Statnote 16: fitting a regression line to data

Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, ‘r squared’ estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. In addition, it is important to check whether the data fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

Statnote 20: non-linear regression: fitting a general polynomial curve

In some circumstances, there may be no scientific model of the relationship between X and Y that can be specified in advance and indeed the objective of the investigation may be to provide a ‘curve of best fit’ for predictive purposes. In such an example, the fitting of successive polynomials may be the best approach. There are various strategies to decide on the polynomial of best fit depending on the objectives of the investigation.

Data methods in optometry. Part 6: fitting a regression line to data

1. Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, r squared estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. 2. Always check whether the data collected fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary. 3. If the regression line is to be used for prediction, it is important to determine whether the prediction involves an individual y value or a mean. Care should be taken if predictions are made close to the extremities of the data and are subject to considerable error if x falls beyond the range of the data. Multiple predictions require correction of the P values. 3. If several individual regression lines have been calculated from a number of similar sets of data, consider whether they should be combined to form a single regression line. 4. If the data exhibit a degree of curvature, then fitting a higher-order polynomial curve may provide a better fit than a straight line. In this case, a test of whether the data depart significantly from a linear regression should be carried out.

Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.

Specialist contact lens fitting

What is meant by the term ‘specialist contact lens fitting’? Or put another way, what would be considered non-specialist contact lens fitting? Is there such a thing as routine contact lens fitting? Soft or silicone hydrogel fitting for daily wear would probably be considered as routine contact lens fitting, but would extended or flexible wear remain in the same category or would they be considered a specialist fit? Different eras will classify different products as being ‘specialist’. Certainly twenty years ago soft toric contact lenses were considered as being speciality lenses but today would be thought of as routine lenses. Conversely, gas permeable lenses were thought of as mainstream twenty years ago but now are considered as speciality lenses. Although this would not be the same globally, as in some countries (such as Netherlands, France and Japan) gas permeable lens fitting remains popular and is not on the decline as in other countries (Canada, Australia and Sweden) [1]. Bandage soft lenses applied after surface laser refractive procedures would be considered as therapeutic lenses but in reality they are just plano thin hydrogel lenses worn constantly for 3–4 days to allow the underlying epithelium to convalesce and are then removed [2]. Some patients find that wearing hydrogel lenses during periods when they suffer from seasonal allergies actually improves their ocular comfort as the contact lens acts as a barrier to the allergen [3] and [4]. Scleral lenses have long been considered speciality lenses, apart from a time when they were the only lenses available but at that time all contact lens work would have been considered speciality practice! Nowadays we see the advent of mini-scleral designs and we see large diameter gas permeable lenses too. It is possible that these lenses increase the popularity of gas permeable lenses again and they become more main stream. So it would seem that the lines between routine and speciality contact lens fitting are not clear. Whether a lens is classed a specialist fit or not would depend on the lens type, why it was fitted, where in the world the fitting was being done and even the era in which it was fitted. This begs the question as to what would be considered entry level knowledge in contact lens fitting. This may not be an issue for most BCLA members or CLAE readers but certainly would be for bodies such as the College of Optometrists (UK) or the Association of British Dispensing Opticians when they are planning the final registration examinations for budding practitioners or when planning the level of higher level qualifications such as College Certificates or Diplomas. Similarly for training institutions when they are planning their course content. This becomes even trickier when trying to devise a qualification that spans across many countries, like the European Diploma in Optometry and Optics. How do we know if the training and examination level is correct? One way would be to analyse things when they go wrong and if patterns of malpractice are seen then maybe that could be used as an indicator to more training being needed. There were 162 Fitness to Practice Hearing at the General Optical Council between 2001 and 2010. Forty-seven of these were clinically related case, 39 fraud related, and 76 others. Of the clinical ones only 3 were contact lens related. So it would appear that as whole, in the profession, contact lens clinical skills are not being questioned too often (although it seems a few of us can’t keep our hands out the cookie jar!).

Comparison of fitting stability of the different soft toric contact lenses

Purpose: To compare lens orientation and rotational recovery of five currently available soft toric lenses. Methods: Twenty subjects were recruited and trialed with each of the study lenses in a random order. Study lenses were PureVision® Toric (B&L), Air Optix® for Astigmatism (Alcon), Biofinity® Toric (CooperVision), Acuvue® Advance for Astigmatism (Vistakon), and Proclear® Toric (CooperVision). Lens orientation in primary position to determine the lens rotation form the vertical position and rotational recovery to primary gaze orientation following a 45° manual misorientation for the different lenses was compared. Results: The Biofinity Toric showed the lowest rotation from the vertical position and the Proclear Toric the highest. Also, the highest and the lowest reorientation speed were related to the Biofinity Toric and the Acuvue Advance for Astigmatism, respectively. The Repeated Measures ANOVA showed a significant difference in the lens rotation (P=. 0.004) and rotational recovery (P<. 0.001) among different contact lenses and the performed multiple comparisons indicated differences in rotation and also in reorientation speed were only seen between the Biofinity Toric when compared to four other lenses (P<. 0.05). Conclusion: Although there was appropriate fitting, based upon lens orientation and reorientation speed, with each of the study lenses it would appear that the optimized ballast technique used in the design of the Biofinity Toric helps reduce lens rotation and improve rotational recovery compared to others.

