Data analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

Statnote 31:analysis of covariance

Analysis of covariance (ANCOVA) is a useful method of ‘error control’, i.e., it can reduce the size of the error variance in an experimental or observational study. An initial measure obtained before the experiment, which is closely related to the final measurement, is used to adjust the final measurements, thus reducing the error variance. When this method is used to reduce the error term, the X variable must not itself be affected by the experimental treatments, because part of the treatment effect would then also be removed. Hence, the method can only be safely used when X is measured before an experiment. A further limitation of the analysis is that only the linear effect of Y on X is being removed and it is possible that Y could be a curvilinear function of X. A question often raised is whether ANCOVA should be used routinely in experiments rather than a randomized blocks or split-plot design, which may also reduce the error variance. The answer to this question depends on the relative precision of the difference methods with reference to each scenario. Considerable judgment is often required to select the best experimental design and statistical help should be sought at an early stage of an investigation.

Performing in a night-time leisure venue: a visual analysis of erotic dance

This article analyses a range of different meanings attached to images of erotic dance, with a particular focus on the 'impression management' (Goffman 1959) enacted by dancers. It presents a visual analysis of the work of a female erotic performer in a lesbian erotic dance venue in the UK. Still photographs, along with observational data and interviews, convey the complexity and skill of an erotic dancer's diverse gendered and sexualised performances. The visual data highlights the extensive 'aesthetic labour' (Nickson et al. 2001) and 'emotional labour' (Hochschild 1983) the dancer must put in to constructing her work 'self'. However, a more ambitious use of the visual is identified: the dancer's own use of images of her work. This use of the visual by dancers themselves highlights a more complex 'impression management' strategy undertaken by a dancer and brings into question the separation of 'real' and 'work' 'selves' in erotic dance. © Sociological Research Online, 1996-2012.

An artificial neural network stratifies the risks of reintervention and mortality after endovascular aneurysm repair:a retrospective observational study

Background Lifelong surveillance after endovascular repair (EVAR) of abdominal aortic aneurysms (AAA) is considered mandatory to detect potentially life-threatening endograft complications. A minority of patients require reintervention but cannot be predictively identified by existing methods. This study aimed to improve the prediction of endograft complications and mortality, through the application of machine-learning techniques. Methods Patients undergoing EVAR at 2 centres were studied from 2004-2010. Pre-operative aneurysm morphology was quantified and endograft complications were recorded up to 5 years following surgery. An artificial neural networks (ANN) approach was used to predict whether patients would be at low- or high-risk of endograft complications (aortic/limb) or mortality. Centre 1 data were used for training and centre 2 data for validation. ANN performance was assessed by Kaplan-Meier analysis to compare the incidence of aortic complications, limb complications, and mortality; in patients predicted to be low-risk, versus those predicted to be high-risk. Results 761 patients aged 75 +/- 7 years underwent EVAR. Mean follow-up was 36+/- 20 months. An ANN was created from morphological features including angulation/length/areas/diameters/ volume/tortuosity of the aneurysm neck/sac/iliac segments. ANN models predicted endograft complications and mortality with excellent discrimination between a low-risk and high-risk group. In external validation, the 5-year rates of freedom from aortic complications, limb complications and mortality were 95.9% vs 67.9%; 99.3% vs 92.0%; and 87.9% vs 79.3% respectively (p0.001) Conclusion This study presents ANN models that stratify the 5-year risk of endograft complications or mortality using routinely available pre-operative data.

