* 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 carried out a multifaceted evaluation of how patients’ background factors influence the “achievement of clinical remission” and “the trajectory of inflammatory markers” with each successive visit (number of treatment interventions) in the treatment of rheumatoid arthritis (RA) patients with a new biologic agent. In data acquired repeatedly over time from the same patient in actual clinical practice (longitudinal data), correlations specific to the data within the same patient arise. Therefore, applying ordinary statistical methods as-is carries the risk of leading to erroneous conclusions.

Through this analysis, I aimed to statistically and correctly handle complex challenges—such as the correlation structure inherent in repeated-measures data and the unavoidable missing laboratory values in clinical data—and to identify the true predictors directly linked to treatment effect. By combining advanced multiple imputation with generalized estimating equations (GEE), Dr.DataScience provided a precise factor analysis and contributed to advancing stratified medicine.

Background and objective

In this case, what was required was to identify the factors for maximizing “the probability of achieving clinical remission” in patients receiving a new biologic agent. The target data are panel data recorded repeatedly from the same patient (patient ID) at each visit. The main objective of the analysis was to quantitatively clarify, using a general model that accounts for the associations among factors, how background factors such as “history of using existing therapeutic drugs,” “presence of a particular autoantibody,” and “presence of comorbidities” influence the achievement of remission.

Data and variables

This analysis used real clinical data spanning multiple cycles, provided by a particular medical institution. The main variables analyzed were as follows.

1. • Cluster variable: ID for patient identification
   • Response variables:
     • Achievement of clinical remission (binary variable: 1 = achieved, 0 = not achieved)
     • Number of pain flares (count data)
     • Inflammatory marker A and inflammatory marker B (continuous variables)
   • Main explanatory variables: history of using existing therapeutic drugs, presence of a particular autoantibody, presence of comorbidities, age, sex (male, female), etc.

Analytical methods

In this case, to address the complex characteristics of real clinical data (within-patient correlation due to repeated measurements, and non-random missingness of some laboratory values), I selected and applied the following statistical methods.

1. Handling of missing values
   • Adopted method: multiple imputation using CART (Classification and Regression Trees)
     Missing values were found in some continuous variables, such as “inflammatory marker A” and “inflammatory marker B.” Although the overall missingness rate was 20% or less, there was an extremely strong correlation between marker A and marker B, and the missingness was biased toward samples with high values of one of them, so there was a risk that it was not missing at random. Because it can flexibly impute even non-linear relationships and avoid multicollinearity when handling strongly correlated variables simultaneously, I adopted multiple imputation using the CART algorithm, and created 50 imputed datasets to ensure stability.
   • Methods not adopted: listwise deletion (complete-case analysis) and mean imputation
     Listwise deletion removes from the analysis the entire data of any patient containing even a single missing value, which reduces the precious sample size and markedly lowers statistical power. Mean imputation, meanwhile, underestimates the variance (variability) of the data and risks distorting the standard errors; I judged it inappropriate as preprocessing for the kind of rigorous multivariate analysis in this case, and therefore did not adopt it.
2. Multivariate analysis
   • Adopted method: generalized estimating equations (GEE)
     Because data are acquired from the same patient at multiple visits, a patient-specific “correlation” exists among the data. I adopted generalized estimating equations (GEE) because they can incorporate this within-cluster correlation structure (here, an “exchangeable” correlation) into the model. Matching the nature of the response variable, I used different GEEs—a “binomial distribution” for remission achievement, a “Poisson distribution” for the number of pain flares, and a “normal (Gaussian) distribution” for the inflammatory markers.
   • Methods not adopted: ordinary logistic regression and generalized linear mixed models (GLMM)
     Ordinary regression requires the premise that “all data are mutually independent,” so applying it to repeated-measures data like this would underestimate the standard errors and risk leading to erroneous significant differences (Type I error); I therefore excluded it. GLMM (mixed models) was also a candidate, but because the objective here was not prediction specific to individual patients but a general model evaluating the average influence of each factor on the target patient population (population-averaged effect), I judged GEE—which has fewer assumptions and tends to be computationally stable—to be optimal.
3. Model goodness-of-fit evaluation
   • Instead of ordinary likelihood-based evaluation indices (such as AIC), I compared multiple model patterns using QIC, which is specialized for GEE, and further calculated the AUC as predictive accuracy to evaluate the model’s validity.

Overview of the main results and clinical considerations

As a result of the multivariate analysis using a general model with GEE, it was confirmed that in all evaluated variable patterns, all three factors—”history of using existing therapeutic drugs,” “presence of a particular autoantibody,” and “presence of comorbidities”—had an independent and significant influence on the achievement of clinical remission.

For example, in the autoantibody-positive patient group, the odds ratio for achieving remission varied significantly compared with the negative group, quantitatively proving it to be a strong predictor (test result for the relevant factor: p = 0.012). On the other hand, basic background factors such as sex (male, female) and age were confirmed not to bring about a statistically significant difference in achieving remission (p = 0.540, etc.).

In addition, I performed the analysis on both the dataset before and the dataset after imputation by multiple imputation using CART, and in neither did the direction or significance of the results fluctuate substantially, confirming that the results were very robust even against missingness in some laboratory values.

Dr.DataScience’s contribution

In this case, Dr.DataScience unraveled the complex structure of longitudinal data that tends to be overlooked by simple aggregation, and created robust evidence directly linked to decision-making in the clinical setting.

1. Optimal method selection for a complex data structure, and presentation of the rationale
   • By not overlooking the “dependency” in repeated-measures data and selecting GEE rather than ordinary regression, I eliminated the risk of misleading clinical judgment. By making clear why that statistical method should be used and what the problems with the alternatives are, I provided a robust analytical foundation capable of withstanding peer review of medical papers.
2. Avoiding information loss through advanced missing-value handling
   • For the “non-random missingness” peculiar to real clinical data and the strong correlation among variables, by applying multiple imputation with the CART algorithm, I derived unbiased, clear analytical results without wasting the precious case data collected.
3. Deriving and evaluating clinical implications
   • Through rigorous evaluation of the general model based on QIC and AUC, I clarified the patient profile that truly contributes to achieving remission. This provided concrete insights for advancing individualized medicine—namely, which patient strata should be prioritized for a particular treatment intervention.