* 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 evaluated in detail how, in patients with dysphagia after stroke, the “timing of transition from tube feeding to full oral intake” affects the subsequent risk of complications (aspiration pneumonia, malnutrition, pressure ulcers, etc.). In real clinical data obtained from multi-facility collaborative observational studies and the like, facility-level tendencies—such as each medical facility’s “unique treatment policy” and “aggressiveness of rehabilitation”—exert an extremely strong influence on individual patients’ results.

Through this analysis, I aimed to statistically and appropriately separate and adjust for the complex confounding factor of “variability among the facilities (hierarchy)” to which a patient belongs—not merely the patient’s individual background factors—and to extract the true clinical risk factors. By making full use of advanced mixed-effects models (random-effects models) and cluster analysis that quantifies each facility’s treatment policy, Dr.DataScience accurately brought to light a risk structure that simple aggregation risked misjudging, and provided objective evidence toward establishing a safer oral-transition protocol.

Background and objective

In this case, what was required was to verify, using patient data collected from multiple medical facilities with recovery-phase rehabilitation wards, “whether transitioning to oral intake early truly raises the risk of aspiration pneumonia and the like.”

A major challenge in the clinical setting is the dilemma that, while advancing the transition to oral intake early can be expected to improve swallowing-function recovery and quality of life (QOL), it also raises the risk of aspiration pneumonia. What further complicates the problem is that the criteria for judging “how early to switch to oral intake” differ greatly by facility. Some facilities are aggressive, and others are conservative.

The main objective of the analysis was to incorporate this strong bias of “facility-by-facility treatment-policy skew” into the statistical model, and, after subtracting the differences among facilities, to clarify how purely “the earliness of the transition timing” affects the probability of each complication. Another important objective was to objectively classify the facilities as a whole into a “facility group promoting early transition” and “other facility groups,” and to evaluate the differences in risk incidence by facility group.

Data and variables

This analysis used registry data of several hundred stroke patients collected from multiple medical facilities. The main variables analyzed were as follows.

1. • Response variables (risk factors): the presence or absence of “occurrence of aspiration pneumonia,” “progression to a malnourished state,” “occurrence of pressure ulcers,” etc., by discharge (each a binary variable).
   • Main explanatory variables: the number of days from onset to transition to oral intake (continuous variable), and a categorical classification by transition timing (early, standard, late, etc.).
   • Covariates (adjustment variables): age, severity score at onset, BMI, length of hospitalization at the acute-phase hospital, etc.
   • Hierarchical variable: the “medical facility ID” to which the patient belongs.

Analytical methods

In this case, to correctly evaluate the hierarchical data structure with facility-by-facility tendencies and to avoid the multicollinearity lurking among many variables, I selected and applied the following advanced statistical methods.

