Estimation of events in cohort studies based on probability of cognitive impairment

Abstract

Background:

Dementia and Alzheimer’s Disease-causing pathologies progress slowly over decades, and participants are recruited cognitively intact, so designing studies to observe enough cases within a feasible timeframe is important.

Objectives:

In this study, we used readily available basic predictors, age, family history, sex, and apolipoprotein E (APOE) 4 allele carriership, to generate cumulative incidence functions for serious cognitive impairments over years of follow-up.

Methods:

The data were taken from the University of Kentucky Alzheimer’s Disease Research Center longitudinal cohort established in 1989. The participants were recruited cognitively unimpaired and aged 60+. The probability of serious cognitive impairment was assessed using a multinomial logistic model, with age, the number of risk factors (family history and APOE4 allele) and sex as predictors.

Results:

We estimated that when two or more risk factors are present, the long-term incidence of clinical mild cognitive impairment (MCI) and dementia is 2.3 to 2.7 times higher than that of the 0-risk group for both sexes, whereas the 0-risk group experienced approximately 7.9% to 11.6% longer observation times for female and 0.9% to 4.8% for male compared to the two or more risks group.

Conclusions:

This study presents the expected cumulative incidence functions over varying follow-up times, and the expected observation time of serious cognitive impairment for given family history, carriership of APOE4, age and sex.

Summary

• Considering that the symptoms of cognitive impairment develop over decades and that many participants are recruited cognitively unimpaired, it is often challenging to design a study to observe enough cases within a feasible timeframe, making it difficult to draw a meaningful conclusion. This study generates a cumulative incidence function of serious cognitive impairment as a function of age, family history, and APOE4 allele carriership.

• We used the data from the University of Kentucky Alzheimer's Disease Research Center longitudinal cohort. The participants were recruited cognitively unimpaired and aged 60+. A multinomial logistic model was used to assess the probability of serious cognitive impairment defined as MCI or dementia. To get the cumulative incidence function, the model was refitted using 1 to 25-year points of follow-up period.

• The study reconfirms that having more risk factors was associated with higher risk and shorter observation time. The cumulative incidence of cognitive events was 2.1 to 2.7 times more frequent for the two or more risk group compared to the 0-risk group. The observation time required to accumulate sufficient data to assess risk was approximately 4% to 12% shorter for transition to clinical mild cognitive impairment (MCI) or dementia for the two or more risk group compared to the 0-risk group.

• The estimated observation time for serious cognitive impairment is shorter when participants were older or possessed more risk factors at recruitment. The expected observation time for clinical MCI or dementia was 2 years shorter for 65- to 70-year-old female and 65-year-old male participants compared to 5-year older participants.

Introduction

The study of dementia risk requires recruitment and follow-up of initially cognitively intact research volunteers. While the precise mechanisms underlying cognitive impairment in later life remain incompletely understood, it is widely recognized to be associated with neurodegeneration, including the accumulation of amyloid-β and neurofibrillary tangles in the brain, as well as reduced glucose metabolism and gray matter volume^1,2 . Given that the pathologies that most frequently cause dementia are slow-moving and develop over decades³, prospective studies on dementia risk must be designed to ensure that enough dementia cases are observed within a short enough timeframe to allow reasonably powered risk assessment. Moreover, such studies are costly, and recruitment and retention are resource-intensive⁴. Thus, careful planning of the study sample is important for maximizing study efficiency.

Clinical enrichment of study populations to increase the probability of trial success is common practice in designing clinical trials. The concept of prognostic enrichment, or prioritizing volunteers who are most likely to experience the event of interest⁵, can be applied to cohort studies designed to answer questions about causes of dementia. Because potential research volunteers are often healthier than the general population⁶, it is important to consider potential selection biases when designing the study sample. In both clinical and observational studies of brain aging and dementia, drivers of participation often include altruism ^7,8, as well as family history of dementia and perceived dementia risk ⁹, among others⁸.

Family history of dementia associates with higher risk of cognitive impairment^2,10–12 . In addition to shared genetic factors ^10,13,14, family history also represents shared environmental and cultural factors that may influence late life cognition, with recent findings relating maternal and paternal history of early onset of memory impairment to brain amyloid-β load¹⁵. Thus, research volunteers with family history of dementia may be more likely to experience cognitive impairment and dementia during follow-up, and moreover, more likely to participate in dementia studies due to personal experience with family members. Aside from being an important driver of participation and risk, family history is also inexpensive and easy to measure by participant self-report.

