Statistics review 1: Presenting and summarising data

This article discusses statistical measures of variability in relation to measures of central tendency and levels of measurement. Three measures of variability used in healthcare research (the range, the interquartile range, and the standard deviation) are described and compared, including their uses and limitations. The article describes how each of the three measures is calculated, and it provides a step-by-step example of calculating the sums of squares, variance, and standard deviation. Graphs of frequency and percentage distributions are used to show how the interquartile range and the standard deviation represent the variability observed within distributions. The article discusses the properties of the normal curve regarding the distribution of scores around the mean in relation to the standard deviation, and illustrates differences in the shapes of normal curves with the same mean but different standard deviations.

Brain activity continuously fluctuates over time, even if the brain is in controlled (e.g., experimentally induced) states. Recent years have seen an increasing interest in understanding the complexity of these temporal variations, for example with respect to developmental changes in brain function or between-person differences in healthy and clinical populations. However, the psychometric reliability of brain signal variability and complexity measures-which is an important precondition for robust individual differences as well as longitudinal research-is not yet sufficiently studied. We examined reliability (split-half correlations) and test-retest correlations for task-free (resting-state) BOLD fMRI as well as split-half correlations for seven functional task data sets from the Human Connectome Project to evaluate their reliability. We observed good to excellent split-half reliability for temporal variability measures derived from rest and task fMRI activation time series (standard deviation, mean absolute successive difference, mean squared successive difference), and moderate test-retest correlations for the same variability measures under rest conditions. Brain signal complexity estimates (several entropy and dimensionality measures) showed moderate to good reliabilities under both, rest and task activation conditions. We calculated the same measures also for time-resolved (dynamic) functional connectivity time series and observed moderate to good reliabilities for variability measures, but poor reliabilities for complexity measures derived from functional connectivity time series. Global (i.e., mean across cortical regions) measures tended to show higher reliability than region-specific variability or complexity estimates. Larger subcortical regions showed similar reliability as cortical regions, but small regions showed lower reliability, especially for complexity measures. Lastly, we also show that reliability scores are only minorly dependent on differences in scan length and replicate our results across different parcellation and denoising strategies. These results suggest that the variability and complexity of BOLD activation time series are robust measures well-suited for individual differences research. Temporal variability of global functional connectivity over time provides an important novel approach to robustly quantifying the dynamics of brain function. PRACTITIONER POINTS: Variability and complexity measures of BOLD activation show good split-half reliability and moderate test-retest reliability. Measures of variability of global functional connectivity over time can robustly quantify neural dynamics. Length of fMRI data has only a minor effect on reliability.

