|Year : 2022 | Volume
| Issue : 1 | Page : 63-69
How to conduct inferential statistics online (Part 2): A brief hands-on guide for biomedical researchers
Shaikat Mondal1, Himel Mondal2, Roopam Panda3
1 Department of Physiology, Raiganj Government Medical College and Hospital, Raiganj, India
2 Department of Physiology, Fakir Mohan Medical College and Hospital, Balasore, Odisha, India
3 Department of Physiology, MKCG Medical College, Berhampur, Odisha, India
|Date of Submission||10-Dec-2021|
|Date of Acceptance||17-Dec-2021|
|Date of Web Publication||23-Mar-2022|
Department of Physiology, Fakir Mohan Medical College and Hospital, Balasore, Odisha
Source of Support: None, Conflict of Interest: None
Introduction: Researchers from developing countries may not have access to statistical software packages. However, descriptive and inferential statistical tests are to conduct to conclude the study. In a previous article (DOI: 10.4103/ijves.ijves_116_21), we described how to conduct some of the common inferential statistical tests online. This article is the second part of the series. Aim: We aimed to provide the examples of some inferential statistical tests used in clinical studies and provide step-by-step guidelines to conduct those tests online. Methods: We prepared a set of data for each statistical test. These data were used to carry out the test online and the steps are briefly described. The result of the test is presented with screenshots and text to get an idea of how to report the result in a manuscript. Results: We described the process of conduct of the following tests online – Receiver operating characteristics curve analysis, Kaplan − Meier estimate, dose-response, logistic regression, multiple linear regression, residual analysis, odd ratio, Bland − Altman plot, Cronbach's alpha, Cohen's kappa, and intraclass correlation coefficient. In addition, a method for random allocation of subjects in groups was also described. All the tests were described with example data available in a supplementary file. Conclusion: In this article, some of the inferential statistics used for clinical studies are described with example data and a step-by-step guide. Any clinician from resource-limited settings may use this guide as a reference for statistical tests. However, the tests described in this article are not a comprehensive list.
Keywords: Bland-Altman, Cronbach's alpha, Kaplan − Meier, logistic regression, Odd ratio, relative risk, receiver operating characteristic curve
|How to cite this article:|
Mondal S, Mondal H, Panda R. How to conduct inferential statistics online (Part 2): A brief hands-on guide for biomedical researchers. Indian J Vasc Endovasc Surg 2022;9:63-9
|How to cite this URL:|
Mondal S, Mondal H, Panda R. How to conduct inferential statistics online (Part 2): A brief hands-on guide for biomedical researchers. Indian J Vasc Endovasc Surg [serial online] 2022 [cited 2022 May 28];9:63-9. Available from: https://www.indjvascsurg.org/text.asp?2022/9/1/63/340501
| Introduction|| |
In a previous article titled “How to conduct descriptive statistics online: A brief hands-on guide for biomedical researchers,” we provided a brief guide on the conduct of some common descriptive statistical tests online. Furthermore, in another article titled “How to conduct inferential statistics online: A brief hands-on guide for biomedical researchers,” we described some of the common inferential statistical tests. In this final article in the series, we aimed to provide a brief guide on the conduct of some inferential statistics that we did not include in the previous article. These tests are commonly used for clinical studies.
| Methods|| |
In this study, we fabricated the data for instructional purposes only. There were no data collected from human subjects. The example study was also created for training purposes. Hence, this study does not require any clearance from the Institutional Ethics Committee.
According to the nature of the data, a variable is divided into categorical/qualitative and numerical/quantitative. In addition, according to manipulation, a variable can be divided into dependent and independent variables. A variable that a researcher can manipulate is called the independent variable. It is also called predictor variable or experimental variable. A variable that is observed in an experiment with manipulating another variable (independent variable) is called a dependent variable. It is also called an outcome variable. An example of independent, dependent, and control variables is shown in [Figure 1].
We listed the websites in [Table 1]. There are some websites that provide multiple tests. However, we tried to include a maximum number of websites.
|Table 1: Websites offering free conduct of some inferential statistical tests|
Click here to view
Receiver operating characteristic curve analysis
There were data of atherogenic index of plasma (AIP) and left ventricular ejection fraction (LVEF) of type 2 diabetic patients. The LVEF of each participant was categorized as “within normal limit” and “lower than lower limit.” A statistical test was to conduct to find the AIP as a tool to diagnose subject with low LVEF. Hence, a receiver operating characteristic (ROC) curve analysis was decided that plots the sensitivity (true positive rate) and 1- specificity (false positive rate).
