一覧 Case Studies Scale-specific correlation analysis and multivariate logistic regression in a patient-reported outcome survey

Scale-specific correlation analysis and multivariate logistic regression in a patient-reported outcome survey

* This article is based on an actual analysis project; however, in light of the confidentiality agreement (NDA) with the client, while maintaining the framework of the medical and healthcare field, specific details such as disease names and variables have been substantially altered from the actual case. We ask for your understanding in advance.

This case is an analysis of large-scale patient-reported outcome (PRO: Patient-Reported Outcome) questionnaire data conducted on a group of patients with functional gastrointestinal disorders, typified by irritable bowel syndrome (IBS). Questionnaire data asking about the subjective intensity of patients’ symptoms and their lifestyle are composed not of continuous numerical values like weight or blood pressure, but of nominal scales answered “yes/no” and ordinal scales such as “never – very often.” Handling these data the same way as continuous variables and applying simple statistical processing carries an extremely high risk of leading to medically erroneous conclusions.

Through this analysis, for questionnaire data that tends to be limited to simple tabulation, I aimed to rigorously discern the nature of each question’s data (the level of measurement) and to combine the statistical method optimal for each, thereby quantitatively evaluating how patients’ background factors influence “concrete behaviors when symptoms worsen (seeing a doctor, taking over-the-counter medicine, refraining from going out, etc.).” By meticulously building a series of analytical procedures from logical missing-value handling to advanced multivariate analysis, Dr.DataScience contributed to creating objective evidence to serve as guidance for concrete lifestyle instruction aimed at improving patients’ quality of life (QOL).

Background and objective

In this case, in a detailed lifestyle and symptom survey conducted on several thousand patients with the target disease who visit medical institutions nationwide, what was required was to clarify “what kind of lifestyle disturbances and stress are strongly linked to negative behaviors when symptoms worsen (such as restricting social activities).”

The subjective evaluation data obtained from questionnaires are an extremely important source of information for understanding patients’ distress in the medical setting. However, because the response formats vary widely by question—free-text responses, multiple-choice formats, graded ratings, etc.—integrating and analyzing them to extract consistent evidence is not easy. The main objective of this analysis was to fit the data obtained from a wide range of questions into appropriate statistical models, comprehensively grasp the correlations among the factors, and then identify the most powerful factor (odds ratio) that triggers a particular behavior such as “refraining from going out.”

Data and variables

This analysis used subjective evaluation data obtained from questionnaire responses. Prior to the analysis, I performed logical data shaping (cleaning) to maintain the consistency of responses. For example, where a respondent answered “no symptoms at all” yet left “the frequency of as-needed medication to suppress symptoms” blank, rather than excluding it as a mere missing value (no data), I logically imputed it as “the lowest value of frequency (zero).” The main variables analyzed were as follows.

    • Nominal-scale variables: sex, the presence or absence of a habit of consuming particular foods (such as high-FODMAP foods) (yes/no), etc.
    • Ordinal-scale variables: frequency of symptoms in the past month (1: never – 5: every day), quality of sleep (5-point rating), subjective stress level (10-point rating), age group (20s, 30s, etc.), etc.
    • Response variables (dummy variables): For the multiple-response question “What action do you take when your symptoms worsen?”, I converted each option (“take over-the-counter medicine,” “take time off work,” “refrain from going out,” etc.) into a binary variable (dummy variable) of “selected = 1, not selected = 0” for use.

Analytical methods

In this case, to rigorously distinguish the differences in the measurement level of the variables and to extract the information the data hold to the maximum extent and accurately, I selected and applied the following statistical methods.

