiver-operating characteristics curve of 0.97.

CONCLUSION

Maternal demographics and hemodynamic changes in the acute phase of labetalol monotherapy provide a powerful tool to identify hypertensive pregnant patients who are unlikely to have their BP controlled by this therapy and will consequently need additional vasodilatory therapy. Copyright © 2016 ISUOG. Published by John Wiley & Sons Ltd.

RESUMEN OBJETIVO

Las embarazadas hipertensas que no responden al tratamiento con labetalol para el control de la presión arterial (PA), pero que requieren terapia vasodilatadora, evolucionan rápidamente hacia una hipertensión severa. Ésta se puede retrasar mediante un diagnóstico precoz y un tratamiento individual. En este estudio se ha tratado de crear modelos de predicción a partir de datos al inicio del tratamiento y al cabo de 1 hora y de 24 horas después del mismo, para identificar a las pacientes que no mostrarán una respuesta constante al labetalol y que por lo tanto necesitarán terapia vasodilatadora. MÉTODOS: La población de estudio incluyó 134 mujeres con hipertensión en un hospital del Reino Unido. El tratamiento con labetalol por vía oral se administró cuando la PA fue >150/100 mm de Hg o >140/90 mm de Hg con enfermedad multisistémica. Se registró la PA y los parámetros hemodinámicos tanto al inicio como al cabo de 1 h y de 24 h después del inicio del tratamiento. Las dosis de Labetalol se ajustaron para mantener la PA en torno a los 135/85 mm de Hg. Las mujeres cuya PA no produjo respuesta, a pesar de haberles administrado la dosis máxima de labetalol (2400 mg/día), recibieron terapia vasodilatadora adicional con nifedipino. Se realizaron análisis de datos mediante logística binaria y longitudinal (modelo mixto), para crear modelos de predicción con los que pronosticar la probabilidad de la necesidad de terapia vasodilatadora en mujeres hipertensas. Los modelos de predicción se crearon a partir de datos al inicio y al cabo de 1 hora y 24 horas del tratamiento, para evaluar el valor de los parámetros hemodinámicos principales con respecto a la capacidad predictiva de la PA, la frecuencia cardíaca y las variables demográficas en estos intervalos.

RESULTADOS

El 22 % de la cohorte necesitó terapia vasodilatadora adicional antes del parto. Estas mujeres tuvieron tasas más altas de hipertensión grave y neonatos más pequeños en edades gestacionales más tempranas. Las mujeres que no respondieron al tratamiento fueron con más frecuencia de raza negra, tuvieron la PA y la resistencia vascular periférica (RVP) más alta, y la frecuencia cardíaca y el gasto cardíaco (GC) más bajos al inicio del tratamiento. Aquellas que necesitaron terapia vasodilatadora mostraron un descenso inicial de la PA y la RVP, que se recuperó al cabo de 24 h, mientras que la PA y la RVP en las que respondieron al labetalol mostraron una disminución constante al cabo de 1 h y de 24 h. El volumen sistólico y el GC no disminuyeron durante la fase aguda del tratamiento en ninguno de los grupos. El mejor modelo para la predicción de la necesidad de vasodilatadores se obtuvo a las 24 h mediante la combinación de la etnia con los cambios longitudinales de la PA y la frecuencia cardíaca. El modelo alcanzó una tasa de detección del 100% para una tasa de falsos positivos del 20% y un área bajo la curva de características operativas del receptor de 0,97. CONCLUSIÓN: Los datos demográficos maternos y los cambios hemodinámicos en la fase aguda de la monoterapia con labetalol constituyen una herramienta poderosa para identificar a las pacientes embarazadas hipertensas con pocas probabilidades de que se les pueda controlar su PA mediante esta terapia y que por lo tanto necesitarán terapia vasodilatadora adicional. : 、(blood pressure,BP),。。,1 h24 h,。 : 134。BP>150/100 mmHgBP>140/90 mmHg。1 h24 hBP。,BP135/85 mmHg。BP,()。logistic(),。1 h24 h,,BP、。 : 22%。。,BP(peripheral vascular resistance,PVR),(cardiac output,CO)。BPPVR,24 h,1 h24 hBPPVR。CO。24hBP。100%,20%,0.97。 : ,BP。.