- Go to https://epitools.ausvet.com.au/roccurves
- You may name the test in “Test name” box; keep the “Data format” as “Stacked” (check the data from supplementary file or example from “Download example data” from website); keep “Confidence interval (CI)” as “0.95;” copy both the columns of data without column headings and paste it in data box (remember to clear the excess row at the end with backspace). Click on the “Submit” button
- You would get the ROC curve with area under the curve along with density curve, frequency distribution, box plot, and other statistical details.
The ROC curve is shown in [Figure 2]a. A carve toward left upper side indicates higher diagnostic capability. The area under the curve was 0.99 which indicates an outstanding diagnostic capability of AIP to detect low LVEF (0 = perfectly inaccurate test, 0.5 = no ability to diagnose patient with or without disease, 0.7 – 0.8 = acceptable, 0.8 – 0.9 = excellent, >0.9 = outstanding, and 1 = perfectly accurate test).
|Figure 2: Statistical test result screenshot – (a) Receiver operating characteristic curve analysis, (b) Kaplan–Meier estimate, (c) Dose response and EC50, (d) Logistic regression, (e) Multiple liner regression, (f) Regression residuals analysis, (g) Odds ratio and relative risk, (h) Bland-Altman plot, (i) Cronbach's alpha, (j) Cohen's Kappa, (k) Intraclass correlation coefficient, (l) Randomization of subjects. High-resolution figures are available in supplementary file (https://doi.org/10.6084/m9.figshare.17036783)|
Click here to view
Kaplan Meier survival analysis
A new drug was administered to reduce lung fibrosis after suffering from COVID-19 in two groups of patients – 16 obese and 16 nonobese (group). They were followed up for months (time) till they were recovered from the fibrosis (event). However, during the course, one person from obese group died due to cardiovascular disease at 9 months and one person did not come for follow-up after 4 months. One person in non-obese group did not come for follow-up after 1 month (censored). For Kaplan − Meier Survival Analysis, group, time, event, and censored data are required. According to the nature of the study, the groups may be different. The time may be in days, fortnight, months, or years. The event may be recovery, achievement of certain level of recovery, or death. The censored are the data not available due to any reason.
- Go to https://www.statskingdom.com/kaplan-meier.html
- Keep chart type as “Confidence interval;” you may name the test; keep “Significance level” as 0.05; keep the data entry option as “Enter raw data directly;” copy the data and paste in the boxes of Time, Event/Censored, and Group column. Click on calculate
- The comparative curve with P value would be shown along with individual curve for obese and nonobese group. Scroll down to get the result of log-rank test. Hover, the mouse over the right upper corner of the graph to get a camera icon and click on that to “Download plot as a png”
The Kaplan − Meier curve is shown in [Figure 2]b. The P value was 0.003 that indicates unequal recovery (survival distribution) among obese and nonobese with quick recovery in non-obese group. In the curve, the plus sign indicates censored data and the shade around the line indicates 95% CI.
Dose response and EC50
A new drug was administered in female patients suffering from certain allergic skin disease. The dose of the drug gradually increased to observe the reduction of percentage of eosinophil count from the initial level. A dose response curve was needed to find the half-maximum effective concentration (EC50) of the drug.
- Go to https://www.aatbio.com/tools/ec50-calculator
- Copy both the column of data including the headings of the column and paste it in “Data Entry” box; click on “Process data”; you may name the axis as “dose” and “response” and set the minimum response to zero and maximum as one with background correction and normalization option ticked. Click on “Calculate EC50”
- The dose-response curve would be shown with the EC50 value. You can right click on the graph to get option to set the minimum and maximum of X- and Y-axis. Take a screenshot if the “Download Graph” does not work.
The dose-response curve is shown in [Figure 2]c. The EC50 of the fictitious drug in reduction of eosinophil count was 45.91. There is an option to calculate the X value from Y value or vice versa from the regression equation of the calculation.
Binary logistic regression
According to different level of body fat percentage and age (independent variables), the depression (dependent variable) was tabulated with “presence of depression” and “absence of depression” (dichotomous). As the dependent variable was categorical with dichotomous distribution, a binomial logistic regression was conducted to ascertain the effects of age and body fat on the likelihood that research participants have depression.
- Go to https://www.statskingdom.com/420logistic_regression.html
- Copy the age column data without heading and paste it in X1, body fat in X2, and Depression in Y (0). Click on the “Calculate” button
- The result will be shown as per newton's method with goodness of fit, Nagelkerke R2 and coefficient table containing significance for each of the independent variables.