Obstructive sleep apnoea is associated with sight threatening retinopathy and predicts the developement of preproliferative and proliferative retinopathy in patients with type 2 diabetes:a longitudinal analysis

troduct I on . An observational longitudinal study. P ur P ose . Assess the relationship between obstructive sleep apnoea (OSA) and DR cross-sectionally and longitudinally. M ethods . Adults with Type 2 diabetes mellitus (T2DM), who were re - cruited from a hospital-based diabetes clinic in the UK. Patients with pre-existing OSA, end-stage renal disease and non-diabetic retinopa - thy were excluded. OSA (apnoea hypopnea index ≥ 5 events/hour) was assessed by a single overnight home-based cardio-respiratory study (Alice PDX, Philips Respironics, USA). DR was assessed us - ing retinal images between 2007 and 2012. Sight threatening diabetic retinopathy (STDR) was defined as presence of pre-proliferative or proliferative DR, maculopathy or photocoagulation. Advanced DR was defined as pre-proliferative or proliferative DR. r esults . 199 patients were included (57.3% (n=114) men, 47.7% (n=95) White Europeans). STDR and OSA prevalence were 38.7% (n=77) and 62.8% respectively. A t b A sel I ne . STR prevalence was higher in patients with OSA (OSA+) compared to those without OSA (OSA-) [48.8% n=61 vs. 21.6% n=16, p<0.001]. After adjustment for confounders, OSA remained independently associated with STR (OR 3.7, 95% CI 1.6-8.9, p=0.006), maculopathy (OR 4.5, 95% CI 1.8-11.4, p=0.002) and advanced DR (OR 3.9, 95% CI 1.02-15.3, p=0.047). Mild and moderate to severe OSA were independently associated with STR and maculopathy and only moderate to severe OSA was associated with advanced DR following adjustment for con - founders. l ong I tud I n A lly . Over the follow-up period of (4.4±1 years), more OSA+ patients progressed from no or background DR to advanced DR (15.3% (n=17) vs. 3% (n=2), p=0.01). OSA was an independent pre - dictor of advanced DR development after adjustment for confounders (OR 6.6, 95% CI 1.2-35.1, p=0.03). OSA did not predict the develop - ment of maculopathy. c onclus I ons . OSA is independently associated with STR and predicts the development of preproliferative and proliferative DR. Intervention - al studies are needed to assess the impact of OSA treatment on DR.

Obstructive sleep apnoea predicts the development of preproliferative and proliferative retinopathy in patients with type 2 diabetes:a longitudinal analysis

Background and aims: Diabetic Retinopathy (DR) is a leading cause of blindness. OSA is associated with increased oxidative and nitrosative stress and endothelial dysfunction in patients with type 2 diabetes (T2DM). Hence, it is plausible that OSA can promote the development and progression of DR. Materials and methods: An observational longitudinal study in adults with T2DM. Patients with pre-existing OSA, end-stage renal disease and non-diabetic retinopathy were excluded. OSA (apnoea hypopnea index ≥ 5 events/hour) was assessed by a single overnight home-based cardio-respiratory monitoring (Alice PDX, etc.). DR was assesses using retinal images between 2007 and 2012. Sight threatening retinopathy (STR) was defined as pre-proliferative or proliferative DR, maculopathy or photocoagulation. Advanced DR was defined as pre-proliferative or proliferative DR. Results: 199 patients were included (57.3% men, 47.7% White Europeans). STR and OSA prevalence were 38.7 % and 62.8% respectively. STR preva-lence was higher in patients with OSA (OSA+) compared to those with-out (OSA-) [48.8% vs. 21.6%, p <0.001]. After adjustment for confounders, OSA remained independently associated with STR (OR 3.7, 95%CI 1.6-8.9, p=0.006, maculopathy (OR 4.5, 1.8-11.4, p=0.002) and advanced DR (OR 3.9, 1.02-15.3, p=0.047). Over 4.4±1 years, more OSA+ patients progressed from no or background DR to advanced DR (15.3% vs. 3%, p=0.01). OSA was an independent predictor of advanced DR development after adjustment (OR 6.6, 95%CI 1.2-35.1, p=0.03). OSA did not predict the development of maculopathy. Patients received continuous positive airway pressure treatment were less likely to develop advanced DR. Conclusion: OSA is independently associated with STR and predicts the development of preproliferative and proliferative DR. Interventional studies are needed to assess the impact of OSA treatment on DR.Supported by: NIHR (UK) and The UK Novo Nordisk Research Foundation.