History and symptom taking in contact lens fitting and aftercare

Aim: To appraise history and symptom taking for contact lens consultations, to determine current practice and to make recommendations for best practice. Method: The peer reviewed academic literature was reviewed and the results informed a survey completed by 256 eye care practitioners (ECPs) on their current practice and influences. Results: The last eye-test date, last contact lens aftercare (for existing wearers) and reason for visit are key questions for most ECPs. Detailed use of contact lens questions are more commonly applied in aftercares than when refitting patients who have previously discontinued wear (87% vs 56% use), whereas questions on ocular and general history, medication and lifestyle were generally more commonly utilised for new patients than in aftercares (72% vs 50%). 75% of ECPs requested patients bring a list of their medication to appointments. Differential diagnosis questioning was thorough in most ECPs (87% of relevant questions asked). Attempts to optimise compliance included oral instruction (95% always) and written patient instructions (95% at least sometimes). Abbreviations were used by 39% of respondents (26% used ones provided by a professional body). Conclusion: There is scope for more consistency in history and symptom taking for contact lens consultations and recommendations are made.

Multi-model fitting based on minimum spanning tree

This paper presents a novel approach to the computation of primitive geometrical structures, where no prior knowledge about the visual scene is available and a high level of noise is expected. We based our work on the grouping principles of proximity and similarity, of points and preliminary models. The former was realized using Minimum Spanning Trees (MST), on which we apply a stable alignment and goodness of fit criteria. As for the latter, we used spectral clustering of preliminary models. The algorithm can be generalized to various model fitting settings, without tuning of run parameters. Experiments demonstrate the significant improvement in the localization accuracy of models in plane, homography and motion segmentation examples. The efficiency of the algorithm is not dependent on fine tuning of run parameters like most others in the field.

Fitting an MSD (Mini Scleral Design) rigid contact lens in advanced keratoconus with INTACS

Keratoconus is a bilateral degenerative disease characterized by a non-inflammatory, progressive central corneal ectasia (typically asymmetric) and decreased vision. In its early stages it may be managed with spectacles and soft contact lenses but more commonly it is managed with rigid contact lenses. In advanced stages, when contact lenses can no longer be fit, have become intolerable, or corneal damage is severe, a penetrating keratoplasty is commonly performed. Alternative surgical techniques, such as the use of intra-stromal corneal ring segments (INTACS) have been developed to try and improve the fit of rigid contact lenses in keratoconic patients and avoid penetrating keratoplasties. This case report follows through the fitting of rigid contact lenses in an advanced keratoconic cornea after an INTACS procedure and discusses clinical findings, treatment options, and the use of mini-scleral and scleral lens designs as they relate to the challenges encountered in managing such a patient. Mini-scleral and scleral lenses are relatively easy to fit, and can be of benefit to many patients, including advanced keratoconic patients, post-INTAC patients and post-penetrating keratoplasty patients. © 2011 British Contact Lens Association.

Serum procalcitonin, interleukin-6, soluble intercellular adhesin molecule-1 and IgG to short-chain exocellular lipoteichoic acid as predictors of infection in total joint prosthesis revision

The diagnosis of prosthetic joint infection and its differentiation from aseptic loosening remains problematic. The definitive laboratory diagnostic test is the recovery of identical infectious agents from multiple intraoperative tissue samples; however, interpretation of positive cultures is often complex as infection is frequently associated with low numbers of commensal microorganisms, in particular the coagulase-negative staphylococci (CNS). In this investigation, the value of serum procalcitonin (PCT), interleukin-6 (IL-6) and soluble intercellular adhesion molecule-1 (sICAM-1) as predictors of infection in revision hip replacement surgery is assessed. Furthermore, the diagnostic value of serum IgG to short-chain exocellular lipoteichoic acid (sce-LTA) is assessed in patients with infection due to CNS. Presurgical levels of conventional serum markers of infection including C-reactive protein (CRP), erythrocyte sedimentation rate (ESR) and white blood cell count (WBC) is also established. Forty-six patients undergoing revision hip surgery were recruited with a presumptive clinical diagnosis of either septic (16 patients) or aseptic loosening (30 patients). The diagnosis was confirmed microbiologically and levels of serum markers were determined. Serum levels of IL-6 and sICAM-1 were significantly raised in patients with septic loosening (P=0.001 and P=0.0002, respectively). Serum IgG to sce-LTA was elevated in three out of four patients with infection due to CNS. In contrast, PCT was not found to be of value in differentiating septic and aseptic loosening. Furthermore, CRP, ESR and WBC were significantly higher (P=0.0001, P=0.0001 and P=0.003, respectively) in patients with septic loosening. Serum levels of IL-6, sICAM-1 and IgG to sce-LTA may provide additional information to facilitate the diagnosis of prosthetic joint infection.