Although over 75 genetic risk loci for Alzheimer’s disease have been identified to date ¹⁶, the APOE4 allele continues to be the major driver of dementia risk^1,17–21 based on both the frequency of carriership (15–25% of the US population ²²) and the magnitude of the effect, although growing evidence suggests heterogeneity of the effect across groups defined by sex and ancestry²³. Furthermore, research suggests that APOE4 and family history have synergistic interactions in amyloid-β accumulation ^15,24 and gray matter atrophy rates²⁵. While potential research volunteers are unlikely to know their APOE genotype, genotyping in the research setting is relatively inexpensive and easy to obtain based on a blood sample or buccal swab.

In this study, we utilized age, family history, and APOE4 allele status and sex as predictors, and used all year points of the follow-up as the dataset to generate cumulative incidence functions for cognitive transitions from non-serious to serious cognitive impairment. (See Study Population for the detailed definition of serious and non-serious cognitive impairment.) The purposes of this study were 1) to determine how family history and the presence of APOE4 affect the probability of transitioning to a state of serious cognitive impairment while considering a person’s age and competing risk of death, 2) to compute the proportion of serious cognitive impairment within each year of follow-up based on the corresponding fitted models, and 3) to present the cumulative incidence function that summarizes the estimated probability of serious cognitive impairment.

Data and Methods

Study Population

Study participant data were drawn from the University of Kentucky Alzheimer’s Disease Research Center (UK-ADRC) longitudinal cohort, which includes approximately annual assessments of cognition. The cohort has been in existence since 1989. 1099 participants who met the inclusion/exclusion criteria were screened for the study during the 1989–2012 period. The participants should have been at least 60 years old, cognitively normal, able and willing to follow up the study, should not have had medical, neurological, and psychiatric conditions affecting cognitive ability, and should have consented to brain donation after death (see Schmitt et al., 2012²⁶, for details). 740 participants who enrolled in the cohort prior to 2005 were considered. The dataset was cut in 2005 for consistency due to an update of the diagnosis criteria of MCI and the protocol. The study cohort was finalized with 649 participants after excluding 72 participants who did not have available APOE genotyping and 19 participants who dropped out after the initial visit (For the cohort enrollment flow chart, see Figure 1 of Abner et al, 2014²⁷).

The results of the annual assessment of a participant were categorized into one of the following states: (1) (transient) normal cognition for age (2) (transient) amnestic mild cognitive impairment (MCI), (3) (transient) mixed MCI, (4) clinical consensus-based MCI, (5) dementia, (6) dropout without dementia, and (7) death without dementia (For the details, see Abner et al., 2012²⁸ pp 2–3).

We describe the criteria for the annual assessment on each category below. The patients were categorized into amnestic MCI or mixed MCI when they got at least one poor score (more than 1.5 standard deviations (SD) below the age-adjusted mean) in episodic memory tests or language and executive function tests (See Table 1 of Abner et al. 2012²⁸ for the full list of tests).

On the other hand, categorization of clinical MCI required 1) a cognitive complaint or more than 1.5 SD decline in cognitive test performance; 2) generally intact global cognition; 3) no or minimal functional impairment; 4) not demented by DSM- IV criteria. A consensus team consists of the examining physician, neuropsychologist, and the clinical research assistant administering the protocol reviewed and reached a consensus on classification.

The same consensus group decided the classification of dementia. The decision based on Diagnostic Statistical Manual of Mental Disorders Fourth Edition (DSM-IV), criteria of the Joint Working Group of the National Institute of the Neurologic and Communication Disorders and Stroke-AD and Related Disorders (NINCDS-ADRDA), NINDS-AIREN criteria for vascular dementia, and the 2005 Dementia with Lewy bodies (DLB) consortium revised criteria (See details in Abner et al., 2012²⁸).

In the follow-up of the UK-ADRC cohort, it was observed that none of the participants diagnosed with clinical MCI reverted to milder transient cognitive states. Based on this observation, serious cognitive impairment was defined in two ways: 1) dementia, or 2) clinical MCI at a given assessment.

