Data methods in optometry. Part 10: non-linear regression analysis

1. The techniques associated with regression, whether linear or non-linear, are some of the most useful statistical procedures that can be applied in clinical studies in optometry. 2. In some cases, there may be no scientific model of the relationship between X and Y that can be specified in advance and the objective may be to provide a ‘curve of best fit’ for predictive purposes. In such cases, the fitting of a general polynomial type curve may be the best approach. 3. An investigator may have a specific model in mind that relates Y to X and the data may provide a test of this hypothesis. Some of these curves can be reduced to a linear regression by transformation, e.g., the exponential and negative exponential decay curves. 4. In some circumstances, e.g., the asymptotic curve or logistic growth law, a more complex process of curve fitting involving non-linear estimation will be required.

Mathematical modelling of patient risks in a hospital environment, using multiple regression analysis

The aim of this research work was primarily to examine the relevance of patient parameters, ward structures, procedures and practices, in respect of the potential hazards of wound cross-infection and nasal colonisation with multiple resistant strains of Staphylococcus aureus, which it is thought might provide a useful indication of a patient's general susceptibility to wound infection. Information from a large cross-sectional survey involving 12,000 patients from some 41 hospitals and 375 wards was collected over a five-year period from 1967-72, and its validity checked before any subsequent analysis was carried out. Many environmental factors and procedures which had previously been thought (but never conclusively proved) to have an influence on wound infection or nasal colonisation rates, were assessed, and subsequently dismissed as not being significant, provided that the standard of the current range of practices and procedures is maintained and not allowed to deteriorate. Retrospective analysis revealed that the probability of wound infection was influenced by the patient's age, duration of pre-operative hospitalisation, sex, type of wound, presence and type of drain, number of patients in ward, and other special risk factors, whilst nasal colonisation was found to be influenced by the patient's age, total duration of hospitalisation, sex, antibiotics, proportion of occupied beds in the ward, average distance between bed centres and special risk factors. A multi-variate regression analysis technique was used to develop statistical models, consisting of variable patient and environmental factors which were found to have a significant influence on the risks pertaining to wound infection and nasal colonisation. A relationship between wound infection and nasal colonisation was then established and this led to the development of a more advanced model for predicting wound infections, taking advantage of the additional knowledge of the patient's state of nasal colonisation prior to operation.

Adherence to antiepileptic medicines in children:a multiple-methods assessment involving dried blood spot sampling

Purpose - To evaluate adherence to prescribed antiepileptic drugs (AEDs) in children with epilepsy using a combination of adherence-assessment methods. Methods - A total of 100 children with epilepsy (≤17 years old) were recruited. Medication adherence was determined via parental and child self-reporting (≥9 years old), medication refill data from general practitioner (GP) prescribing records, and via AED concentrations in dried blood spot (DBS) samples obtained from children at the clinic and via self- or parental-led sampling in children's own homes. The latter were assessed using population pharmacokinetic modeling. Patients were deemed nonadherent if any of these measures were indicative of nonadherence with the prescribed treatment. In addition, beliefs about medicines, parental confidence in seizure management, and the presence of depressed mood in parents were evaluated to examine their association with nonadherence in the participating children. Key Findings - The overall rate of nonadherence in children with epilepsy was 33%. Logistic regression analysis indicated that children with generalized epilepsy (vs. focal epilepsy) were more likely (odds ratio [OR] 4.7, 95% confidence interval [CI] 1.37–15.81) to be classified as nonadherent as were children whose parents have depressed mood (OR 3.6, 95% CI 1.16–11.41). Significance - This is the first study to apply the novel methodology of determining adherence via AED concentrations in clinic and home DBS samples. The present findings show that the latter, with further development, could be a useful approach to adherence assessment when combined with other measures including parent and child self-reporting. Seizure type and parental depressed mood were strongly predictive of nonadherence.

Regression analysis of ranked segment parameters for optic nerve head classification:a pilot study