The result is shown in [Figure 2]d. The logistic regression model was statistically significant, χ2 (2) = 36.5, P < 0.0001. The regression model explained 73% (Nagelkerke R2) of the variance in depression. However, age (P = 0.86) and body fat (P = 0.86) as independent variable were not significant predictor of depression.
Multiple linear regressions
There were age, height, weight, and body fat (independent variables) and resting respiratory exchange ratio (RER) (dependent variable) data of 20 research participants. Multiple linear regressing was selected to check if these independent variables are significant predictor of the resting RER.
- Go to https://www.statskingdom.com/410multi_linear_regression.html
- Insert one more column as we had four columns. Name the column heading as “age,” “height,” “weight” and “body fat” in X variables and “resting RER” as Y variable. Copy the respective column of data and paste it without column heading. Click on “Calculate” button
- Result would be shown with overall regression and individual variables along with correlation and ANOVA details. You can take screenshots of the result page for further use.
The result is shown in [Figure 2]e. The multiple linear regression model was statistically significant, F (1, 18) = 27.13, P < 0.0001. However, individually only the body fat significantly predicted (P < 0.001) the resting RER. The age (P = 0.97), height (P = 0.73), and weight (P = 0.77) were not significant predictor of resting RER.
Regression residuals analysis
A study was conducted to find a way to calculate arm span of persons from the height. This would help to get arm span of person with amputated upper limbs. The height was taken as an independent variable and arm span was taken as a dependent variable. Suppose, calculated regression equation was: Arm span = 28.691 + 0.8092 × Height. With this equation, from each height, we can calculate the predicted arm span. Then each residual (i.e., observed arm span – predicted arm span) is calculated and plotted against predicted value. The regression residuals plot would give us an idea about the goodness of fit of a regression model visually.
- Go to https://mathcracker.com/regression-residuals-calculator
- Copy height data without column heading and paste it in “Independent variable X sample data;” copy arm span data without column heading and paste it in “Dependent variable Y sample data;” name the variables. Click on “CALCULATE”
- Scroll down to get the regression equation and plot. Take a screenshot of the plot.
The plot is shown in [Figure 2]f. The residuals indicate how far the prediction differs from the observed value. Hence, researchers would like to get residuals as low as possible where the points stay near the 0 line.
Relative risk and odds ratio
An effect of a new drug on coronary artery disease (CAD) was to assess. A group of patients having risk of CAD were assigned in either in placebo group or drug group. At the end of two years, patients suffered from CAD were tabulated in 2 × 2 contingency table to calculate the relative risk and odds ratio (OR).
- Go to https://www.socscistatistics.com/biostatistics/default2.aspx
- Input the data in the groups where “Group 1” is placebo group (or exposed to risk) and “Group 2” is drug group (or unexposed to risk). Fill the “Bad outcome” (Presence of CAD) and “Good outcome” (Absence of CAD). Click on the “calculate” button
- The result would be shown both for relative risk and OR with details of the calculation. The result is also shown if group is interchanged.
The result is shown in [Figure 2]g. Patients receiving placebo has (RR = 1.65; 95% CI: 0.9187 to 2.9547) 1.65 times higher risk of developing CAD in comparison to patients treated with the drug. For every 1.85 (OR = 1.85; 95% CI: 0.9060 to 3.7751) persons suffered from CAD in placebo group, 1 person would suffer from CAD in drug group.
As the primary website from where we calculated RR and OD, does not provide 95% CI, alternative websites were used - https://www.medcalc.org/calc/relative_risk.php and https://www.scistat.com/statisticaltests/odds_ratio.php for 95% CI of RR and OR, respectively.
A sample of diabetic people was taken to compare the blood sugar level measured by laboratory method and a new glucose monitor (i.e., glucometer). The agreement between the two methods may be tested by correlation coefficient. However, correlation does not study the difference between the two variables. For clinical applicability of the glucometer, the difference between the blood glucose reading from a glucometer and that acquired from a laboratory should not differ substantially. Hence, in this case, Bland − Altman plot is one of the important analysis.
- Go to https://huygens.science.uva.nl/BA-plotteR
- Click on the bullet of “Paste data” and paste the copied two columns of data with column heading in the box; click on the “Submit data” and keep “Delimeter” as “Tab (from Excel)”; Select the “Measurement 1” as “Laboratory” and “Measurement 2” as “Glucometer” and optionally, units as “mg/dl”; Click on the “Plot” tab
- The plot would be shown. Click on the “Download png-file” to save the image. Click on the “Data Summary” tab to get the analysis details (difference, upper limit and lower limit of agreement, intercept and slope) with a Q-Q plot.