The Number of Risk Factors

In this study, we introduce the number of risk factors as a predictor. Both family history and APOE4 are significant risk factors; however, they overlap and potentially interact with each other. Notably, individuals with one risk showed similar rates of cognitive events, with 44.4% of those with a positive family history but no APOE4 allele, and 46.9% of those with a negative family history but one APOE4 allele, developing dementia or clinical MCI after being followed up until terminating event, such as dementia, drop out, and death, occur for all patients. The UK-ADRC had only 9 participants who had two APOE4 alleles, a much stronger risk factor than a single APOE4 allele. Considering 20 parameters are estimated, we decided not to add the indicator variable for participants with double APOE4 alleles. In addition, the APOE4 and family history are known to be correlated, and it was expected to cause a multicollinearity issue. To streamline our analysis and address compounding risk, we reduced the degree of freedom by grouping the factors into three categories: 0, 1, and two or more risks and avoided possible multicollinearity issue.

Selection of Covariates

As covariates, possession of APOE4 and APOE2 alleles, family history, age at entry, sex, years of education, and interaction between these risk factors and the age at entry were considered. Likelihood ratio test and Hosmer Lemeshow goodness-of-fit test were conducted on 14 combinations of covariates. As serious cognitive impairment was defined in two ways, clinical-MCI-or-dementia, and dementia, 28 models were fitted. We observed that 1) adding APOE2 did not significantly improve the model in the likelihood ratio tests. 2) Whenever a model contained family history and APOE4 as covariates, substituting those covariates with the number of risks improved in terms of goodness-of-fit tests and the likelihood-ratio tests. 3) Interaction between risk factors (family history, APOE4, and the number of risks) and age at entry, and education were not significant risk factors in the given cohort and always lowered the p-value of the goodness of fit test. 4) Age at entry, the number of risks, and sex were significant risk factors given other covariates. Considering 1)-4), we chose the final model with age at entry, the number of risks, and sex as covariates. The p-value of the goodness-of-fit test was 0.7371 for this model.

Statistical Method

To compute the probability of serious cognitive impairment, a multinomial logistic model with the outcomes: not serious cognitive impairment, serious cognitive impairment, death, and dropout was used. Age at baseline, the number of risk factors, and sex were used as predictors. The logistic model was fitted on data with different follow-up times. A 10-year follow-up data indicates that the model did not consider events that occurred after 10 years of follow-up. Different follow-up times were used to simulate different lengths of study. 1 to 25-year datasets were produced, and the logistic model was refitted on each dataset. The estimated probabilities of serious cognitive impairment for each dataset and group were plotted as a cumulative incidence function and presented in Figures 2 to 5. The LOGISTIC procedure in PC-SAS, version 9.4 (SAS Institute, Inc.) was used to fit the models.

Figure 2:

Predicted Cumulative Number of Conversions to Dementia & Clinical MCI by Follow-up Year among 100 Participants Recruited at Age 70

Results

Descriptive Statistics

Table 1 shows the baseline demographic information. 30.4% of the subjects had at least one APOE4 allele and 17.1% had at least one APOE2 allele. 38.7% had a positive family history. They spent 15.9 years on education on average (15.9±2.5). The participants were recruited at the age of 74.0 on average. 50.07% of participants were aged between 70 and 80 at the time of recruitment. They were followed up 11.0 years (11.0±6.3) and their cognitive status was assessed 8.6 times (8.6±5.2) on average. The subjects with positive family history of dementia tended to be recruited at younger ages (71.3 ± 6.9) and slightly less tended to possess APOE2 (15.1%, 38/251; See Table 6 in Appendix for details) compared to those without a positive family history (75.8± 7.2; 18.3%, 73/398).

Table 1:

Participant demographics in the UK-ADRC cohort data (n=649)

Baseline Demographic
Age at entry (years)  Quantiles (min, 25th, median, 75th, max)	74.0±7.4 (60, 69, 74, 79, 99)
Following time (years)  Quantiles (min, 25th, median, 75th, max)	11.0±6.3 (0, 6, 11, 16, 31)
Education (years)	15.9±2.5
Number of cognitive measures (per person)	8.6±5.2
Apolipoprotein: number of ϵ4 alleles
0	452 (69.7%)
1	188 (29.0%)
2	9 (1.4%)
Apolipoprotein: number of ϵ2 alleles
0	538 (82.9%)
1	111 (17.1%)
Family history
Positive	251(38.7%)
Negative	398(61.3%)
Number of risks
0	298 (45.9%)
1	251 (38.7%)
2+	100 (15.4%)
Sex
Male	234 (36.1%)
Female	415 (63.9%)
Total	649 (100.0%)

Following time is defined as date of terminating event (diagnosis of dementia, dropout, or death)- date of second visit.