Purpose: To determine whether curve-fitting analysis of the ranked segment distributions of topographic optic nerve head (ONH) parameters, derived using the Heidelberg Retina Tomograph (HRT), provide a more effective statistical descriptor to differentiate the normal from the glaucomatous ONH. Methods: The sample comprised of 22 normal control subjects (mean age 66.9 years; S.D. 7.8) and 22 glaucoma patients (mean age 72.1 years; S.D. 6.9) confirmed by reproducible visual field defects on the Humphrey Field Analyser. Three 10°-images of the ONH were obtained using the HRT. The mean topography image was determined and the HRT software was used to calculate the rim volume, rim area to disc area ratio, normalised rim area to disc area ratio and retinal nerve fibre cross-sectional area for each patient at 10°-sectoral intervals. The values were ranked in descending order, and each ranked-segment curve of ordered values was fitted using the least squares method. Results: There was no difference in disc area between the groups. The group mean cup-disc area ratio was significantly lower in the normal group (0.204 ± 0.16) compared with the glaucoma group (0.533 ± 0.083) (p < 0.001). The visual field indices, mean deviation and corrected pattern S.D., were significantly greater (p < 0.001) in the glaucoma group (-9.09 dB ± 3.3 and 7.91 ± 3.4, respectively) compared with the normal group (-0.15 dB ± 0.9 and 0.95 dB ± 0.8, respectively). Univariate linear regression provided the best overall fit to the ranked segment data. The equation parameters of the regression line manually applied to the normalised rim area-disc area and the rim area-disc area ratio data, correctly classified 100% of normal subjects and glaucoma patients. In this study sample, the regression analysis of ranked segment parameters method was more effective than conventional ranked segment analysis, in which glaucoma patients were misclassified in approximately 50% of cases. Further investigation in larger samples will enable the calculation of confidence intervals for normality. These reference standards will then need to be investigated for an independent sample to fully validate the technique. Conclusions: Using a curve-fitting approach to fit ranked segment curves retains information relating to the topographic nature of neural loss. Such methodology appears to overcome some of the deficiencies of conventional ranked segment analysis, and subject to validation in larger scale studies, may potentially be of clinical utility for detecting and monitoring glaucomatous damage. © 2007 The College of Optometrists.

Evaluating the additionality of public sector assistance to Irish firms: a question of ownership?

This article presents an innovative approach to estimating the additionality of financial assistance awarded to firms by an Irish regional development agency. The 'self assessment approach' is used to derive estimates of deadweight and displacement for firms in the Shannon region of Ireland. Irish studies have derived high estimates of deadweight by international standards. In light of this, and the fact that successive Irish governments have placed emphasis on Foreign Direct Investment as an engine for growth, the primary objective here is to address the question of whether the type of firm ownership matters with respect to resulting deadweight and/or displacement estimates. The latter question is addressed using logistic regression analysis to test whether, ceteris paribus, firm ownership is a key-determining factor for estimates of deadweight and/or displacement. The results show that ownership does not matter in the case of deadweight, but regarding displacement there are differences between indigenous and foreign-owned firms albeit at very low levels. More precisely, as expected, indigenously owned firms are more likely to lead to higher estimates of displacement.

Patient anxiety and experiences associated with an outpatient "one-stop" "see and treat" hysteroscopy clinic

BACKGROUND: "One-stop" outpatient hysteroscopy clinics have become well established for the investigation and treatment of women with abnormal uterine bleeding. However, the advantages of these clinics may be offset by patient factors such as anxiety, pain, and dissatisfaction. This study aimed to establish patients' views and experiences of outpatient service delivery in the context of a one-stop diagnostic and therapeutic hysteroscopy clinic, to determine the amount of anxiety experienced by these women and compare this with other settings, and to determine any predictors for patient preferences. METHODS: The 20-item State-Trait Anxiety Inventory was given to 240 women attending a one-stop hysteroscopy clinic: to 73 consecutive women before their appointment in a general gynecology clinic and to 36 consecutive women attending a chronic pelvic pain clinic. The results were compared with published data for the normal female population, for women awaiting major surgery, and for women awaiting a colposcopy clinic appointment. In addition, a questionnaire designed to ascertain patients' views and experiences was used. Logistic regression analysis was used to delineate the predictive values of diagnostic or therapeutic hysteroscopy, and to determine their effect on the preference of patients to have the procedure performed under general anesthesia in the future. RESULTS: Women attending the hysteroscopy clinic in this study reported significantly higher levels of anxiety than those attending the general gynecology clinic (median, 45 vs 39; p = 0.004), but the levels of anxiety were comparable with those of women attending the chronic pelvic pain clinic (median, 45 vs 46; p = 0.8). As compared with the data from the normal female population (mean, 35.7) and those reported for women awaiting major surgery (mean, 41.2), the levels of anxiety experienced before outpatient hysteroscopy clinic treatment were found to be higher (mean, 45.7). Only women awaiting colposcopy (6-item mean score, 51.1 +/- 13.3) experienced significantly higher anxiety scores than the women awaiting outpatient hysteroscopy (6-item mean score, 47.3 +/- 13.9; p = 0.002). Despite their anxiety, most women are satisfied with the outpatient hysteroscopy "see and treat" service. High levels of anxiety, particularly concerning pain but not operative intervention, were significant predictors of patients desiring a future procedure to be performed under general anesthesia. CONCLUSIONS: Outpatient hysteroscopy is associated with significant anxiety, which increases the likelihood of intolerance for the outpatient procedure. However, among those undergoing operative therapeutic procedures, dissatisfaction was not associated with the outpatient setting.