Some Thoughts About Data Type, Distribution, and Statistical Significance

Johnson and Mickevich (1977) claimed to demonstrate an association between within-population variability and evolutionary rate for both allozyme loci and morphological characters in the atherinid fish genus Menidia. Their paper is extremely interesting for at least two reasons. First, it purports to demonstrate an evolutionary phenomenon exhibited by both electrophoretic and morphological characters; second, if their conclusions are correct it should be possible to estimate the relative likelihood of future evolutionary change for different characters within a lineage based solely upon measurements of present-day variability of those characters within that lineage. Johnson and Mickevich used two data sets: 24 allozyme loci sampled from 22 populations in five species of Menidia, and 22 morphological characters from a partly different set of 22 For the 16 populations that were represented in both of these data sets, phylogenetic trees constructed separately from the two different types of data provide . . nearly perfect congruence. The differences between the two trees are slight rearrangements within species. ... (Mickevich and Johnson, 1976). Two measures of evolutionary change were used: phenetic distance, or range of divergence, and patristic distance, the amount of change over a phylogenetic tree. For the allozyme loci, these quantities were based upon frequency differences between populations for each allele at a locus; the sum over these alleles was used as the measure of evolutionary change for the locus. By subtracting the phenetic from the patristic distance, an estimate of the repetitive portion of evolutionary change was also obtained. This represents reversals and parallel and convergent evolution, all of which contribute to the patristic but not to the phenetic distance. For both data sets, this repetitive component gives the highest correlation with intrapopulation variability, and the phenetic gives the lowest. Within-population variability was measured by the information statistic, H, for the allozyme data. For the morphometric characters, within-population variability was measured by the average standard deviation (divided by the grand mean) and measures of evolutionary change were computed between population means (also divided by the grand mean for that character). The point that I hope to make in this note is that there were several potential biases in the analyses performed by Johnson and Mickevich. First, they did not adequately correct for the possible contribution of sampling variance to their correlations. This bias applies to both the morphological and the allozyme data and is especially important for the repetitive component of the patristic distance. Second, their measures of variability and evolutionary change for the allozyme loci are not entirely free to vary independently, and a correlation between them, for certain frequency ranges, is unsurprising. This, too, is especially important for the repetitive component. Third, their measures of variability and change for the allozyme loci are both the result of summation processes across the number of alleles per locus. A correlation could result because different loci have different numbers of alleles. When this effect is removed, the correlation is primarily a function of the repetitive component for essentially invariant loci. Fourth, the gap-coding used for the morphological characters could introduce circular logic by giving relatively less-variable characters more weight in the construction of the phylogenetic tree. Since tree construction techniques minimize repetitive evolution, this weighting could result in a correlation between variability and apparent repetitive evolution. I do not claim that Johnson and Mickevich's conclusions are incorrect; only that they have presented no convincing evidence for those conclusions. Hopefully, future attempts to examine the relationship between variability and evolutionary rate will take some of these potential sources of bias into consideration. Are the correlations artifacts of sampling error? Sokal (1976) observed that in the absence of amonggroup differences the range of divergence among sample means should be correlated with the withingroup standard deviation. This is because the sampling variance of the mean is then proportional to the within-group variance. Johnson and Mickevich attempted to correct for this effect in the morphological data by omitting two characters that show no statistically significant differences . . between any pair of populations. Even though this procedure should reduce the bias, the fact that the amonggroup variance is partly composed of the withingroup variance (Sokal and Rohlf, 1969, p. 193) should still cause some correlation between the withinand among-group variability. A more appropriate method of analysis, at least for the phenetic component, would be to estimate variance components at the two levels as was done by Sokal (1976). Dr. Johnson informs me that he believes the in-

The first-line treatment of obstructive sleep apnea syndrome in children is adenotonsillectomy, but this may result in perioperative respiratory adverse events (PRAEs). The primary aim of this study is to examine whether the McGill oximetry score (MOS) and other polysomnography parameters can predict major PRAEs following adenotonsillectomy. We secondarily evaluated the MOS interrater reliability and correlation with other polysomnography parameters. This retrospective study included all children aged 0-18 years who underwent preoperative polysomnography between June 2010 and January 2016 prior to adenotonsillectomy at a tertiary pediatric institution. Oximetries from polysomnograms were assigned an MOS. Univariable and multivariable models for prediction of major PRAEs were constructed. MOS was correlated with polysomnography parameters and interrater reliability was evaluated. This study included 106 children; 15 had a major PRAE. A multivariable prediction model that combined MOS and age showed evidence for the ability to predict major PRAEs with an area under the receiver operating characteristic curve of 0.68 (95% confidence interval: 0.52, 0.84), whereby increased MOS and younger age were associated with PRAEs, but apnea-hypopnea index was not. MOS had excellent interrater reliability (κ = 0.95) and was highly correlated with oxygen saturation nadir and cumulative time percentage with oxygen saturation less than 90%. A prediction model including MOS and age may predict PRAEs following adenotonsillectomy. This suggests that nocturnal oximetry provides the most essential information of polysomnography measures to direct postoperative monitoring following adenotonsillectomy. Xiao L, Barrowman N, Momoli F, etal. Polysomnography parameters as predictors of respiratory adverse events following adenotonsillectomy in children. J Clin Sleep Med. 2021;17(11):2215-2223.