1. Visual evaluation of the data distribution and optimization of the correlation analysis
   • Adopted method: distribution confirmation by kernel density estimation, and the use of various correlation coefficients according to scale
     Prior to modeling, I visually evaluated the distribution shape of all continuous variables using kernel density estimation. As a result, because “age” and “BMI” showed shapes close to a normal distribution, I adopted the parametric method “Pearson correlation coefficient.” On the other hand, because variables such as “length of hospitalization at the acute-phase hospital” showed an extremely skewed non-normal distribution, I applied the rank-based nonparametric method “Spearman’s rank correlation coefficient.” Furthermore, I used “Cramér’s V” between nominal variables and the “correlation ratio” between continuous and nominal variables, accurately quantifying the relationships among variables. I confirmed that the VIF (variance inflation factor) calculated from this was all below 3.0, eliminating the problem of multicollinearity in advance.
   • Method not adopted: uniform application of Pearson correlation analysis to all variables
     Applying the Pearson correlation coefficient uniformly to everything while ignoring the distribution shape of the data carries the risk of over- or under-estimating the strength of the correlation for non-normally distributed data, so I strictly excluded it.
2. Multivariate analysis accounting for inter-facility variability
   • Adopted method: mixed-effects logistic regression model (comparison of random-intercept and random-slope models)
     As long as patients belong to particular facilities, there is “within-facility correlation,” whereby patients at the same facility tend to have similar results. To adjust for this hierarchical variability, I built both a “random-intercept model” that adjusts for differences in baseline risk by facility, and a “random-intercept + random-slope model” that assumes the degree of influence (slope) of oral-transition timing also differs by facility. I compared and evaluated the goodness-of-fit of both models using AIC (Akaike Information Criterion) and AUC (area under the ROC curve), and adopted, for each response variable, the optimal model with the smaller AIC and higher predictive accuracy.
   • Method not adopted: ordinary logistic regression analysis
     Ordinary logistic regression stands on the premise that “all patient data are mutually independent.” Applying this directly to multi-facility data carries a very high risk of mistaking facility skew for individual-patient characteristics, underestimating the standard errors, and producing “spurious significant differences” for variables that are not truly significant (a Type I error); I therefore refrained from adopting it as the method for the main analysis.
3. Objective classification of facility policy
   • Adopted method: K-means cluster analysis combined with the elbow method
     Rather than classifying facilities by a simple mean value, I classified all patients by the K-means method based on the distribution of “oral-transition timing.” In doing so, to determine the optimal number of clusters, I used the “elbow method (a technique that finds the point where the decrease in the sum of squares bends)” and objectively defined four groups. Of these, I calculated for each facility the occupancy proportion of the cluster to which the most patients who transitioned earliest belonged, and strictly defined facilities whose proportion exceeded the upper quartile (the third quartile) as “early-transition-promoting facilities.”
4. Comparison of incidence and multiple-comparison correction
   • Adopted methods: Fisher’s exact test and the Holm method
     I evaluated whether there was a difference in the incidence of each complication between “early-transition-promoting facilities” and “other facilities.” Because, for complications with low incidence, cases where cells with an expected frequency of less than 5 exceeded 20% occurred frequently, I preferentially adopted “Fisher’s exact test,” which can calculate exact probabilities even with a small number of samples, rather than the chi-squared test. Also, to prevent the increase in false positives (the problem of multiple testing) caused by testing multiple complications simultaneously, I performed rigorous correction of p-values using the “Holm method,” which can control the Type I error while maintaining more power than the Bonferroni method.
   • Methods not adopted: application of the chi-squared test that does not meet the conditions, and multiple testing without correction
     The chi-squared test that does not meet the expected-frequency conditions calculates erroneous p-values, so I did not adopt it. Also, judging significance without performing multiple-comparison correction markedly undermines statistical reliability, so I strictly avoided it.

Overview of the main results and clinical considerations

As a result of the rigorous multivariate analysis using a mixed-effects model, it was confirmed that the result that appeared significant in univariate analysis (ordinary logistic regression)—”an increase in aspiration-pneumonia risk due to early transition to oral intake”—lost its significance in the multivariate analysis (for example, p = 0.145).

This result strongly suggests that what governed the occurrence of aspiration pneumonia was not so much “the transition timing itself” as the underlying “severity score,” “length of acute-phase hospitalization,” and even “facility-by-facility management systems (the part absorbed as a random effect).” It became clear that ordinary analysis had mistaken the influence of these confounders for “the influence of transition timing.”

On the other hand, in the comparison between the “early-transition-promoting facilities” identified by cluster analysis and “other facilities,” it became clear that the risk of “malnourished state” was statistically significantly lower in the early-promoting facilities (p = 0.012 after Holm correction). This is highly valuable evidence in actual clinical practice: a facility protocol of attempting oral intake early greatly contributes to improving patients’ nutritional status without markedly increasing pneumonia risk.

Dr.DataScience’s contribution

In this case, Dr.DataScience precisely controlled the hierarchical bias lurking behind multi-facility data and derived true clinical insights not misled by spurious correlations.

1. Building the optimal model for a hierarchical data structure
   • Avoiding the trap of ordinary regression analysis that ignores inter-facility variability, I appropriately built mixed-effects models (random intercept, random slope) through objective model selection using AIC and AUC. This prevented overestimation of each variable’s odds ratio and provided robust, medically valid objective evidence.
2. Achieving objective facility classification using machine-learning methods
   • By quantitatively redefining the vague concept of “facility aggressiveness” through K-means cluster analysis using the elbow method, I achieved a highly reproducible subgroup analysis free from subjectivity.
3. Raising the evidence level through application of a rigorous testing process
   • I thoroughly used test methods according to the data distribution and expected frequencies (Fisher’s exact test and various correlation coefficients) and multiple-comparison correction by the Holm method. Through an analytical procedure that pursued statistical validity down to the finest detail, I provided the client with an extremely reliable analysis report fully capable of withstanding the peer-review process of academic papers.