Provision of primary care to patients with chronic cough in the community pharmacy setting

BACKGROUND: Community pharmacies are at the forefront of primary care providers and have an important role in the referral of patients to a medical practitioner for review when necessary. Chronic cough is a common disorder in the community and requires medical assessment. The proficiency of community pharmacy staff to refer patients with chronic cough is currently unknown. OBJECTIVE: To assess the ability of community pharmacy staff to recognize and medically refer patients with a chronic nonproductive cough. METHODS: Following ethics approval, a simulated patient study of 156 community pharmacies in Perth, Western Australia, was conducted over a 3-month period. Simulated patients presented to the pharmacy requesting treatment for a cough. The simulated patient required a referral based on a designated scenario. Demographic details, assessment questions, and advice provided were recorded by the simulated patient immediately postvisit. A logistic regression analysis was performed, with referral for medical assessment as the dependent variable. RESULTS: Of the 155 community pharmacies included in the analysis, 38% provided appropriate medical referral. Cough suppressants were provided as therapy in 72% of all visits. Predictors of medical referral were assessment of symptom duration, medical history, current medications being taken, frequency of reliever use, and the position of the pharmacy staff member conducting the consultation. A third of community pharmacies provided appropriate primary care by recommending medical referral advice to patients with chronic cough. The majority of pharmacy staff members acquired information from the patient that suggested a need for medical referral, yet did not provide referral advice. CONCLUSIONS: Appropriate medical referral is more likely when adequate assessment is undertaken and when a pharmacist is directly involved in the consultation. This highlights the need for pharmacies to ensure that processes are in place for patients to access the pharmacist.

A simultaneous examination of the effects of salesperson relationship-building activities and marketing activities on retail buyers' purchase decisions

Firms’ contemporary selling practices often not only demand that salespeople meet sales quotas, but also that they build strong, profitable relationships with customers. Given the belief that relationship-building activities can develop closer customer ties and improve sales performance, scholars have increasingly studied salesperson behaviors aimed at nurturing buyer-salesperson relations. However, while previous sales research has investigated the effects of a number of relational activities on performance outcomes in isolation, knowledge about their effectiveness in comparison to other important performance drivers is virtually absent. The present study provides some first theoretical and empirical insights into this research gap by simultaneously examining the role of specific salesperson relationship-building activities, and product-focused variables, in retail buyers’ new product purchase decisions. Following an extensive literature review, a two-part qualitative field study was conducted to explore salesperson relationship-building activities that are regarded as important by retail buyers. Two key relational behaviors were suggested by the customer-centric and retail industry-specific data; salesperson consultation (communication-based) and salesperson helping behavior (action-based). Drawing on this as well as extant literature, a conceptual framework was developed concerning the influences of these relationship-building activities and other product-focused factors on retail buyers’ new product acceptance. The study’s quantitative component contained a mail and web survey of U.S. retail buyers, resulting in a total dataset of 192 responses. After a comprehensive measure validation process, the theoretical hypotheses were tested using logistic regression analysis. Contrary to existing assertions, the results suggest that salesperson relationship-building activities themselves do not directly and/or indirectly influence purchase decisions, but instead can moderate the effects of product-focused determinants on retail buyers’ new product selections. Data on actual purchase decisions provide a high level of external validity to the findings. The study closes with a concluding discussion, including theoretical and managerial implications of the findings, limitations of the research, and directions for future inquiry.

Potential risk factors for medication non-adherence in patients with chronic obstructive pulmonary disease (COPD)

Aims - To investigate the effect of a range of demographic and psychosocial variables on medication adherence in chronic obstructive pulmonary disease (COPD) patients managed in a secondary care setting. Methods - A total of 173 patients with a confirmed diagnosis of COPD, recruited from an outpatient clinic in Northern Ireland, participated in the study. Data collection was carried out via face-to-face interviews and through review of patients’ medical charts. Social and demographic variables, co-morbidity, self-reported drug adherence (Morisky scale), Hospital Anxiety and Depression (HAD) scale, COPD knowledge, Health Belief Model (HBM) and self-efficacy scales were determined for each patient. Results - Participants were aged 67 ± 9.7 (mean ± SD) years, 56 % female and took a mean (SD) of 8.2 ± 3.4 drugs. Low adherence with medications was present in 29.5 % of the patients. Demographic variables (gender, age, marital status, living arrangements and occupation) were not associated with adherence. A range of clinical and psychosocial variables, on the other hand, were found to be associated with medication adherence, i.e. beliefs regarding medication effectiveness, severity of COPD, smoking status, presence of co-morbid illness, depressed mood, self-efficacy, perceived susceptibility and perceived barriers within the HBM (p < 0.05). Logistic regression analysis showed that perceived ineffectiveness of medication, presence of co-morbid illness, depressed mood and perceived barriers were independently associated with medication non-adherence in the study (P < 0.05). Conclusions - Adherence in COPD patients is influenced more by patients’ perception of their health and medication effectiveness, the presence of depressed mood and co-morbid illness than by demographic factors or disease severity.