The plot is shown in [Figure 2]h. It is a plot of differences between laboratory glucose and glucometer glucose versus the mean of the two measurements. The middle dotted line is the mean and upper and lower dotted line is + 1.96 and − 1.96 standard deviation, respectively. The result showed that the difference was 9.07, upper limit of agreement was 35.43, lower limit of agreement was − 17.30, and intercept at 14.06. Majority of the differences were within the upper and lower limits.
A new questionnaire was developed for the assessment of preoperative stress before exploratory laparotomy. The questionnaire was composed of six items (questions) with 5-point Likert type response options. The questionnaire was distributed among 31 patients and their responses were used to find the internal consistency of the questionnaire (how well the questionnaire measure what it supposed to measure by finding correlations between different items).
- Go to http://www.wessa.net/rwasp_cronbach.wasp
- Copy all columns of data and paste it in the box below “Data X”; name the columns as Q1 to Q6. Click on the “Compute” button
- The overall Cronbach's alpha with alpha if any item deleted is shown. This is important to decide which question to exclude to increase the internal consistency of the scale (questionnaire). A screenshot may be captured for keeping record of the result.
The Cronbach's alpha was 0.8972 [Figure 2]i. It indicates a good level of internal consistency (<0.5 = unacceptable, 5 to < 0.6 = poor, 6 to < 0.7 = questionable, 7 to < 0.8 = acceptable, 0.8 to < 0.9 = Good, and > 0.9 = excellent).
A low-cost smartphone adapter was developed to capture the photomicrographs. Histopathological slides of 20 patients were captured with the help of the adapter and sent to two pathologists to diagnose the case from the photomicrograph. The degree of agreement between the observers was to test by Cohen's Kappa. A table was prepared with the following categories – both observer diagnosed, first observer diagnosed and second observer did not diagnose, first observer did not diagnose and second observer diagnosed, and both observer did not diagnose.
- Go to https://www.graphpad.com/quickcalcs/kappa1.cfm
- Keep the categories as “2 categories”; fill the table with the following data AA = 13, AB = 1, BA = 0, BB = 6. Click on the “Calculate now”
- The Kappa would be shown with 95% CI. A list containing interpretation would also be shown. A screenshot of the result may be captured for further use.
Calculated Cohen's Kappa was 0.886 (95% CI: 0.671 to 1) [Figure 2]j. This indicates almost a perfect agreement between two observers (≤0 = no agreement, 0.01–0.20 = none to slight, 0.21–0.40 = fair, 0.41–0.60 = moderate, 0.61–0.80 = substantial, ≥0.81 = almost perfect agreement). Hence, photomicrograph captured with the help of the new adapter may be used for the remote diagnosis with nearly perfect interrater agreement.
Intraclass correlation coefficient
Systolic blood pressure of 22 research participants where measured by two observers with a new aneroid sphygmomanometer with both odd and even marking on the gauge. The consistency of measurements was to check by intraclass correlation coefficient (ICC).
- Go to http://vassarstats.net/icc.html
- Copy both column of the data without the column headings and paste it in the box designated as “Data Entry:” Click on the “Calculate” button
- The result would be shown with ANOVA summary. The result page screenshot may be taken for further use.
The result screenshot is shown in [Figure 2]k. The ICC was 0.97 and it indicates an excellent inter-rater agreement in the measurement of systolic blood pressure by two raters (i.e., measurers or observers or operators) (<0.5 = poor, 0.5 – 0.75 = moderate, 0.76 – 0.9 = good, and >0.90 = excellent reliability). There are several models of ICC as described by Koo et al. The website we used to calculate ICC allows a measurement by two raters or two measurements by a single rater. We could not find online calculator for other models.
Random assignment of subjects
A sample of 60 subjects needs a simple random allocation of 20 subjects in placebo group, treatment Group 1, and treatment Group 2.
- Go to https://www.graphpad.com/quickcalcs/randomize1.cfm
- Assign “20”; subject to each of “3” groups; repeat “1” times. Click on “Do it!”
- The result would be shown. This can be copied and pasted in any spreadsheet. A screenshot may also be taken.
Truncated list of allocation is shown in [Figure 2]l. The groups are indicated as A, B, and C.
| Results|| |
A total of 11 statistical tests - receiver operating characteristics curve analysis, Kaplan − Meier estimate, dose response, logistic regression, multiple liner regression, residual analysis, OR and Relative risk, Bland − Altman plot, Cronbach's alpha, Cohen's Kappa, ICC were described with successful conduct in the public domain websites. In addition, a method of random allocation of subjects was also described as it is important for clinical studies. The websites are listed in [Table 1] for quick access.
