Statnote 4: what if the data are not normal?

When testing the difference between two groups, if previous data indicate non-normality, then either transform the data if they comprise percentages, integers or scores or use a non-parametric test. If there is uncertainty whether the data are normally distributed, then deviations from normality are likely to be small if the data are measurements to three significant figures. Unless there is clear evidence that the distribution is non-normal, it is more efficient to use the conventional t-tests. It is poor statistical practice to carry out both the parametric and non-parametric tests on a set of data and then choose the result that is most convenient to the investigator!

Statnote 18: comparison of regression lines

In many circumstances, it may be of interest to discover whether two or more regression lines are the same. Regression lines may differ in three properties, viz., in residual variance, in slope, and in elevation; all of which can be tested using analysis of covariance. If there are no significant differences between regression lines, an investigator may which to combine the data from different studies and fit a single regression line to the whole of the data.

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.

Data analysis methods in optometry Part 3: the analysis of frequencies and proportions

In some studies, the data are not measurements but comprise counts or frequencies of particular events. In such cases, an investigator may be interested in whether one specific event happens more frequently than another or whether an event occurs with a frequency predicted by a scientific model.

Data analysis methods in optometry Part 4: an introduction to analysis of variance (ANOVA)

In any investigation in optometry involving more that two treatment or patient groups, an investigator should be using ANOVA to analyse the results assuming that the data conform reasonably well to the assumptions of the analysis. Ideally, specific null hypotheses should be built into the experiment from the start so that the treatments variation can be partitioned to test these effects directly. If 'post-hoc' tests are used, then an experimenter should examine the degree of protection offered by the test against the possibilities of making either a type 1 or a type 2 error. All experimenters should be aware of the complexity of ANOVA. The present article describes only one common form of the analysis, viz., that which applies to a single classification of the treatments in a randomised design. There are many different forms of the analysis each of which is appropriate to the analysis of a specific experimental design. The uses of some of the most common forms of ANOVA in optometry have been described in a further article. If in any doubt, an investigator should consult a statistician with experience of the analysis of experiments in optometry since once embarked upon an experiment with an unsuitable design, there may be little that a statistician can do to help.

Data analysis methods in optometry Part 7: multiple linear regression

Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

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.

Statistical analysis in microbiology:statnotes

This book is aimed primarily at microbiologists who are undertaking research and who require a basic knowledge of statistics to analyse their experimental data. Computer software employing a wide range of data analysis methods is widely available to experimental scientists. The availability of this software, however, makes it essential that investigators understand the basic principles of statistics. Statistical analysis of data can be complex with many different methods of approach, each of which applies in a particular experimental circumstance. Hence, it is possible to apply an incorrect statistical method to data and to draw the wrong conclusions from an experiment. The purpose of this book, which has its origin in a series of articles published in the Society for Applied Microbiology journal ‘The Microbiologist’, is an attempt to present the basic logic of statistics as clearly as possible and therefore, to dispel some of the myths that often surround the subject. The 28 ‘Statnotes’ deal with various topics that are likely to be encountered, including the nature of variables, the comparison of means of two or more groups, non-parametric statistics, analysis of variance, correlating variables, and more complex methods such as multiple linear regression and principal components analysis. In each case, the relevant statistical method is illustrated with examples drawn from experiments in microbiological research. The text incorporates a glossary of the most commonly used statistical terms and there are two appendices designed to aid the investigator in the selection of the most appropriate test.

Statnote 25: Stepwise multiple regression

An investigator may also wish to select a small subset of the X variables which give the best prediction of the Y variable. In this case, the question is how many variables should the regression equation include? One method would be to calculate the regression of Y on every subset of the X variables and choose the subset that gives the smallest mean square deviation from the regression. Most investigators, however, prefer to use a ‘stepwise multiple regression’ procedure. There are two forms of this analysis called the ‘step-up’ (or ‘forward’) method and the ‘step-down’ (or ‘backward’) method. This Statnote illustrates the use of stepwise multiple regression with reference to the scenario introduced in Statnote 24, viz., the influence of climatic variables on the growth of the crustose lichen Rhizocarpon geographicum (L.)DC.

The SECURE study:long-term safety of Ranibizumab 0.5 mg in neovascular age-related macular degeneration