Introduction. Research on celiac disease is based on a descriptive and inferential variety of techniques that allow summarizing data and extrapolating the target population. The aim of this study was to identify descriptive and inferential statistical methods used in International Journal of Celiac Disease. Material and method. The sample of this study was defined based on all original articles published in the journal mentioned above in 2013- 2014 period. We evaluated the descriptive statistics, the number and type of inferential statistical methods used. Results. Of the eight articles analyzed, one study was a randomzat clinical trial, the remaining studies were cross- sectional studies. The articles have used both quantitative and qualitative data. The indicator of central tendency on data was mean (n = 5, 62.5 %) or the median with interquartile range (n = 1, 12.5 %) and the dispersion of data was estimatedonly by the standard deviation in 5 studies (62.5 %). Quantitative data were used in raw form, except for one study using Z scores. Qualitative data were summarized using absolute and relative frequencies (n = 7, 87.5 %). The statistical software was mentioned in all studies. All articles except one used the inferential statistical methods or statistical tests. Most articles (87.5 %) used common tests as Student's t- test (37.5), analysis of variance/covariance (25 %), Kruskal -Wallis test (12.5 %), χ2 test (50 %), and Fisher's exact test (12.5 %). A specified significance level was noted in 62.5 % of the articles and the significance level was estimated in 6 studies (75 %). Conclusion. Results showed that a proper understanding of standard statistical methods leads to a proper interpretation of clinical research hypothesis. If necessary, the advanced statistical analysis should be performed by a multidisciplinary collaboration with specialists in biostatistics or epidemiology.

Quantifying diagnostic and etiologic management costs of perimenopausal abnormal uterine bleeding and postmenopausal bleeding

CHAPTER 5 - Variance, Standard Deviation, Skewness, and Kurtosis. Moments

Predicting Post-Heart Transplant Composite Renal Outcome Risk in Adults: A Machine Learning Decision Tool

5 - measures of variability

d’Esterre, CD1, 3 Qazi, E1, 3 Patil, S1, 3 Almekhlafi, M3, 1 Lee, T2, 3 Demchuk, A1, 3 Goyal, M1, 3 Menon, B1, 3; 1. University of Calgary, Calgary, AB; 2. University of Western Ontario, London, ON; 3. Calgary Stroke Program, Calgary, AB Background : For ischemic stroke, CT Perfusion (CTP) may change thrombolytic/endovascular treatment decisions when compared to NCCT/CTA alone. Two distinct thresholds may be useful in this regard: separation of 1) non-salvageable tissue (infarct core) from salvageable electrically silent tissue (penumbra), and 2) penumbra from benign oligemia (hypoperfused, but will survive if clot persists). Methods : CTP (120s,8cm) was performed on 180 patients within 12hrs of ischemic stroke. Two patient cohorts were analyzed: (1) recanalization (TICI 2b,3) 6s. For group (2) CBF, CBV, and Tmax values were obtained from within the final infarct region, and total ipsilateral hemisphere, excluding infarction. CBF, CBV and Tmax were used in univariate regression models. Results : For group (1)[n=11], mean time from CTP to recanalization was 60±19min. CBF parameter (thresholds for gray and white matter 7.2 and 5.2 ml•min-1•(100g)-1) had the highest sensitivity (90.9%) and specificity (81.8%) for infarction. For group (2)[n=15], the Tmax parameter (thresholds for gray and white matter 11.3s and 11.8s) had the highest sensitivity (86.6%) and specificity (80.0%) for penumbra. Conclusion : Knowing the status of recanalization within 90mins of CTP allows for accurate delineation of infarct core, as …

The purpose of this retrospective cohort study was to describe the outcome of 107 patients with chronic kidney disease (CKD) admitted to a pre-dialysis interdisciplinary management program from 1990 to 2006. The events of interest were progression to CKD stage 5 (renal survival), patient survival, hypertension, and somatic growth. Survival was studied by the Kaplan-Meier method. Patients were classified into four groups according to their primary renal disease: congenital nephro-uropathies; glomerular diseases; cystic disease, and miscellaneous. Median follow-up time was 94 months [Interquartile (IQ) range 38-145]. The probability of reaching CKD stage 5 was estimated to be 36% by 5 years after admission. As a whole, the mean estimated glomerular filtration rate (GFR) decrease per year was 5.8 ml/min per 1.73 m(2) body surface area [standard deviation (SD) 12.4]. The glomerular diseases group showed a median rate of GFR deterioration of 10 ml/min per 1.73 m(2) per year (IQ range -24 to -5.7), whereas the median rate of GFR deterioration for the groups with cystic diseases, congenital nephro-uropathies, and miscellanea were 2.5 ml/min (IQ range -10 to +0.34), 2.2 ml/min (IQ range -5.0 to -0.52), and 0.36 ml/min (IQ range -2.5 to +2.6), respectively (P < 0.001). The results of this study support the view that children and adolescents with glomerular diseases present a faster deterioration of renal function. Therefore, patients with glomerular diseases need to be referred early to a pediatric nephrology center so that suboptimal pre-dialysis care might possibly be avoided.

