Follow along

Plan for today

  • Dementia
    • Overview
    • Determinants
    • Linking procrastination
  • Markov models
    • Using Markov models for dementia
    • Preliminary data analysis
  • Conclusions
  • Time permitting: Goodness of fit metrics

Dementia & Procrastination

Dementia & Procrastination

What is dementia

  • Dementia is a syndrome characterized by the progressive and typically irreversible decline of cognitive function.
  • It encompasses a range of conditions, including Alzheimer’s disease, vascular dementia, and Lewy body dementia.
  • As a major public health concern, dementia impacts millions worldwide1, straining healthcare systems and caregivers.
  • Given its growing prevalence, identifying modifiable risk factors is essential for prevention and early intervention.

Dementia & Procrastination

The Role of Mild Cognitive Impairment

  • MCI involves cognitive changes—such as memory lapses or impaired decision-making—that exceed normal aging but don’t yet meet dementia criteria.
  • Often a precursor to dementia2–4, MCI significantly raises the risk of progression, making early detection and intervention critical

Dementia & Procrastination

Apathy: A Key Behavioral Symptom

  • Among the most common behavioral changes in MCI and dementia is apathy — a loss of motivation and goal-directed behavior.
  • Research shows apathy nearly doubles the risk of progressing to dementia5, highlighting its role as a potential early marker

Dementia & Procrastination

Procrastination: A Parallel Dysfunction?

  • Unlike apathy, procrastination involves delaying tasks despite intent, suggesting a conflict in executive function rather than pure disengagement.
  • Both behaviors point to impairments in goal-oriented decision-making, a core deficit in MCI and dementia.

Research question

Could procrastination, like apathy, signal broader cognitive and motivational decline?

Markov Models

Markov Models

Core Concept

To analyze longitudinal patterns of cognitive decline, we used a discrete-time, first-order Markov model.

  • The model hinges on the Markov property:
    • Let \(X_t\) denote an individual’s cognitive state at time \(t\), where \(X_t \in S = \{1, 2, \dots, K\}\).
    • Transition to state \(j\) at \(t + 1\) depends only on state \(i\) at \(t\).

Markov property

\[P(X_{t+1} = j \vert X_t = i, X_{t-1} = i_{t-1}, \dots X_0 = i_0) = P(X_{t+1} = j \vert X_t = i)\]

Markov Models

Transition Matrices

These probabilities, denoted \(p_{ij}\) are called transition probabilities.

\[ P = \begin{bmatrix} p_{11} & \cdots & p_{1K} \\ \vdots & \ddots & \vdots \\ p_{K1} & \cdots & p_{KK} \\ \end{bmatrix} \]

\[ P^{(t)} = \begin{bmatrix} p_{11}^{(t)} & \cdots& p_{1K}^{(t)} \\ \vdots & \ddots & \vdots \\ p_{K1}^{(t)} & \cdots & p_{KK}^{(t)} \\ \end{bmatrix} \]

\[ P^{(t)} = \begin{bmatrix} p_{11}^{(t)} & p_{12}^{(t)} & p_{13}^{(t)} \\ p_{21}^{(t)} & p_{22}^{(t)} & p_{23}^{(t)} \\ 0 & 0 & 1 \\ \end{bmatrix} \]

  • Rows: Current state \((t)\)
  • Columns: Next state \((t + 1)\)

Formally: \(p_{ij} = P(X_{t+1} = j \vert X_t = i)\)

Markov Models

Discrete Time Models

  • We capture time-varying transition probabilities using multinomial logistic regression.
  1. Model Specification (for \(K=3\) states with state \(K\) as reference):
    • Log-odds of transitioning to state \(j\) vs. state \(K\):

\[ \log \left( \frac{p_{ij}^{(t)}}{p_{iK}^{(t)}} \right) = \underbrace{\alpha_j^{(t)}}_{\text{intercept}} + \underbrace{\boldsymbol{\beta}_j^{(t)^T} \boldsymbol{X}^{(t)}}_{\text{covariate effects}} \quad \text{for } j = 1, \dots, K-1 \]

