Examination of Matching Methods,Sparse Effects,and Limitations in a Nationwide Database Study on Alzheimer’s Disease

We read with great interest the paper authored by Akada et al. [1] in the Journal of Alzheimer’s Disease. The authors aimed to assess the levels of activities of daily living (ADL) in patients with Alzheimer’s disease at the time of diagnosis and identify the risk factors associated with decreased ADL levels during long-term care, using data from a national database. They found that hip fractures independently predicted decreased ADL (p = 0.020 for men and p = 0.001 for women) using a multivariable logistic regression model. This study contributes significantly to expand the knowledge on the issue; however, further research is required.

The authors compared various risk factors between groups of patients with decreased and preserved ADL levels. They found that the adjusted odds ratio (OR) of hip fractures in patients with decreased ADL levels was higher in men (1.95-fold) than in women (1.51-fold) with Alzheimer’s disease. Therefore, a decreased ADL performance was significantly associated with hip fractures in both sexes. However, sparse effects may be present in male patients; the wide 95% confidence interval (CI) of the OR (1.12–3.51; p = 0.020) in fact suggests a potential disparity in the effects between men and women. Previous studies have emphasized the impact of “monotone likelihood,” a unique condition in dataset analysis [2, 3]. From a clinical perspective, caution is advised when interpreting the calculated OR value due to the wide CI. Addressing this concern could involve reformulating the interval estimation based on profile-penalized log-likelihood [3]. This viewpoint, as discussed in my previous publication [4], can also be applied to hazard ratios in the Cox proportional hazards regression models in clinical studies.

In addition, the inappropriateness of the outcome variable and covariate collinearity may have had a role in the resulting wide CI of the estimate under the logistic regression analysis. In fact, the patients were divided into two groups based on their Barthel Index (BI) scores, with a cut-off of 65 [1]. This choice may have affected the reliability of the outcome variable, as the criterion of BI≥65 to indicate preserved ADL lacks physiological relevance. When the patients were divided based on the lowest BI during the 3-year observation period, heterogeneity was observed at the time of assessment, reducing the clinical relevance of the criterion (of BI).

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Fig. 1

Plot of the profile-penalized log-likelihood function for the significant risk variable (illustration of an unbalanced clinical dataset using the R package logistf).

Another example of a wide CI is from a clinical study based on a Colombian national survey [5] to investigate the use of ultrasound guidance for central venous catheterization. Comparing anesthesiologists with consistent ultrasonographic equipment availability and those without it, the crude OR indicated a 27.4-fold increase in its usage when it was always available. However, after adjusting for age, sex, and type of anesthesia practice, the estimated effect increased, whereas the CI widened considerably (adjusted OR = 38.6; 95% CI: 18.5–80.3). Therefore, occasionally the adjusted (i.e., multivariable) OR may be higher than the univariate OR. A similar pattern was observed in this study [1], where Akada et al. compared the rate of hip fractures between ADL-decreased and ADL-preserved groups. The univariate OR of hip fractures in the ADL-decreased group (n = 1,208) compared to the ADL-preserved group (n = 1,208) was calculated as 1.89. However, the multivariable OR was 1.95, indicating a stronger association (>1.89) after adjusting for other risk variables.

In this study [1], it may be beneficial to perform nested propensity-score matching separately for men and women, based on the standardized mean difference results (i.e., standardized mean difference < 0.1). In clinical practice, exact propensity-score matching may be more efficient than nested matching, resulting in a standardized mean difference close to or equal to zero after matching. Additionally, performing propensity-score matching simultaneously for age, BI, and sex might increase the analysis efficiency compared to separate matching for sex alone. Notably, this study [1] adhered to the principle of matching factors by excluding them as covariates in the logistic regression model, avoiding the introduction of additional bias when explaining the study results. However, a comprehensive confounder selection should be conducted before the matching, and the subsequent analysis should use appropriate statistical techniques, such as conditional logistic regression [6].

A previous study on Alzheimer’s disease has indicated that cognitive reserve, brain reserve, and brain maintenance can influence the occurrence of functional impairment [7]. Therefore, important confounders to consider are some lifestyle variables, such as smoking, alcohol consumption, and exercise, which can affect cognitive and brain reserve and brain maintenance, as well as the presence of comorbidities [8]. These considerations highlight the limitations of the nationwide database study [1]. Furthermore, a common recall bias may have influenced the ADL measurements, and underestimation of the number of entries due to Alzheimer’s disease could also have affected the results. The diagnostic bias in Alzheimer’s disease can be controlled by examining the number of entries using specific image test results, such as magnetic resonance imaging, computed tomography. However, the subsequent uncertainty about cause–effect relationships limits the reliability of national database studies. In brief, Akada et al. [1] may not wish to reanalyze their data and modify the inflated odds ratio; nonetheless, they may consider citing this commentary if feasible.

In conclusion, the issue of wide CIs extends beyond univariate models when a risk factor is included in the final multivariable model [1]. The sample size, number of events, level of correlation with the outcome, collinearity between covariates, level of balance, and number of binary covariates can influence the prevalence of monotone likelihood in multivariable regression. The logistf package [9] for the R software (version 4.2.2; R Core Team [2022], https://www.R-project.org/) provides a modification to address spare effects using Firth regression. Generally, this modification narrows a wide CI (Fig. 1), making it more reliable. Monotonic likelihood was observed in the logistic regression model.