Background Laparoscopic fundoplication (LF) is considered as standard surgical antireflux therapy. However, even if performed in specialized centers, the procedure can be followed by long-term side effects dysphagia, gas bloating or inability to belch. Especially patients with motility disorders (IEM) and concurrent GERD are prone to postoperative dysphagia after LF. The aim of this study is the evaluation of electrical stimulation (EST) of the lower esophageal sphincter (LES) in patients with IEM and GERD and its impact on procedure-related gastrointestinal side effects such as dysphagia. Methods This is a prospective, open-label, non-randomized single-center study. All variables are depicted as median and interquartile range (IQR) or 95% confidence intervals (CIs) or mean with standard deviation (SD). Ineffective esophageal motility (IEM) was defined as a Distal Contractile Integral (DCI) below 450 mmHg-s-cm in ≥ 5 of out 10 swallows. Differences in GERD health-related quality of life (HRQL) scores before and after treatment were compared with paired t-test due to a normal distribution. P-values &lt; 0.05 were considered significant. Results Between 05/2015 and 10/2017 twenty patients were treated with LES-stimulation for GERD. Thirteen patients (61.9%) presented with IEM in esophageal manometry before surgery and were included in this analysis. DCI was 91 (IQR 30.5–331.5) mmHg-s-cm. Median 24-hours esophageal pH at baseline was 10.2% (IQR 4.4–21.5). Fifty-seven percent of patients were treated with PPI at time of surgery. Nine patients (69.2%) presented with typical GERD symptoms whereas 6 patients (46.2%) also presented with atypical GERD symptoms. BMI was 26.1 (SD 4.9). Eight patients (61.5%) showed a hiatal hernia at the time of surgery and underwent also hiatal repair. Operating time was 59 minutes (IQR 34.5–70.25). HRQL for heartburn at baseline was 21.1 (SD 5.4) and improved to 7.3 after surgery (SD 6.7) at follow up of one month (mean difference 13.8 (CI 12.5–15.1) P &lt; 0.001). HRQL for regurgitation at baseline was 18.69 (SD 6.9) and improved to 3.84 (SD 2.4) (mean difference 14.9 (CI 13.95–15.76) P &lt; 0.001). No patients showed any clinical signs of dysphagia nor impaired findings in postoperative contrast swallow. Gastrointestinal side effects such as the inability to belch or bloating were not seen in any patients. There were no severe adverse events related to the procedure, but one patient need re-do surgery and re-implantation of the LES-stimulation due to a breaking of the lead close to the implanted pulse generator after one year. Conclusion LES-EST was introduced as a potential alternative technique to avoid side effects of LF. It was demonstrated that LES-EST significantly raises the LES pressure and improved GERD symptoms such as heartburn and regurgitation. The advantage of this procedure is that the anatomy of the esophageal-gastric junction is not altered dramatically. Disclosure All authors have declared no conflicts of interest.

Based on the available evidence from RCTs, early treatment with ACE inhibitors or ARBs may be comparably beneficial for people with a dystrophinopathy; however, the certainty of evidence is very low. Very low-certainty evidence indicates that adding eplerenone might give additional benefit when early cardiomyopathy is detected. No clinically meaningful effect was seen for growth hormone or idebenone, although the certainty of the evidence is also very low.

Routine Management, Healthcare Resource Use and Patient/Caregiver-Reported Outcomes of Patients with Transfusion-Dependent β-Thalassaemia in the United Kingdom: A Mixed Methods Observational Study