The screenshots of the result page are presented in [Figure 2]. High-resolution images along with example can be downloaded from Figshare (https://doi.org/10.6084/m9.figshare. 17036783).
| Discussion|| |
This was the second article of a series that discussed inferential statistics that can be conducted online. Another article was about the conduct of descriptive statistics including visualization of data. Among the inferential tests, some tests and graphing method were missed in the previous article. Hence, this article was prepared. We successfully conducted the tests online without registering for any account in the websites. This gives freedom to users to conduct test without hassle of opening and confirming account.
Although we included many of the tests, we do not claim it to be comprehensive. Many of the tests are also not available online. In addition, some have limitations. For example, there are several models of ICC. However, online conduct allows only two of the models. Hence, this guide should be considered as an introductory basic guide for researchers from the settings where access to statistical software package is limited.,
| Conclusion|| |
We discussed with example data how to run some of the inferential statistical tests that were not available in the previous article in this series. All the tests described in this article can be conducted online without installing any software in computers. The steps were explained briefly for each website. Researchers from resource-limited settings can conduct the tests without buying costly statistical software package.
Supplementary file with the data, web links, and result is found from the following link: https://doi.org/10.6084/m9.figshare. 17036783.
We would like to thank Sarika Mondal and Ahana Aarshi for allowing their precious time during preparation of this article.
Financial support and sponsorship
Conflicts of interest
There are no conflicts of interest.
| References|| |
Mondal H, Swain SM, Mondal S. How to conduct descriptive statistics online: A brief hands-on guide for biomedical researchers. Indian J Vasc Endovasc Surg 2022; In Press. [doi: 10.4103/ijves.ijves_103_21].
Mondal S, Saha S, Mondal H, De R, Majumder R, Saha K. How to conduct inferential statistics online: A brief hands-on guide for biomedical researchers. Indian J Vasc Endovasc Surg 2022; In Press. [doi: 10.4103/ijves.ijves_116_21].
Flannelly LT, Flannelly KJ, Jankowski KR. Independent, dependent, and other variables in healthcare and chaplaincy research. J Health Care Chaplain 2014;20:161-70.
Hajian-Tilaki K. Receiver Operating Characteristic (ROC) curve analysis for medical diagnostic test evaluation. Caspian J Intern Med 2013;4:627-35.
Mandrekar JN. Receiver operating characteristic curve in diagnostic test assessment. J Thorac Oncol 2010;5:1315-6.
Rich JT, Neely JG, Paniello RC, Voelker CC, Nussenbaum B, Wang EW. A practical guide to understanding Kaplan-Meier curves. Otolaryngol Head Neck Surg 2010;143:331-6.
Jiang X, Kopp-Schneider A. Summarizing EC50 estimates from multiple dose-response experiments: A comparison of a meta-analysis strategy to a mixed-effects model approach. Biom J 2014;56:493-512.
Bewick V, Cheek L, Ball J. Statistics review 14: Logistic regression. Crit Care 2005;9:112-8.
Eberly LE. Multiple linear regression. Methods Mol Biol 2007;404:165-87.
Topp R, Gómez G. Residual analysis in linear regression models with an interval-censored covariate. Stat Med 2004;23:3377-91.
Andrade C. Understanding relative risk, odds ratio, and related terms: As simple as it can get. J Clin Psychiatry 2015;76:e857-61.
Giavarina D. Understanding bland Altman analysis. Biochem Med (Zagreb) 2015;25:141-51.
Taber KS. The use of Cronbach's alpha when developing and reporting research instruments in science education. Res Sci Educ 2018;48:1273-96.
Polata G, Damci A, Turkoglu H, Gurgun AP. Identification of root causes of construction and demolition (C&D) waste: The case of turkey. Procedia Eng 2017;196:948-55.
McHugh ML. Interrater reliability: The kappa statistic. Biochem Med (Zagreb) 2012;22:276-82.
Hazra A, Gogtay N. Biostatistics series module 6: Correlation and linear regression. Indian J Dermatol 2016;61:593-601.
] [Full text]
Koo TK, Li MY. A guideline of selecting and reporting intraclass correlation coefficients for reliability research. J Chiropr Med 2016;15:155-63.
Lim CY, In J. Randomization in clinical studies. Korean J Anesthesiol 2019;72:221-32.
Mondal H, Mondal S, Majumder R, De R. Conduct common statistical tests online. Indian Dermatol Online J 2022; In Press. [doi: 10.4103/idoj.IDOJ_605_21].
[Figure 1], [Figure 2]