Identifying subgroups of enhanced predictive accuracy from longitudinal biomarker data using tree-based approaches: applications to fetal growth

Longitudinal monitoring of biomarkers is often helpful for predicting disease or a poor clinical outcome. In this paper, We consider the prediction of both large and small-for-gestational-age births using longitudinal ultrasound measurements, and attempt to identify subgroups of women for whom prediction is more (or less) accurate, should they exist. We propose a tree-based approach to identifying such subgroups, and a pruning algorithm which explicitly incorporates a desired type-I error rate, allowing us to control the risk of false discovery of subgroups. The proposed methods are applied to data from the Scandinavian Fetal Growth Study, and are evaluated via simulations.

Single and Serial Fetal Biometry to Detect Preterm and Term Small- and Large-for-Gestational-Age Neonates: A Longitudinal Cohort Study

Objectives

To assess the value of single and serial fetal biometry for the prediction of small- (SGA) and large-for-gestational-age (LGA) neonates delivered preterm or at term.

Methods

A cohort study of 3,971 women with singleton pregnancies was conducted from the first trimester until delivery with 3,440 pregnancies (17,334 scans) meeting the following inclusion criteria: 1) delivery of a live neonate after 33 gestational weeks and 2) two or more ultrasound examinations with fetal biometry parameters obtained at ≤36 weeks. Primary outcomes were SGA (<5^th centile) and LGA (>95^th centile) at birth based on INTERGROWTH-21^st gender-specific standards. Fetus-specific estimated fetal weight (EFW) trajectories were calculated by linear mixed-effects models using data up to a fixed gestational age (GA) cutoff (28, 32, or 36 weeks) for fetuses having two or more measurements before the GA cutoff and not already delivered. A screen test positive for single biometry was based on Z-scores of EFW at the last scan before each GA cut-off so that the false positive rate (FPR) was 10%. Similarly, a screen test positive for the longitudinal analysis was based on the projected (extrapolated) EFW at 40 weeks from all available measurements before each cutoff for each fetus.

Results

Fetal abdominal and head circumference measurements, as well as birth weights in the Detroit population, matched well to the INTERGROWTH-21^st standards, yet this was not the case for biparietal diameter (BPD) and femur length (FL) (up to 9% and 10% discrepancy for mean and confidence intervals, respectively), mainly due to differences in the measurement technique. Single biometry based on EFW at the last scan at ≤32 weeks (GA IQR: 27.4–30.9 weeks) had a sensitivity of 50% and 53% (FPR = 10%) to detect preterm and term SGA and LGA neonates, respectively (AUC of 82% both). For the detection of LGA using data up to 32- and 36-week cutoffs, single biometry analysis had higher sensitivity than longitudinal analysis (52% vs 46% and 62% vs 52%, respectively; both p<0.05). Restricting the analysis to subjects with the last observation taken within two weeks from the cutoff, the sensitivity for detection of LGA, but not SGA, increased to 65% and 72% for single biometry at the 32- and 36-week cutoffs, respectively. SGA screening performance was higher for preterm (<37 weeks) than for term cases (73% vs 46% sensitivity; p<0.05) for single biometry at ≤32 weeks.

Conclusions

When growth abnormalities are defined based on birth weight, growth velocity (captured in the longitudinal analysis) does not provide additional information when compared to the last measurement for predicting SGA and LGA neonates, with both approaches detecting one-half of the neonates (FPR = 10%) from data collected at ≤32 weeks. Unlike for SGA, LGA detection can be improved if ultrasound scans are scheduled as close as possible to the gestational-age cutoff when a decision regarding the clinical management of the patient needs to be made. Screening performance for SGA is higher for neonates that will be delivered preterm.

