Quantile Generalized Additive Model a Robust Alternative to Generalized Additive Model

Nonparametric regression is an approach used when the structure of the relationship between the response and the predictor variable is unknown. It tries to estimate the structure of this relationship since there is no predetermined form. The generalized additive model (GAM) and quantile generalized additive (QGAM) model provides an attractive framework for nonparametric regression. The QGAM focuses on the features of the response beyond the central tendency, while the GAM focuses on the mean response. The analysis was done using gam and qgam packages in R, using data set on live-births, fertility-rate and birth-rate, where, live-birth is the response with fertility-rate and birth-rate as the predictors. The spline basis function was used while selecting the smoothing parameter by marginal loss minimization technique. The result shows that the basis dimension used was sufficient. The QGAM results show the effect of the smooth functions on the response variable at 25th, 50th, 75th and 95th quantiles, while the GAM showed only the effect of the predictors on the mean response. The results also reveal that the QGAM have lower Akaike information criterion (AIC) and Generalized cross-validation (GVC) than the GAM, hence producing a better model. It was also observed that the QGAM and the GAM at the 50th quantile had the same R2adj(77%), meaning that both models were able to explain the same percentage of variation in the models, this we attribute to the fact that mean regression and median regression are approximately the same, hence the observation is in agreement with existing literature. The plots reveal that some of the residuals of the GAM were seen to fall outside the confidence band while in QGAM all the residuals fell within the confidence band producing a better smooth.

Trajectories of Pain After Cardiac Surgery: Implications for Measurement, Reporting, and Individualized Treatment

Background: Postoperative pain after cardiac surgery is a significant problem, but studies often report pain value as an average of the study cohort, obscuring clinically meaningful differences in pain trajectories. We sought to characterize heterogeneity in postoperative pain experiences. Methods: We enrolled patients undergoing a cardiac surgery at a tertiary care center between January 2019 and February 2020. Participants received an electronically-delivered questionnaire every 3 days for 30 days to assess incision site pain level. We evaluated the variability in pain trajectories over 30 days by the cohort-level mean with confidence band and latent classes identified by group-based trajectory model. Group-based trajectory model estimated the probability of belonging to a specific trajectory of pain. Results: Of 92 patients enrolled, 75 provided ≥3 questionnaire responses. The cohort-level mean showed a gradual and consistent decline in the mean pain level, but the confidence bands covered most of the pain score range. The individual-level trajectories varied substantially across patients. Group-based trajectory model identified 4 pain trajectories: persistently low (n=9, 12%), moderate declining (initially mid-level, followed by decline; n=26, 35%), high declining (initially high-level, followed by decline; n=33, 44%), and persistently high pain (n=7, 9%). Persistently high pain and high declining groups did not seem to be clearly distinguishable until approximately postoperative day 10. Patients in persistently low pain trajectory class had a numerically lower median age than the other 3 classes and were below the lower confidence band of the cohort-level approach. Patients in the persistently high pain trajectory class had a longer median length of hospital stay than the other 3 classes and were often higher than the upper confidence band of the cohort-level approach. Conclusions: We identified 4 trajectories of postoperative pain that were not evident from a cohort-level mean, which has been a common way of reporting pain level. This study provides key information about the patient experience and indicates the need to understand variation among sites and surgeons and to investigate determinants of different experience and interventions to mitigate persistently high pain.

Robust inference in deconvolution

Kotlarski's identity has been widely used in applied economic research based on repeated‐measurement or panel models with latent variables. However, how to conduct inference for these models has been an open question for two decades. This paper addresses this open problem by constructing a novel confidence band for the density function of a latent variable in repeated measurement error model. The confidence band builds on our finding that we can rewrite Kotlarski's identity as a system of linear moment restrictions. Our approach is robust in that we do not require the completeness. The confidence band controls the asymptotic size uniformly over a class of data generating processes, and it is consistent against all fixed alternatives. Simulation studies support our theoretical results.