Data Analysis

Data Analysis

Our Dataset

  • Analyses were conducted using a secondary data source called the Health and Retirement Study (HRS)6,7.
  • We focused on four biennial waves of HRS data (2016 - 2022).
ID 2016 2018 2020 2022
1 Normal Cognition Normal Cognition Normal Cognition Normal Cognition
2 Normal Cognition Normal Cognition Normal Cognition Normal Cognition
3 Dementia Dementia Dementia Dementia
4 Normal Cognition Normal Cognition Normal Cognition Normal Cognition
5 MCI Normal Cognition Normal Cognition Normal Cognition
6 Normal Cognition Normal Cognition Normal Cognition Normal Cognition
Table 1: Cognition data from the HRS (2016 - 2022)

Data Analysis

Our Dataset

Figure 1: Cognitive transitions across time (with dementia as an absorbing state)

Data Analysis

Our Dataset

# Pivoting to long format
data_long <- data |>
  dplyr::inner_join(df[, covariates], by = "ID") |>
  pivot_and_factorise() |>
  dplyr::group_by(ID) |>
  dplyr::mutate(Age = Age - (2022 - as.numeric(as.character(wave)))) |>
  dplyr::ungroup()

output_data(data_long)
ID Wave Status Procrastination
1 2016 1 22
1 2018 1 22
1 2020 1 22
1 2022 1 22
2 2016 1 41
2 2018 1 41
2 2020 1 41
2 2022 1 41
Table 2: Pivoted data

Data Analysis

Our Dataset

data_stack <- data_long |>
  dplyr::group_by(ID) |>
  dplyr::mutate(status_prev = dplyr::lag(status), .after = status) |>
  dplyr::filter(!is.na(Total_p), Age >= 50) |>
  dplyr::ungroup() |>
  dplyr::filter(wave != 2016)

output_data(data_stack, lag = TRUE)
ID Wave Status (t) Status (t-1) Procrastination
1 2018 1 1 22
1 2020 1 1 22
1 2022 1 1 22
2 2018 1 1 41
2 2020 1 1 41
2 2022 1 1 41
3 2018 3 3 60
3 2020 3 3 60
Table 3: Data with new t - 1 column

Data Analysis

Transition Frequencies

Figure 2: Transition frequencies between cognitive states for each time period.

Data Analysis

Modelling

# Model 1: Baseline model (reference: NC)
fit_1a <- nnet::multinom(
  status ~ Gender + Age + Education_tri + Total_dep_2016,
  family = multinomial, data = data_stack, trace = FALSE)

# Model 2: With procrastination (reference: NC)
fit_2a <- nnet::multinom(
  status ~ Gender + Age + Education_tri + Total_dep_2016 + Total_p,
  family = multinomial, data = data_stack, trace = FALSE)

# Model 3: Full model with previous state (reference NC)
fit_3a <- nnet::multinom(
  status ~ Gender + Age + Education_tri + Total_dep_2016 + Total_p + status_prev, 
  family = multinomial, data = data_stack, trace = FALSE)
# Model 4: Additive time effects
fit_4a <- nnet::multinom(
  status ~ Gender + Age + Education_tri + Total_dep_2016 + Total_p + status_prev + wave, 
  family = multinomial, data = data_stack, trace = FALSE)

# Model 5: State-specific time effects
fit_5a <- nnet::multinom(
  status ~ Gender + Age + Education_tri + Total_dep_2016 + Total_p + (status_prev * wave), 
  family = multinomial, data = data_stack, trace = FALSE)

# Model 6: Full time interactions
fit_6a <- nnet::multinom(
  status ~ (Gender + Age + Education_tri + Total_dep_2016 + Total_p + status_prev) * wave, 
  family = multinomial, data = data_stack, trace = FALSE)

Table 4 & Table 5 present likelihood ratio tests for each model

Model Resid. df Resid. Dev Test Df LR stat. Pr(Chi)
Baseline 5100 2661.692 NA NA NA
Procrastination 5098 2653.172 1 vs 2 2 8.519 0.014
Procrastination + Previous Status 5094 2070.128 2 vs 3 4 583.044 0.000
Table 4: Likelihood ratio test for stationary models
Model Resid. df Resid. Dev Test Df LR stat. Pr(Chi)
Stationary 5094 2070.128 NA NA NA
Additive 5090 2055.454 1 vs 2 4 14.675 0.005
State-Time Interactions 5082 2049.679 2 vs 3 8 5.775 0.672
Full Interactions 5058 1989.068 3 vs 4 24 60.610 0.000
Table 5: Likelihood ratio test for non-stationary models

\(\text{LRT} = -2 \times \ell_{\text{reduced}} - \ell_{\text{full}}\)

Data Analysis

Visualisation

Figure 3: Estimated odds ratios for the stationary model.
Figure 4: Predicted transition probabilities from the stationary model.
Figure 5: Estimated transition matrix.