  1. Correlation analysis and association evaluation according to measurement level
    • Adopted methods: Spearman’s rank correlation coefficient, Cramér’s V, the Cochran–Armitage test
      Because the variables in the questionnaire data have mixed scales, I rigorously used different methods.
      ・For correlations between variables where order has meaning, such as “quality of sleep (ordinal scale)” and “frequency of symptoms (ordinal scale),” I adopted Spearman’s rank correlation coefficient.
      ・To evaluate the strength of association between categorical variables, such as “sex (nominal scale)” and “presence or absence of consuming particular foods (nominal scale),” I adopted Cramér’s V. I extracted those with a coefficient of 0.50 or more as “correlated,” and 0.70 or more as “strongly correlated.”
      ・To evaluate how a factor that changes in stages affects a particular proportion (whether there is a trend), such as “age group (ordinal scale)” and “presence or absence of a particular behavior (nominal scale),” I adopted the Cochran–Armitage test and used its p-value to evaluate the association.
    • Method not adopted: Pearson correlation coefficient
      The Pearson correlation coefficient presupposes “equally spaced continuous numerical values” such as height and weight. There is no guarantee anywhere that the interval between a questionnaire’s “1: never” and “2: occasionally” is mathematically equal to the interval between “4: often” and “5: every day.” Forcibly applying the Pearson correlation coefficient to such ordinal scales would completely misjudge the strength of the correlation, so I did not use it at all in this analysis.
  2. Evaluation of differences among multiple groups
    • Adopted method: Kruskal–Wallis test
      I adopted it to evaluate whether there was a difference in “frequency of symptoms (ordinal scale)” among three or more groups, namely “age groups (six groups from the 20s to 70s and above).” This is a nonparametric method that does not assume a normal distribution and is optimal for group comparisons of questionnaire data.
    • Method not adopted: one-way analysis of variance (ANOVA)
      One-way analysis of variance presupposes that the data follow a normal distribution and that the variance (variability) of each group is equal. Because questionnaire response scores often skew toward particular responses and do not meet the assumption of a normal distribution, I judged it inappropriate and refrained from using it.
  3. Multivariate evaluation of behavioral factors
    • Adopted method: multivariate logistic regression analysis
      To identify the factors that trigger a particular behavior such as “refraining from going out” (a 0/1 dummy variable), I performed multivariate logistic regression analysis simultaneously entering multiple explanatory variables that were significant in the correlation analysis (quality of sleep, stress level, etc.). This calculated, as “odds ratios,” the influence each factor independently has on the behavior, after adjusting for the mutual influence (confounding) among variables.

Overview of the main results and clinical considerations

As a result of the meticulous correlation analysis and association evaluation, it became clear that there are complex links between individual lifestyle habits and symptoms. For example, Spearman’s rank correlation coefficient confirmed a significant moderate or stronger positive correlation between “subjective stress level (ordinal)” and “frequency of symptoms (ordinal).” Also, the Cochran–Armitage test found a significant trend (p = 0.004) whereby, as “age group (ordinal)” rises, the proportion of “consuming foods high in particular fats (nominal)” significantly decreases.

In the group comparison using the Kruskal–Wallis test, a clear statistically significant difference in symptom frequency was found by age group (p = 0.021), suggesting that younger groups have a higher frequency of symptoms.

Furthermore, as a result of the multivariate logistic regression analysis, it was found that, for the response variable “refraining from going out (restriction of social activity),” not only “frequency of symptoms” but also “subjective stress level” independently exerted an extremely strong influence. Specifically, it was quantitatively shown that for each one-step worsening of the subjective stress level, the odds ratio of taking the action of refraining from going out rose to 1.85 (p = 0.012).

From these results, solid evidence was obtained toward formulating a comprehensive treatment policy: to prevent adverse effects on patients’ social lives (such as refraining from going out), not only drug therapy that suppresses the gastrointestinal symptoms themselves, but also psychosocial approaches such as stress control of the underlying causes, and lifestyle instruction specialized for younger groups, are extremely important.

Dr.DataScience’s contribution

In this case, Dr.DataScience thoroughly applied appropriate statistical approaches to subjective, difficult-to-handle questionnaire data, elevating vague tendencies into robust clinical evidence.

  1. Rigorous method selection matched to the nature of the data
    • I accurately identified the scale of the data (nominal/ordinal) and completely excluded parametric methods whose assumptions do not match, such as the Pearson correlation coefficient and analysis of variance. By appropriately using nonparametric methods such as Spearman, Cramér’s V, the Cochran–Armitage test, and the Kruskal–Wallis test, I prevented statistical fallacies and ensured the reliability of the analysis results.
  2. Preventing information loss through logical data imputation
    • Rather than discarding “no response” as a mere missing value, where it could be logically inferred from the response status of other questions, I imputed an appropriate value (such as the minimum value). This made it possible to achieve a high-precision analysis while maintaining a sufficient sample size, without wasting precious patient data.
  3. Extracting the true factors with a multivariate model and contributing to decision-making
    • Going beyond simple tabulation and two-variable correlations, by using multivariate logistic regression analysis to adjust for confounders, I showed “the most powerful factor that restricts social activity” as a clear numerical value—the odds ratio. This provided extremely practical insights for field physicians to formulate concrete intervention plans regarding “which patients should be prioritized for what kind of guidance.”

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