Introduction
The worldwide increase in the elderly population has heightened the significance of research on mitigating cognitive decline through non-pharmacological methods. Within this realm of study, The Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) study has emerged as a pivotal investigation (Tennstedt and Unverzagt 2013). Starting in the late 1990s, the ACTIVE study embarked on a quest to address a central inquiry: can cognitive function in older people be enhanced and sustained through tailored training interventions? This randomized controlled trial encompassed 2,832 participants aged 65 and above and examined the effects of three distinct cognitive training programs, targeting memory, reasoning, and processing speed. In this report, we provide an overview of the long-term impact, mainly focusing on the effects of speed training on older adults, utilizing a longitudinal data analysis model, specifically the Generalized Estimating Equations (GEE) framework.
Research Question
The speed of cognitive processing significantly declines with age, impacting various aspects of daily life, including driving, hazard recognition, and other time-sensitive tasks (Giuli et al. 2016). This decline raises concerns about the overall quality of life for older adults. Given this context, we aim to understand how cognitive training, including potential boosters, baseline processing speed, and subsequent speed or cognitive assessments, influences the evolution of processing speed over time. We consider various speed measurement tasks, such as complex reaction time (CRT), timed instrumental activities of daily living (TIADL) tasks, and activities of daily living timing (ADLT) to provide a comprehensive analysis (Rebok et al. 2014). By addressing this research question, we contribute valuable insights into enhancing the cognitive well-being and quality of life for the elderly population.
Method
To assess the effectiveness of cognitive training on adults, this report relies on data directly from the ACTIVE study. We conducted a data cleaning process, including variable mutation, column combination, removing outliers, etc., to perform the following on longitudinal data analysis. The whole population includes 2802 people whose average age is 73.63276 with a mean speed baseline of 938.0526. Since we aim to focus on the long-run impact of the training, we filter the population to those who participated at least once in the study from year three. 1934 people remained, with an average age of 72.92554 and an average speed of 890.1282.
| Group | Participants | Mean.Age | Mean.SpeedBase |
|---|---|---|---|
| Adult when after Year 3 | 1934 | 72.92554 | 890.1282 |
| Whole Population | 2802 | 73.63276 | 938.0526 |
To address our research question effectively, we made thoughtful
variable selections. We introduced an interaction term between “Years”
and “Speed of Processing Group”
(INTGRP == "Speed of Processing Training) to focus on the
long-term effects of speed processing. Our previous visualizations
indicated no substantial differences between other cognitive groups and
the control group. Therefore, we included only the speed group for a
direct comparison with the control group. We also incorporated
subsequent speed and cognitive assessments, including categorized
“Activities of Daily Living Timing”
(ADLT_group == "ADLT3+")(“Activities of Daily Living,”
n.d.), “Timed Instrumental Activities of Daily Living”
(TIADL) (“Instrumental
Activity of Daily Living,” n.d.), and “Complex Reaction
Time” (CRT). Moreover, we examined the potential impact of
cognitive training booster programs by introducing the
BOOSTER variable. This involved an interaction term with
“Speed of Processing Group”
(INTGRP == "Speed of Processing Training). We also and
include a visualization below as a reference. Finally, we centered
participants’ baseline age at 65 (ageOld), allowing for a
more straightforward interpretation since age significantly influences
cognitive abilities, especially processing speed.
To answer the our research question, we chose the Generalized Estimating Equations (GEE) model, well-suited for correlated observational data in studies like ACTIVE, where measurements often show continuity over time. The “ar1” correlated structure in GEE assumes correlations between a data point and the one immediately preceding it, with the strength of this correlation weakening over time intervals. Also, compared to ordinary generalized linear models (GLM), GEE has significant advantages. GLM can’t handle correlations between observations, while GEE is designed for such clustered data (LIANG and ZEGER 1986). Moreover, GEE provides robust standard errors, ensuring accurate estimates even with incorrect correlation matrix specifications.