Conclusion

Conclusion

Wrapping up

  • Preliminary results suggest that procrastination is associated with cognitive decline.
  • Older adults with higher levels of procrastination have:
    • An increased probability of transitioning to MCI.
    • A decreased probability of transitioning back to NC
  • Procrastination is a complex behavior that may signal broader cognitive and motivational decline.

Future (side) project

Future research

A new goodness of fit metric

Figure 6: Observed vs. estimated transition matrix.

Future research

A new goodness of fit metric

Manhattan Distance

\[D_{\text{Manhattan}}(P, \hat{P}) = \sum_{i=1}^{m}\sum_{j=1}^{n} |p_{ij} - \hat{p}_{ij}|\]


Frobenius Norm

\[D_{\text{Frobenius}}(P, \hat{P}) = \sqrt{\sum_{i=1}^{m}\sum_{j=1}^{n} |p_{ij} - \hat{p}_{ij}|^2}\]

Maximum Difference

\[D_{\text{Max}}(A, B) = \max_{\substack{1 \leq i \leq m \\ 1 \leq j \leq n}} |a_{ij} - b_{ij}|\]


Kullback-Leibler Divergence

\[ D_{\text{KL}}(P \parallel \hat{P}) = \sum_{i=1}^{m}\sum_{j=1}^{n} p_{ij} \log\left(\frac{p_{ij}}{\hat{p}_{ij}}\right) \]

and others

Future research

A new goodness of fit metric

Figure 7: Distance metrics between observed and estimated transition matrices.

References

1. Nichols, E., Steinmetz, J. D., Vollset, S. E., Fukutaki, K., Chalek, J., Abd-Allah, F., Abdoli, A., Abualhasan, A., Abu-Gharbieh, E., Akram, T. T., et al. (2022). Estimation of the global prevalence of dementia in 2019 and forecasted prevalence in 2050: An analysis for the global burden of disease study 2019. The Lancet Public Health, 7(2), e105–e125. https://doi.org/10.1016/S2468-2667(21)00249-8
2. Cooper, C., Sommerlad, A., Lyketsos, C. G., & Livingston, G. (2015). Modifiable predictors of dementia in mild cognitive impairment: A systematic review and meta-analysis. American Journal of Psychiatry, 172(4), 323–334. https://doi.org/10.1176/appi.ajp.2014.14070878
3. Shigemizu, D., Akiyama, S., Higaki, S., Sugimoto, T., Sakurai, T., Boroevich, K. A., Sharma, A., Tsunoda, T., Ochiya, T., Niida, S., & Ozaki, K. (2020). Prognosis prediction model for conversion from mild cognitive impairment to alzheimer’s disease created by integrative analysis of multi-omics data. Alzheimer’s Research & Therapy, 12, 1–12. https://doi.org/10.1186/s13195-020-00716-0
4. Tschanz, J., Welsh-Bohmer, K., Lyketsos, C., Corcoran, C., Green, R. C., Hayden, K., Norton, M. C., Zandi, P., Toone, L., West, N., et al. (2006). Conversion to dementia from mild cognitive disorder: The cache county study. Neurology, 67(2), 229–234. https://doi.org/10.1212/01.wnl.0000224748.48011.84
5. Dalen, J. W. van, Wanrooij, L. L. van, Charante, E. P. M. van, Brayne, C., Gool, W. A. van, & Richard, E. (2018). Association of apathy with risk of incident dementia: A systematic review and meta-analysis. JAMA Psychiatry, 75(10), 1012–1021. https://doi.org/10.1001/jamapsychiatry.2018.1877
6. Fisher, G. G., & Ryan, L. H. (2018). Overview of the health and retirement study and introduction to the special issue. Work, Aging and Retirement, 4(1), 1–9. https://doi.org/10.1093/workar/wax032
7. Langa, K. M. (2023). Langa-weir classification of cognitive function (1995-2020). Survey Research Center Institute for Social Research University of Michigan. https://hrsdata.isr.umich.edu/sites/default/files/documentation/data-descriptions/1680034270/Data\_Description\_Langa\_Weir\_Classifications2020.pdf

Wrapping up

Thank you

These slides were built with
, , and Quarto