2. Types of data and data collation for efficient processing

Authors: A Indrayan

Abstract

Data are the soul of most empirical research. Adequate data collection and their proper collation are essential to arrive at right conclusions. These conclusions are mostly drawn from the statistical analysis of properly collated data. Since the methods of statistical analysis are different for different types of data, a clear understanding of various types of data is necessary for their efficient processing. Whereas broad types of data—quantitative and qualitative—are well known, some researchers struggle with the proper collation of ordinal data and quantitative categories. Additionally, some young researchers need guidance on preparing tables to communicate their results effectively. Graphics add muscles to the skeleton of data and need to be judiciously chosen. This article provides details of various types of data, their adequacy, and their proper collation, including a brief on tables and graphics. Almost all medical researchers carry out these activities – thus, this may have wide ramifications. Although this article primarily targets postgraduate students and young researchers, our interaction with a diverse group of researchers suggests that many experienced researchers may also find this article useful in the management of their data for reaching the right conclusions.

Introduction

Most modern-day medical research relies on empirical data collected from a group of healthy or sick subjects. These data are searched for hidden messages regarding the type and extent of the health problems, their etiology, and the effect of ameliorating steps. Data take us away from beliefs and opinions and tend to objectivise the evidence. An essential feature of a successful research is that the data are correctly collected through valid and reliable tools which are tested and found adequate. Wrong data cannot lead to right conclusion, no matter how meticulously analyzed.

The search for the hidden messages in the mass of data is done through the rigors of statistical analysis which are tailored for the types of data in hand. Therefore, a clear understanding of various types of data is crucial for their proper collation and efficient processing. This article presents a statistical classification of various types of data and provides guidance on how different types are collated before they are subjected to the analysis. Our review of published papers and extensive interaction with researchers of all hues suggest that this is an ambivalent zone. Some researchers are not fully conversant with various types of data and the methods for their proper collation – thus falter in the analysis and interpretation. This article focuses on aspects, which in our opinion, not commonly known or are generally inadequately understood. Postgraduate students and new researchers may particularly benefit by this exposition but may be refreshing for all the medical researchers.

Types of Data

It is well known that basically two types of data are collected for any medical research – (i) qualitative and (ii) quantitative. These are statistically called variables as they vary from person to person and time to time. However, for establishing foundation for future articles in this series, a subclassification in brief is as follows. A summary is in Figure 1. Some of these nuances are not fully described in the literature.

Qualitative data are characteristics such as site of cancer, severity of disease, gender, and blood group. Some characteristics, such as severity, could be perceptional. These are said to be on nominal scale when these are simply names without any order. Blood groups O, A, B, and AB are nominal as they have no order – none is higher or more than any other. But qualitative data can also be ordinal, such as disease severity categorized into mild, moderate, serious, and critical. When using such categories, it is necessary to provide unambiguous and replicable definitions of each category to minimize subjectivity and to ensure uniform interpretation. Some papers, such as by Tsai et al.,[1] do not provide clear definitions of mild, moderate, and severe varicose veins, and this can hinder replicability. Qualitative data can be dichotomous such as gender (male or female) and outcome such as hospital survival (discharged or died). The type of cancer is polytomous, where the possibilities are sites such as mouth, lung, and esophagus or types such as sarcoma, leukemia, and lymphoma. Statistically, all qualitative data have a limited number of possible categories and therefore considered discrete. This term is shortly explained for those who want to know.

Quantitative data are measurements recorded in numerical form and said to be on metric scale. These are the highest idealization of data when correctly measured. Blood glucose level, duration of hospitalization, hemoglobin level, and family size are popular examples. The metric scale is subdivided into a ratio scale where there is an absolute zero enabling to say that a particular value is twice or k-times of the other (such as 4 kg loss of weight after a diet regimen is 4 times of the loss of 1 kg), and interval scales where there is no absolute zero such as birth weight. For example, body temperature 103°F may look just 5% higher than normal but has severe implications. Quantitative data can be discrete with a limited set of possible values such as number of diarrhoeal episodes during the past 1 year and parity of women. These occurrences can be easily counted, generally, by a single digit (0–9). Continuous data are the ones with theoretically infinite possibilities within a range. The systolic blood pressure can be 137.52 mmHg if we have an instrument to measure it to that accuracy. Such accuracy is not needed, and its measurement in integers does not make it discrete.