Objective - To evaluate long-term safety of intravitreal ranibizumab 0.5-mg injections in neovascular age-related macular degeneration (nAMD). Design - Twenty-four–month, open-label, multicenter, phase IV extension study. Participants - Two hundred thirty-four patients previously treated with ranibizumab for 12 months in the EXCITE/SUSTAIN study. Methods - Ranibizumab 0.5 mg administered at the investigator's discretion as per the European summary of product characteristics 2007 (SmPC, i.e., ranibizumab was administered if a patient experienced a best-corrected visual acuity [BCVA] loss of >5 Early Treatment Diabetic Retinopathy Study letters measured against the highest visual acuity [VA] value obtained in SECURE or previous studies [EXCITE and SUSTAIN], attributable to the presence or progression of active nAMD in the investigator's opinion). Main Outcome Measures - Incidence of ocular or nonocular adverse events (AEs) and serious AEs, mean change in BCVA from baseline over time, and the number of injections. Results - Of 234 enrolled patients, 210 (89.7%) completed the study. Patients received 6.1 (mean) ranibizumab injections over 24 months. Approximately 42% of patients had 7 or more visits at which ranibizumab was not administered, although they had experienced a VA loss of more than 5 letters, indicating either an undertreatment or that factors other than VA loss were considered for retreatment decision by the investigator. The most frequent ocular AEs (study eye) were retinal hemorrhage (12.8%; 1 event related to study drug), cataract (11.5%; 1 event related to treatment procedure), and increased intraocular pressure (6.4%; 1 event related to study drug). Cataract reported as serious due to hospitalization for cataract surgery occurred in 2.6% of patients; none was suspected to be related to study drug or procedure. Main nonocular AEs were hypertension and nasopharyngitis (9.0% each). Arterial thromboembolic events were reported in 5.6% of the patients. Five (2.1%) deaths occurred during the study, none related to the study drug or procedure. At month 24, mean BCVA declined by 4.3 letters from the SECURE baseline. Conclusions - The SECURE study showed that ranibizumab administered as per a VA-guided flexible dosing regimen recommended in the European ranibizumab SmPC at the investigator's discretion was well tolerated over 2 years. No new safety signals were identified in patients who received ranibizumab for a total of 3 years. On average, patients lost BCVA from the SECURE study baseline, which may be the result of disease progression or possible undertreatment.

Dietary analysis and patterns of nutritional supplement use in normal and age-related macular disease affected subjects:a prospective cross-sectional study

Background: Poor diet is thought to be a risk factor for many diseases, including age-related macular disease (ARMD), which is the leading cause of blind registration in those aged over 60 years in the developed world. The aims of this study were 1) to evaluate the dietary food intake of three subject groups: participants under the age of 50 years without ARMD (U50), participants over the age of 50 years without ARMD (O50), and participants with ARMD (AMD), and 2) to obtain information on nutritional supplement usage. Methods: A prospective cross-sectional study designed in a clinical practice setting. Seventy-four participants were divided into three groups: U50; 20 participants aged < 50 years, from 21 to 40 (mean ± SD, 37.7 ± 10.1 years), O50; 27 participants aged > 50 years, from 52 to 77 (62.7 ± 6.8 years), and ARMD; 27 participants aged > 50 years with ARMD, from 55 to 79 (66.0 ± 5.8 years). Participants were issued with a three-day food diary, and were also asked to provide details of any daily nutritional supplements. The diaries were analysed using FoodBase 2000 software. Data were input by one investigator and statistically analysed using Microsoft Excel for Microsoft Windows XP software, employing unpaired t-tests. Results: Group O50 consumed significantly more vitamin C (t = 3.049, p = 0.005) and significantly more fibre (t = 2.107, p = 0.041) than group U50. Group ARMD consumed significantly more protein (t = 3.487, p = 0.001) and zinc (t = 2.252, p = 0.029) than group O50. The ARMD group consumed the highest percentage of specific ocular health supplements and the U50 group consumed the most multivitamins. Conclusions: We did not detect a deficiency of any specific nutrient in the diets of those with ARMD compared with age- and gender-matched controls. ARMD patients may be aware of research into use of nutritional supplementation to prevent progression of their condition.

Clinical performance of daily disposable soft contact lenses using sustained release technology

Purpose: Polyvinyl alcohol (PVA) is a successful tear film stabiliser and is widely used in comfort drops and some soft contact lens materials. A PVA-containing lens, nelfilcon A has been modified to include additional (non-functional) PVA in order to provide improved comfort. This study aims to examine the clinical performance of this nelfilcon A lens with AquaRelease™ (AquaRelease). Methods: Two contralateral, investigator masked, open label, subjective and objective evaluations were conducted. The first examined the effect of adding increased molecular weight PVA to nelfilcon A (n = 5), and the second compared this AquaRelease lens to ocufilcon B (n = 34). The principal measures were non-invasive break-up time (NIBUT) and subjective comfort, which were assessed at the beginning and end of a week of daily wear, and three times throughout 1 day at 8, 12 and 16 h. Results: All subjects successfully completed the daily wearing schedule of 16 h. On initial insertion, subjective comfort and NIBUT improved for AquaRelease than original nelfilcon A lenses (p < 0.05). Initial comfort was better for AquaRelease compared to ocufilcon B lenses (p = 0.01); however, NIBUT was not statistically different (11.7 ± 15.6 s versus 8.4 ± 6.8 s; p = 0.26). Subjective comfort decreased with time (p < 0.001), but there was no significant difference between AquaRelease and ocufilcon B lenses (p = 0.16). NIBUT was not significantly affected by time (p = 0.56) or between lenses (p = 0.33). At the end of a weeks' wear, subjective initial, end-of-day, overall comfort and vision were rated significantly better with AquaRelease than ocufilcon B (p < 0.01). Conclusions: Release of additional non-functionalised PVA from the nelfilcon A lenses appears to enhance comfortable contact lens wear. © 2006 British Contact Lens Association.