Data cleaning & Final Model
mod <- df_cleaned %>%
drop_na(Speed, Years, INTGRP, ageOld, ADLT_group, BOOSTER, IMMRAW, CRT, TIADL, SpeedBase, BOOSTER) %>%
geeM::geem(Speed ~ Years * (INTGRP == "Speed of Processing Training") + (INTGRP == "Speed of Processing Training") : BOOSTER + ageOld + (ADLT_group == "ADLT3+") + CRT + TIADL + SpeedBase,
data = ., id = AID, corstr = 'ar1')
mod %>% summary() ## Estimates Model SE
## (Intercept) 150.3000 15.08000
## Years 20.5200 1.17900
## INTGRP == "Speed of Processing Training"TRUE -106.7000 15.84000
## ageOld 8.2890 0.70270
## ADLT_group == "ADLT3+"TRUE 60.8800 22.12000
## CRT 40.3100 2.23000
## TIADL 80.7400 5.46700
## SpeedBase 0.4375 0.01423
## Years:INTGRP == "Speed of Processing Training"TRUE 4.6690 2.13300
## INTGRP == "Speed of Processing Training"FALSE:BOOSTER -0.0324 8.01300
## INTGRP == "Speed of Processing Training"TRUE:BOOSTER -143.4000 13.35000
## Robust SE wald
## (Intercept) 20.16000 7.455000
## Years 1.39700 14.690000
## INTGRP == "Speed of Processing Training"TRUE 15.55000 -6.867000
## ageOld 0.84030 9.863000
## ADLT_group == "ADLT3+"TRUE 29.72000 2.048000
## CRT 3.08200 13.080000
## TIADL 7.22000 11.180000
## SpeedBase 0.02385 18.340000
## Years:INTGRP == "Speed of Processing Training"TRUE 2.19100 2.131000
## INTGRP == "Speed of Processing Training"FALSE:BOOSTER 8.05300 -0.004024
## INTGRP == "Speed of Processing Training"TRUE:BOOSTER 14.54000 -9.863000
## p
## (Intercept) 0.00000
## Years 0.00000
## INTGRP == "Speed of Processing Training"TRUE 0.00000
## ageOld 0.00000
## ADLT_group == "ADLT3+"TRUE 0.04053
## CRT 0.00000
## TIADL 0.00000
## SpeedBase 0.00000
## Years:INTGRP == "Speed of Processing Training"TRUE 0.03311
## INTGRP == "Speed of Processing Training"FALSE:BOOSTER 0.99680
## INTGRP == "Speed of Processing Training"TRUE:BOOSTER 0.00000
##
## Estimated Correlation Parameter: 0.3625
## Correlation Structure: ar1
## Est. Scale Parameter: 33080
##
## Number of GEE iterations: 7
## Number of Clusters: 1897 Maximum Cluster Size: 3
## Number of observations with nonzero weight: 4074We can represent the information in the table with the following functions for a more straightforward view, \[ \begin{aligned} & \quad \; E(\text{Speed}\;|\; \text{Years, SpeedTraining, BOOSTER, ageOld, ADLT3+, CRT, TIADL, SpeedBase}) \\ & = \beta_0 + \beta_1\text{Years} + \beta_21_{\text{SpeedTraining}} + \beta_3\text{ageOld} +\beta_41_{\text{ADLT3+}}+\beta_5\text{CRT} + \beta_6\text{TIADL}+ \beta_7\text{SpeedBase} + \beta_8\text{Years:}1_{\text{SpeedTraining}} + \\ & \quad \beta_91_{\text{SpeedTraining=FALSE}}:1_\text{BOOSTER} + \beta_{10}1_{\text{SpeedTraining=TRUE}}:1_\text{BOOSTER} \end{aligned} \]
Based on the model’s summary output, the coefficient values align
with our expectations for study in the long run (Years$$3).
For instance, we anticipate that the time required for processing speed
will increase as participants’ age increases, resulting in a positive
coefficient of 8.28 for each additional year beyond 65. Similarly, when
a participant exhibits a slower baseline speed, as indicated by the
SpeedBase variable, and experiences a slower speed
processing performance in other speed measurement tasks such as
CRT and TIADL, or demonstrates a relatively
higher degree of dependence on others in their daily life
(ADLT_group == "ADLT3+"), they are expected to have a
longer speed processing time, as measured by our outcome variable
speed.
Furthermore, the summary results of mod2 indicate that the majority
of coefficients in this model, except
INTGRP == "Speed of Processing Training"FALSE:BOOSTER, have
an absolute value of the Wald test value greater than 2, indicating
their significant contribution to the model. Additionally, the p-values
further support the majority of coefficients are statistically
significant. In addition, it is reasonable why
INTGRP == "Speed of Processing Training"FALSE:BOOSTER has
such a high p-value in the context of this study. The study does not
allow people in the control group to receive any follow-on booster
training, so it isn’t very meaningful to interpret this coefficient.
Conclusions
Using GEE model with “ar1” correlation matrix, we believe that, on average, people who are assigned to the cognitive training for speed processing and did not take booster training are -83.355 (\(-106.7000 + 4.6690*5\)) more faster in speed processing at study year 5 than people in the control group. This is a statistically significant difference with an all-negative 95% confidence interval from -30.345 to -136.365. In addition, people assigned to the cognitive training for speed processing and took booster training are -143.3676 (\(-0.0324-143.4000\)) more faster in speed processing than people who received speed training but did not take booster training. This is also a statistically significant difference with an all-negative 95% confidence interval from -98.1816 to -188.5536. Our visualization also verifies those two findings.
One limitation of our model is that we prioritize simplicity, assuming a general linear relationship between predictors and the outcome. While we created numerous visualizations and carefully narrowed our research question to ensure that each variable exhibits a general linear relationship with the outcome speed, we could potentially enhance the model’s accuracy by incorporating splines to capture small curvatures. We would also appreciate consulting with an expert to refine the variable selection process and ensure the predictors in the model align with a psychiatric perspective. Nonetheless, this model effectively reflects the study’s outcome, providing valuable insights into the factors influencing processing speed in older adults and offering a solid foundation for further research in this field.
Acknowledgements
We really appreciate our instructor Brianna Heggeseth for providing this fantastic course. :)