Continuous data are sometimes categorized for easy understanding. For example, BMI can be categorized as thin (<18.5), normal (18.5–23.0), overweight (23.0–28.0), and obese (≥28.0). Thus, a quantitative measurement is converted to ordinal – in this case, polytomous because of multiple categories. Many medical professionals are comfortable with such ordinal categories in place of exact measurements. The categories can also be dichotomous such as Hb < 11.0 g/dL as anemia and Hb ≥ 11.0 g/dL as nonanemia. Quantitative categories remain ordinal despite being dichotomous, whereas qualitative M/F categories for gender are not ordinal. But succumbing to dichotomous categories of quantitative data for ease of analysis and interpretation can backfire because the gradient is lost that can be important in some situations, particularly in research where exactitude is of paramount importance. When needed, all such categorizations should be done at the time of collation, but the collection and recording should be exact values. In case needed, the exact values then can be used to locate the point of inflexion with significant medical implications. This cannot be done with quantitative categories.

Some researchers[2] score ordinal categories (e.g., none = 0, mild = 1, moderate = 2, serious = 3, and critical = 4) to enable quantitative analysis (some may even call them codes ignoring that the codes cannot be added). However, this approach is valid only if the differences in categories are proportional. For instance, this implies a moderate case is twice as much as a mild case, and two mild cases equal one moderate case. This is a severe limitation that some ignore, and report mean and SD of these scores as done by Dubé et al.[3] for the severity of otitis media. Such scores should reflect the relative importance of the categories for the relevant outcome, such as mortality in critical cases versus mortality in mild cases that could be 10 times and not 4 times.

Statisticians generally discourage categorizing continuous data for two reasons. First, the subtle differences in the values are lost, such as BMI 18.0 is considered the same as 22.9 in the 18.0–22.9 category. Second, most of such categorizations are arbitrary, and different cutoffs can provide different results.[4] Some researchers may manipulate categories to give results to their liking. The cutoffs can also vary from population to population, such as BMI 18.5–22.9 for India and 20.0–24.9 for Europe.[5] Also, the ROC curve-based cutoffs (Youden index) for best discrimination of the known outcomes can be very different from the cutoff (P-index) for best prediction of the anticipated unknown outcomes.[6] This error is very common. Thus, all cutoffs must be judiciously devised, preferably with medical implications.

The number of patients admitted to a large hospital in a day is theoretically discrete but is treated as continuous for the purpose of analysis because it has a large number of possible values from, say, 0 to 500. A thumb rule is to treat discrete ordinal data with 8 or more observed values as continuous for analysis. Similarly, continuous data such as age in completed years when categorized into 8 or more categories such as 0–1, 1–4, 5–14, 15–24, 25–34,…, 85–94, and 95+ can be treated as continuous at the midvalue of the class intervals, although this amounts to approximation. As mentioned earlier, all calculations should preferably be on the exact values and not categories.

All ordinal data have underlying continuum but are expressed ordinally for convenience of understanding or because no exact measurement is available. In place of subjective mild/moderate/serious/critical categories, scoring systems are now increasingly used to quantitatively measure the ordinal characteristics such as for severity of disease. For example, Massuda et al.[7] used such scores for Cochlear bleeding. The researchers should use valid scores in place of ordinal categories whenever available, and many are already available. If not available for the problem in hand, the relevant scores can be easily devised by using odds ratios in the logistic regression. Details about development and validation of scoring systems will be provided in a future article of this series.

Data collation

Collation is the process of arranging the data for its meaningful interpretation so that complete and truthful story contained in the data is easily revealed. The first step is to examine the data for missing values and outliers. While there is no universally accepted rule, our experience suggests that less than 5% missing values can be ignored, particularly if they occur randomly. However, caution is necessary since missing values are rarely random. Multiple imputation is a useful method for estimating the missing values when the covariates used for imputation are not missing.[8] However, imputing a substantial number of missing values (say, more than 10%) can introduce bias.[8] It is advisable to make extra efforts to fill in the missing values as much as possible by revisiting the patient or reviewing the records.

Use laboratory investigation and other directly measured values as much as possible as they are often much more reliable than the data obtained by interview or examination. Check the data for consistency; for example, a female is not wrongly entered male and shown pregnant, and the age is not entered as 27 instead of 72. Such errors are common and have been frequently encountered in the datasets submitted to us during our statistical consultations. Calculate indexes (such as BMI) and scores (such as APACHE-II) before collation if required for the study. Examine the outliers to determine whether they are mistyped values (such as Hb level 11.9 mistyped as 119) that can be corrected, or genuine. Genuine outliers must be thoroughly investigated as they may contain important new findings. Most researchers ignore them. However, for the purpose of statistical analysis, excluding clear outliers is a better strategy because they can distort all the results. Any exclusions should be noted with an explanation.

