A joint estimation approach for monotonic regression functions in general dimensions

Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information borrowing, for efficiency gains, when jointly estimating multiple monotonic regression functions. We introduce such a methodology by extending the isotonic regression problem presented in the article "The isotonic regression problem and its dual" (Barlow and Brunk, 1972). The presented approach can be applied to both fixed and random designs and any number of explanatory variables (regressors). Our framework penalizes pairwise differences in the values (levels) of the monotonic function estimates, with the weight of penalty being determined based on a statistical test, which results in information being shared across data sets if similarities in the regression functions exist. Function estimates are subsequently derived using an iterative optimization routine that uses existing solution algorithms for the isotonic regression problem. Simulation studies for normally and binomially distributed response data illustrate that function estimates are consistently improved if similarities between functions exist, and are not oversmoothed otherwise. We further apply our methodology to analyse two public health data sets: neonatal mortality data for Porto Alegre, Brazil, and stroke patient data for North West England

Chromosomal microarray testing in adults with intellectual disability presenting with comorbid psychiatric disorders.

Chromosomal copy-number variations (CNVs) are a class of genetic variants highly implicated in the aetiology of neurodevelopmental disorders, including intellectual disabilities (ID), schizophrenia and autism spectrum disorders (ASD). Yet the majority of adults with idiopathic ID presenting to psychiatric services have not been tested for CNVs. We undertook genome-wide chromosomal microarray analysis (CMA) of 202 adults with idiopathic ID recruited from community and in-patient ID psychiatry services across England. CNV pathogenicity was assessed using standard clinical diagnostic methods and participants underwent comprehensive medical and psychiatric phenotyping. We found an 11% yield of likely pathogenic CNVs (22/202). CNVs at recurrent loci, including the 15q11-q13 and 16p11.2-p13.11 regions were most frequently observed. We observed an increased frequency of 16p11.2 duplications compared with those reported in single-disorder cohorts. CNVs were also identified in genes known to effect neurodevelopment, namely NRXN1 and GRIN2B. Furthermore deletions at 2q13, 12q21.2-21.31 and 19q13.32, and duplications at 4p16.3, 13q32.3-33.3 and Xq24-25 were observed. Routine CMA in ID psychiatry could uncover ~11% new genetic diagnoses with potential implications for patient management. We advocate greater consideration of CMA in the assessment of adults with idiopathic ID presenting to psychiatry services

Contour plots of the smooth estimates of the residual spatial variation in the log odds of IFEE.

<p>These were obtained when using the observed location data of the owner/carer location (top left) and also when using each of the five perturbed sets of co-ordinates.</p

Graphical illustration of the estimated relationship between the log odds of IFEE (‘contribution to log odds’) and day of year.

<p>The seasonal estimate (parametric) derives from a Generalised Additive Model formulation and is adjusted for horse age (smooth) and the geographical location of the horse/horse owner (smooth). The dotted horizontal line is at log-odds  = 0.</p

Geographic locations, <i>x</i> = (<i>x</i>1, <i>x</i>2) = (Easting, Northing), of case and control horses.

<p>The point map depicts the geographical location of the 85 cases (red triangles) of idiopathic focal eosinophilic enteritis (IFEE) and 848 randomly selected controls (‘+’) in the present study. The green circle shows the location of the Philip Leverhulme Equine Hospital (PLEH).</p

Contour plot of the smooth estimate of residual spatial variation in the log odds of IFEE.

<p>This is adjusted for day in year (parametric day of year and season effects) and horse age (smooth). The closed circular contours centred at Easting  = <i>x</i>1 = 370000 and Northing  = <i>x</i>2 = 4 25000 indicates an increase in the log odds in this region. A zero contour value corresponds to an odds of 1, positive values correspond to odds in excess of one and negative values to odds of less than one. The green circle shows the location of the Philip Leverhulme Equine Hospital (PLEH).</p

The typical visual appearance of an idiopathic focal eosinophilic enteritis IFEE lesion at laparotomy.

<p>The lesion is grossly hyperaemic and spans all or part of the circumference of the small intestine (small bowel). Palpably the tissues are markedly thickened at the site of the lesion and most commonly there is obstruction of ingesta proximal to the lesion(s) resulting in a simple obstruction of the bowel.</p

Minimum and maximum values of the estimated parameters and associated <i>p</i>-values resulting from GAM model fits to the five sets of randomly permuted location data.

<p>Minimum and maximum values of the estimated parameters and associated <i>p</i>-values resulting from GAM model fits to the five sets of randomly permuted location data.</p

Parameter estimates relating to the time (day in year) and seasonal effects for the final fitted model.

<p>Parameter estimates relating to the time (day in year) and seasonal effects for the final fitted model.</p