Longitudinal/Mixed models
Presenter: Charley Budgeon
When: Thursday, July 14, 2016 Time: 11:00 AM - 12:30 PM
Room: Esquimalt (Level 1)
Session Synopsis:
Constructing longitudinal disease progression curves with an application to Alzheimers Disease
Frequently, in many areas of research, the data recorded on individuals is sparse and short-term. An example of this is Alzheimers Disease, where in the larger longitudinal data sets, each individual may have only been followed up for 2-3 years, and measurements based on disease biomarkers may have only been taken a handful of times during this period. Our objective is to investigate and evaluate methods that can reconstruct and quantify the underlying long-term longitudinal trajectories for disease markers using individuals short term follow up data. Simulated sparse follow-up data for a pre-specified number of individuals were created to investigate possible approaches to this problem. A four-step modeling approach was adopted that 1) determined individual slopes and anchor points, 2) fitted and reciprocated polynomials, 3) integrated and 4) inverted the resulting curve to obtain the underlying longitudinal trajectories. Non-negative polynomials were fitted in step 2) as the roots of the fitted polynomial can fall inside the range of the data and subsequently creates problems in the integration step after reciprocating the polynomial. In order to provide an estimate of the variability bootstrapping confidence intervals were evaluated. Variations of the approach were considered to determine an optimal methodology: mixed models were contrasted to linear regression in step 1) and different orders of polynomials were considered in step 2). Our research shows that simple modeling techniques are able to reconstruct generalized underlying longitudinal trajectories from individuals sparse, short-term follow-up data. All methods accurately reproduced the underlying curve. The mixed model variations performed better than those using linear regression and there were minimal differences between the different order polynomials. These methods were illustrated using the well-known real world Alzheimers Disease Neuroimaging Initiative (ADNI) data.
Longitudinal/Mixed models
Presenter: Loumpiana Koulai
When: Thursday, July 14, 2016 Time: 11:00 AM - 12:30 PM
Room: Esquimalt (Level 1)
Session Synopsis:
Estimating HIV Seroconversion Time Using Biomarkers of Recent Infection
Knowledge of the time at which an HIV infected individual seroconverts, plays a vital role in the design and implementation of interventions to reduce the impact of the HIV epidemic. Historically, various methods have been proposed to estimate the time of seroconversion, including deriving the conditional distribution of the time of seroconversion given measures such as CD4 counts. Increasingly, other biomarkers are being developed to distinguish between recent and long-term HIV infection, based on the immune response to HIV. We explore the possibility of using single or repeated measures of one/more such biomarkers to estimate the seroconversion time. Univariate and multivariate non-linear mixed-effects models are used, to estimate the evolution over time since seroconversion of one/more biomarkers in a cohort of patients with known seroconversion times. Given the resulting knowledge on growth pattern/s, we investigate the possibility of estimating the seroconversion time for a new individual based on a limited number of serial measurements of one/more biomarkers taken after HIV diagnosis. Estimation is performed in a Bayesian framework, and results are expressed in terms of a posterior distribution for the seroconversion time. The method is illustrated using both real and simulated data. We explore a number of scenarios regarding the proximity of the seroconversion time to the date of diagnosis and the number of measurements. We assess the value of combining biomarkers with similar as well as different growth patterns in terms of bias and accuracy of the resulting estimate. Preliminary results suggest that multivariate models lead to more accurate estimates with smaller bias and MSE, compared to univariate models. Using multiple biomarkers also results in a significant improvement in terms of precision, especially for individuals who seroconverted long before the first positive HIV test date. The choice of biomarkers is crucial to the quality of the estimates, with biomarkers characterised by very steep growth/decline allowing a more accurate estimation. We have demonstrated that it is possible to estimate the seroconversion time at an individual-level using longitudinal measurements of one/more biomarkers of recent infection. The quality of the estimation, however, depends crucially on the particular characteristics of the chosen biomarkers, as well as on the timing of the measurements.
Longitudinal/Mixed models
Presenter: Toshiro Tango
When: Thursday, July 14, 2016 Time: 11:00 AM - 12:30 PM
Room: Esquimalt (Level 1)
Session Synopsis:
New Repeated Measures Design and Sample Size for Randomized Controlled Trials
For the analysis of longitudinal or repeated measures data, generalized linear mixed-effects models provide a flexible and powerful tool to deal with heterogeneity among subject response profiles. However, the typical statistical design adopted in usual randomized controlled trials is an ANCOVA type analysis using a pre-defined pair of "pre-post" data, in which pre-(baseline) data is used as a covariate for adjustment together with other covariates. Then, the major design issue is to calculate the sample size or the number of subjects allocated to each treatment group. In this paper, we propose a new repeated measures design and sample size calculations combined with generalized linear mixed-effects models that depend not only on the number of subjects but on the number of repeated measures before and after randomization per subject used for the analysis. The main advantages of the proposed design combined with generalized linear mixed-effects models are 1) it can easily handle missing data by applying the likelihood-based ignorable analyses under the missing at random assumption and 2) it may lead to a reduction in sample size, compared with the simple pre-post design. The proposed designs and the sample size calculations are illustrated with real data arising from randomized controlled trials.
Longitudinal/Mixed models
Presenter: Martin Boer
When: Thursday, July 14, 2016 Time: 11:00 AM - 12:30 PM
Room: Esquimalt (Level 1)
Session Synopsis:
The analysis of field trial experiments using mixed models and 2D P-splines.
An important aim of the analysis of agricultural field trials is to obtain good predictions for the genotypes tested in the experiment, by correcting for spatial effects. In practice this correction turns out to be complicated, since there can be different types of spatial effects; those due to management interventions applied to the field plots and due to various kinds of erratic spatial trends. A mixed model framework for the analysis of field trials will be presented that includes discrete row and column effects together with a smooth spatial effect modelled by a two dimensional penalized spline basis (P-splines; Eilers and Marx, 1996; Eilers, Marx and Durban, 2015). This P-splines basis consists of five random effects. The first two terms are smoothing terms in the row and the column direction. The second pair of terms are interactions between a linear trend in one direction with a smoothing term in the other direction. The fifth random component is the interaction between smooth terms in the row and column direction. To explain the new 2D P-splines mixed model approach, a uniformity trial will be used to introduce the basic concepts. The advantage of uniformity trials is that all plots have the same genotype, so the variation in the field should be purely spatial, and a detailed comparison can be made between different approaches to correct for spatial effects. Next it will be shown how the 2D-splines approach can be used for the analysis of field experiments with the aim to compare the performance of different genotypes, and to obtain good estimates for genotypic BLUEs, genotypic BLUPs and generalized heritability. The 2D P-splines approach has several advantages over other mixed models for field trial analysis. First of all, the new approach is very robust. A second advantage is that a model selection step, often used in mixed model spatial analysis, is not needed. Furthermore, it will be shown that the method can easily deal with irregular field layouts. The 2D P-splines method has been implemented in the R-package SpATS. The SpATS-package is easy to use and produces predictions for the genotypes and calculates the generalized heritability. References: Eilers, P.H.C., and Marx, B.D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89-121. Eilers, P.H.C., Marx, B.D. and M. Durbán (2015) Twenty years of P-splines. SORT 39, 149-186.