Statnote 39: The binomial distribution: comparing two proportions

Many populations consist of two classes only, e.g., alive or dead, present or absent, clean or dirty, infected or non-infected, and it is the proportion or percentage of observations that fall into one of these classes that is of interest to an investigator. An observation that falls into one of the two classes is considered a ‘success’ (S), and ‘p’ is defined as the proportion of observations falling into that class. If a random sample of size ‘n’ is obtained from a population, the probability of obtaining 0, 1, 2, 3, etc., successes is then given by the binomial distribution. The binomial distribution can be used as the basis of a number of statistical tests but is most useful when comparing two proportions. This statnote describes two such scenarios in which the binomial distribution is used to compare: (1) two proportions when the samples are independent and (2) two proportions when the samples are paired.

Discovering biomarkers for antidepressant response:protocol from the Canadian biomarker integration network in depression (CAN-BIND) and clinical characteristics of the first patient cohort

Background: Major Depressive Disorder (MDD) is among the most prevalent and disabling medical conditions worldwide. Identification of clinical and biological markers ("biomarkers") of treatment response could personalize clinical decisions and lead to better outcomes. This paper describes the aims, design, and methods of a discovery study of biomarkers in antidepressant treatment response, conducted by the Canadian Biomarker Integration Network in Depression (CAN-BIND). The CAN-BIND research program investigates and identifies biomarkers that help to predict outcomes in patients with MDD treated with antidepressant medication. The primary objective of this initial study (known as CAN-BIND-1) is to identify individual and integrated neuroimaging, electrophysiological, molecular, and clinical predictors of response to sequential antidepressant monotherapy and adjunctive therapy in MDD. Methods: CAN-BIND-1 is a multisite initiative involving 6 academic health centres working collaboratively with other universities and research centres. In the 16-week protocol, patients with MDD are treated with a first-line antidepressant (escitalopram 10-20 mg/d) that, if clinically warranted after eight weeks, is augmented with an evidence-based, add-on medication (aripiprazole 2-10 mg/d). Comprehensive datasets are obtained using clinical rating scales; behavioural, dimensional, and functioning/quality of life measures; neurocognitive testing; genomic, genetic, and proteomic profiling from blood samples; combined structural and functional magnetic resonance imaging; and electroencephalography. De-identified data from all sites are aggregated within a secure neuroinformatics platform for data integration, management, storage, and analyses. Statistical analyses will include multivariate and machine-learning techniques to identify predictors, moderators, and mediators of treatment response. Discussion: From June 2013 to February 2015, a cohort of 134 participants (85 outpatients with MDD and 49 healthy participants) has been evaluated at baseline. The clinical characteristics of this cohort are similar to other studies of MDD. Recruitment at all sites is ongoing to a target sample of 290 participants. CAN-BIND will identify biomarkers of treatment response in MDD through extensive clinical, molecular, and imaging assessments, in order to improve treatment practice and clinical outcomes. It will also create an innovative, robust platform and database for future research. Trial registration: ClinicalTrials.gov identifier NCT01655706. Registered July 27, 2012.

Effects of service-learning on student attitudes toward academic engagement and civic responsibility

This empirical study explored the impact of service-learning participation on high school students' attitudes toward academic engagement and civic responsibility. This study focused whether a group of high school students who participated in a service-learning project had more positive attitudes toward academic engagement and civic responsibility than their high school peers who did not participate in a service learning project. ^ Data were collected from 67 volunteer students as participants in grades 9–12. A service-learning treatment group of 34 high school students was examined relative to a comparison group of 33 high school students with similar demographic and academic characteristics. The investigator used questionnaires, an oral history/service-learning project, and interviews with the teacher-coordinators of the project to collect the data. The two surveys, one investigating high school students' attitudes about academic engagement, the other investigating high school students' attitudes toward civic responsibility, were administered in a pre-treatment/post-treatment design. There were 90 days between the pre-treatment and post-treatment administrations. A factor analysis of the civic responsibility instrument and multivariate analysis of gain scores were used to compare the means of the total aggregate scores of the treatment and comparison groups. Factor analysis was performed on the academic engagement instrument but it was determined that only the total scores could be used in subsequent analyses. Results were used to determine the efficacy of service-learning as interpreted in student attitudes toward academic engagement and student attitudes toward civic responsibility. ^ The study found no significant difference between the academic engagement and the civic responsibility attitudes of a high school service-learning project group and a high school comparison group with comparable school and similar demographic characteristics. One of the implications for educational practice and policy from the study results is a need to design and implement more powerful studies, studies implemented at many sites rather than just at two sites that were the basis of this study, and studies that investigate the research questions over longer time periods. Although it was not a focus of the study, the investigator concluded that service learning projects such as this might be more effective if they were better aligned with Dewey's principles. ^