A class of joint models for multivariate longitudinal measurements and a binary event

Predicting binary events such as newborns with large birthweight is important for obstetricians in their attempt to reduce both maternal and fetal morbidity and mortality. Such predictions have been a challenge in obstetric practice, where longitudinal ultrasound measurements taken at multiple gestational times during pregnancy may be useful for predicting various poor pregnancy outcomes. The focus of this article is on developing a flexible class of joint models for the multivariate longitudinal ultrasound measurements that can be used for predicting a binary event at birth. A skewed multivariate random effects model is proposed for the ultrasound measurements, and the skewed generalized t-link is assumed for the link function relating the binary event and the underlying longitudinal processes. We consider a shared random effect to link the two processes together. Markov chain Monte Carlo sampling is used to carry out Bayesian posterior computation. Several variations of the proposed model are considered and compared via the deviance information criterion, the logarithm of pseudomarginal likelihood, and with a training-test set prediction paradigm. The proposed methodology is illustrated with data from the NICHD Successive Small-for-Gestational-Age Births study, a large prospective fetal growth cohort conducted in Norway and Sweden.

Joint analysis of longitudinal and survival data measured on nested timescales by using shared parameter models: an application to fecundity data

We consider the joint modelling, analysis and prediction of a longitudinal binary process and a discrete time-to-event outcome. We consider data from a prospective pregnancy study, which provides day level information regarding the behaviour of couples attempting to conceive. Reproductive epidemiologists are particularly interested in developing a model for individualized predictions of time to pregnancy (TTP). A couple's intercourse behaviour should be an integral part of such a model and is one of the main focuses of the paper. In our motivating data, the intercourse observations are a long series of binary data with a periodic probability of success and the amount of available intercourse data is a function of both the menstrual cycle length and TTP. Moreover, these variables are dependent and observed on different, and nested, timescales (TTP is measured in menstrual cycles whereas intercourse is measured on days within a menstrual cycle) further complicating its analysis. Here, we propose a semiparametric shared parameter model for the joint modelling of the binary longitudinal data (intercourse behaviour) and the discrete survival outcome (TTP). Further, we develop couple-based dynamic predictions for the intercourse profiles, which in turn are used to assess the risk for subfertility (i.e. TTP longer than six menstrual cycles).

Combination of longitudinal biomarkers in predicting binary events

In disease screening, the combination of multiple biomarkers often substantially improves the diagnostic accuracy over a single marker. This is particularly true for longitudinal biomarkers where individual trajectory may improve the diagnosis. We propose a pattern mixture model (PMM) framework to predict a binary disease status from a longitudinal sequence of biomarkers. The marker distribution given the disease status is estimated from a linear mixed effects model. A likelihood ratio statistic is computed as the combination rule, which is optimal in the sense of the maximum receiver operating characteristic (ROC) curve under the correctly specified mixed effects model. The individual disease risk score is then estimated by Bayes' theorem, and we derive the analytical form of the 95% confidence interval. We show that this PMM is an approximation to the shared random effects (SRE) model proposed by Albert (2012. A linear mixed model for predicting a binary event from longitudinal data under random effects mis-specification. Statistics in Medicine 31: (2), 143-154). Further, with extensive simulation studies, we found that the PMM is more robust than the SRE model under wide classes of models. This new PPM approach for combining biomarkers is motivated by and applied to a fetal growth study, where the interest is in predicting macrosomia using longitudinal ultrasound measurements.

Predicting large fetuses at birth: do multiple ultrasound examinations and longitudinal statistical modelling improve prediction?

Predicting large fetuses at birth has long been a challenge in obstetric practice. We examined whether ultrasound examinations at multiple times during pregnancy improve the accuracy of prediction using repeated, longitudinal statistical modelling, and whether adding maternal characteristics improves the accuracy of prediction. We used data from a previous study conducted in Norway and Sweden from 1986 to 1989 in which each pregnant woman had four ultrasound examinations at around 17, 25, 33 and 37 weeks of gestation. At birth, infant size was classified as large-for-gestational age (LGA, >90th centile) and macrosomia (>4000 g) or not. We used a longitudinal random effects model with quadratic fixed and random effects to predict term LGA and macrosomia at birth. Receiver-operator curves and mean-squared error were used to measure accuracy of the prediction. Ultrasound examination around 37 weeks had the best accuracy in predicting LGA and macrosomia at birth. Adding multiple ultrasound examinations at earlier gestations did not improve the accuracy. Adjusting for maternal characteristics had limited impact on the accuracy of prediction. Thus, a single ultrasound examination at late gestation close to birth is the simplest method currently available to predict LGA and macrosomia.