Optimising the diagnostic performance of the Geriatric Depression Scale

The aim of this work is to empirically generate a shortened version of the Geriatric Depression Scale (GDS), with the intention of maximising the diagnostic performance in the detection of depression compared with previously GDS validated versions, while optimizing the size of the instrument. A total of 233 individuals (128 from a Day Hospital, 105 randomly selected from the community) aged 60 or over completed the GDS and other measures. The 30 GDS items were entered in the Day Hospital sample as independent variables in a stepwise logistic regression analysis predicting diagnosis of Major Depression. A final solution of 10 items was retained, which correctly classified 97.4% of cases. The diagnostic performance of these 10 GDS items was analysed in the random sample with a receiver operating characteristic (ROC) curve. Sensitivity (100%), specificity (97.2%), positive (81.8%) and negative (100%) predictive power, and the area under the curve (0.994) were comparable with values for GDS-30 and higher compared with GDS-15, GDS-10 and GDS-5. In addition, the new scale proposed had excellent fit when testing its unidimensionality with CFA for categorical outcomes (e.g., CFI=0.99). The 10-item version of the GDS proposed here, the GDS-R, seems to retain the diagnostic performance for detecting depression in older adults of the GDS-30 items, while increasing the sensitivity and predictive values relative to other shortened versions.

Health beliefs affect the correct replacement of daily disposable contact lenses:predicting compliance with the Health Belief Model and the Theory of Planned Behaviour

Purpose: To assess the compliance of Daily Disposable Contact Lenses (DDCLs) wearers with replacing lenses at a manufacturer-recommended replacement frequency. To evaluate the ability of two different Health Behavioural Theories (HBT), The Health Belief Model (HBM) and The Theory of Planned Behaviour (TPB), in predicting compliance. Method: A multi-centre survey was conducted using a questionnaire completed anonymously by contact lens wearers during the purchase of DDCLs. Results: Three hundred and fifty-four questionnaires were returned. The survey comprised 58.5% females and 41.5% males (mean age 34. ±. 12. years). Twenty-three percent of respondents were non-compliant with manufacturer-recommended replacement frequency (re-using DDCLs at least once). The main reason for re-using DDCLs was "to save money" (35%). Predictions of compliance behaviour (past behaviour or future intentions) on the basis of the two HBT was investigated through logistic regression analysis: both TPB factors (subjective norms and perceived behavioural control) were significant (p. <. 0.01); HBM was less predictive with only the severity (past behaviour and future intentions) and perceived benefit (only for past behaviour) as significant factors (p. <. 0.05). Conclusions: Non-compliance with DDCLs replacement is widespread, affecting 1 out of 4 Italian wearers. Results from the TPB model show that the involvement of persons socially close to the wearers (subjective norms) and the improvement of the procedure of behavioural control of daily replacement (behavioural control) are of paramount importance in improving compliance. With reference to the HBM, it is important to warn DDCLs wearers of the severity of a contact-lens-related eye infection, and to underline the possibility of its prevention.

Global variations and time trends in the prevalence of childhood myopia, a systematic review and quantitative meta-analysis:implications for aetiology and early prevention

The aim of this review was to quantify the global variation in childhood myopia prevalence over time taking account of demographic and study design factors. A systematic review identified population-based surveys with estimates of childhood myopia prevalence published by February 2015. Multilevel binomial logistic regression of log odds of myopia was used to examine the association with age, gender, urban versus rural setting and survey year, among populations of different ethnic origins, adjusting for study design factors. 143 published articles (42 countries, 374 349 subjects aged 1- 18 years, 74 847 myopia cases) were included. Increase in myopia prevalence with age varied by ethnicity. East Asians showed the highest prevalence, reaching 69% (95% credible intervals (CrI) 61% to 77%) at 15 years of age (86% among Singaporean-Chinese). Blacks in Africa had the lowest prevalence; 5.5% at 15 years (95% CrI 3% to 9%). Time trends in myopia prevalence over the last decade were small in whites, increased by 23% in East Asians, with a weaker increase among South Asians. Children from urban environments have 2.6 times the odds of myopia compared with those from rural environments. In whites and East Asians sex differences emerge at about 9 years of age; by late adolescence girls are twice as likely as boys to be myopic. Marked ethnic differences in age-specific prevalence of myopia exist. Rapid increases in myopia prevalence over time, particularly in East Asians, combined with a universally higher risk of myopia in urban settings, suggest that environmental factors play an important role in myopia development, which may offer scope for prevention.