We all know that qualitative data are collated in terms of counts and percentages. For counts, care is needed when the same person can have multiple episodes, such as asthma and angina attacks, or when organs (eyes, knees) are counted. These organs may be strongly correlated, and their results need to be adjusted at the time of analysis though mostly ignored as done by Amaral et al.[9] in their study on eyes. The percentages can be used to explore the trend in the case of ordinal categories. An error sometimes made in qualitative data is that the categories are assigned codes and their mean and SD are reported. Ganzael and Pazy[10] reported the mean and SD of sex 0.53 and 0.50, respectively, for their subjects! Codes are not scores, and they are not amenable to mathematical operations.

Quantitative data are typically collated in terms of mean and standard deviation (SD), or median and interquartile range (IQR) when the distribution is highly skewed. A distribution becomes highly skewed when some extreme values or outliers are present which are valid and cannot be excluded. Generally, the mean (SD) and median (IQR) should have one decimal more than actual measurements. When preparing tables for publishing a paper, quantitative data such as age and fasting glucose level have to be divided into categories, with counts and percentages presented. But do not forget to give mean and SD also based on exact values. Age can be categorized as 0–5, 5–15, and so on, with an explicit understanding that the endpoint of one interval is included in the next. To avoid ambiguity and ensure uniformity, age is categorized as 0–4, 5–14, and so forth, using age in completed years. This is considered the standard format. In this categorization, a child of age 4 years and 11 months goes into 1–4 years group since the age is in completed years. Such categories are preferable over 0–9, 10–19, 20–29, and so on because the digit preference for zero introduces bias.[11] Categories such as 0–10, 11–20, 21–30, and so forth, as used by Gao et al.[12] and several others, do not follow the standard format and hinder comparability across studies besides introducing digit preference bias.

Medical researchers across the world generally make tables for communicating their results effectively in a summarized manner. For guidance on making tables, see Divecha et al.[13] It would be helpful to reiterate that the groups under comparison such as males and females should be in adjacent columns, showing the total and counts with percentages out of total cases in that group [see illustration in Table 1], and give exact P values where needed. P < 0.05 or asterisks (*) for significance are now not considered adequate. Percentages should be uniformly to one decimal place, and P values to 3 decimals with small P values reported as P < 0.001. Percentages should add up to 100 for mutually exclusive categories. Multiple responses, where the same persons can be in two or more categories simultaneously (such as diabetes and hypertension to the same person), should be clearly stated. Using standard error (SE) of mean in place of SD in the results is not appropriate as it conveys a misleading message about the variability of individual measurements. This misuse is quite common as done by several authors including Chen at al.,[14] who reported mean age, years of marriage, and years of education with SEs in place of SDs. SE measures sampling variability for an estimate such as mean, and not for individual values, and drastically reduces for large n.

The second aspect of collation is visualization such as graphics. They add muscles to the skeleton. Scatter plots and regressions are good for exploring the relationship between two quantitative measurements such as Hb and AST levels. Pie (or donut) charts are effective to show the size of segments of categories when the total is 100%. An important feature of pie chart is that they can be proportionately scaled to represent groups of different sizes (e.g. group I with n = 400 with twice the diameter (4 times area) compared to group II with n = 100). Some researchers, such as Taheri et al.,[15] do not exploit this feature for unequal n and end up with inadequate representation. Pie chart has features such as wedging and exploding to make an impact on the reader.

Box (and whiskers) plots are often used to depict the median, IQR, and the minimum and the maximum values (or the outliers) as they can be effectively used for comparison of scatter and shift in the median values in two or more groups. If the measurements have different units such as skeletal mass and handgrip strength, use standardized values for comparison. These are calculated as , where is the sample mean and s is the sample SD. Newspapers during and after CoViD extensively used innovative diagrams from which lessons can be drawn regarding their structure, legends, and use of color, although some are inadequately drawn. There are several other types of graphs such as forest plot, radar, waterfall, and funnel charts for special purposes, besides bar chart (simple, multiple, divided) for routine purposes. Guidelines for some graphs are presented by Divecha et al.[13] For other technicalities, such as scaling of the axes, spacing, sizing, and legends, see Indrayan and Malhotra.[16]

Next: P values, Power, and Medical Significance

Conflicts of interest

There are no conflicts of interest.