Table 2 presents the results obtained over a 10-year follow-up period. Within 10 years of follow-up, 12.2% transitioned to demented, 21.2% transitioned to dementia or clinical MCI, while 25.4% died without transitioning to dementia and 23.0% died without transitioning to clinical MCI or dementia.

Table 2:

Number of Cognitive Events for Two Different Definitions of a Serious Cognitive Impairment after 10 Years of Follow-up

	Serious Cognitive Impairment
	Clinical MCI or Dementia	Dementia
Not Serious Cognitive Impairment	305 (47.0%)	341 (52.5%)
Serious Cognitive Impairment  Dementia	137 (21.2%)   79	79 (12.2%)   79
Clinical MCI without dementia	58	-
Dropout without Serious Cognitive Impairment	149 (23.0%)	165 (25.4%)
With clinical MCI	-	16
Without clinical MCI	149	149
Death without Serious Cognitive Impairment	58 (8.9%)	64 (9.9%)
With clinical MCI	-	6
Without clinical MCI	58	58
Total	649 (100.0%)	649 (100.0%)

Modeling of 10-year Incidence

In the analysis using “dementia and clinical MCI” as a serious cognitive event, participants with two or more risks had a significantly higher chance of transitioning to MCI or dementia compared to the 0-risk group (Odds Ratio: 2.77, p-value: 0.022). Single risk factor did not significantly increase the transition risk (Odds Ratio: 1.929, p-value: 0.5419).

Table 4 and Figure 1 show the computed probability from the 10-year dataset as a function of age at enrollment. Based on Table 4, participants with two or more risks had an approximately 2.5 times higher chance of transition to MCI or dementia both for males and females within 10 years of follow-up compared to the participants that had none of the studied risks, regardless of the age of entry or definition of the cognitive impairment. Figure 1 shows a trend of increasing probability as age at entry increases. As shown in Table 4, the probability of transition to MCI or dementia for females increased by 14% (from 80 to 85 years old) to 82% (from 60 to 65 years old) with five years increase in age at recruitment. For male participants, the chance was 81% (from 60 to 65 years old) and 5% (from 80 to 85 years old) higher. The upward trend weakens when the participant is recruited at 85 or older. Consequently, an 80-year-old participant was approximately 5.0 and 6.4 times more likely to develop dementia or clinical MCI within 10 years compared to a 0-risks 60-year-old male and female participant. The transition was 4.7 and 5.9 times more likely for the 1-risk group; it was 4.6 and 5.6 times more likely for the 2-risk group. Additionally, aside from the participants with two or more risks, the chance of cognitive impairment appeared to rise until 85 years of age, reaching its highest point at 85, irrespective of risk status.

Table 4:

Predicted Ten-year Probability of a Serious Cognitive Event as a Function of Age at Entry and Number of Risk Factors

		Serious Cognitive Impairment
		Clinical MCI or Dementia			Dementia
Sex	Age at Entry	0 risks	1 risk	2+ risks	0 risks	1 risk	2+ risks
Female	60	0.028	0.052	0.074	0.023	0.040	0.049
	65	0.051	0.094	0.132	0.042	0.072	0.087
	70	0.088	0.158	0.218	0.071	0.121	0.148
	75	0.136	0.237	0.321	0.110	0.185	0.228
	80	0.180	0.308	0.414	0.149	0.251	0.315
	85	0.205	0.349	0.470	0.177	0.301	0.385
	90	0.206	0.355	0.487	0.188	0.323	0.423
Male	60	0.032	0.061	0.086	0.015	0.026	0.032
	65	0.058	0.106	0.149	0.027	0.046	0.057
	70	0.094	0.170	0.235	0.044	0.077	0.097
	75	0.134	0.237	0.326	0.065	0.116	0.149
	80	0.161	0.284	0.394	0.085	0.153	0.204
	85	0.169	0.300	0.422	0.095	0.177	0.243
	90	0.160	0.290	0.417	0.097	0.183	0.260

Figure 1:

Predicted Probability of Dementia After 10 Years of Follow-up for UK-ADRC cohort Participants

To compare the results with previous studies, we take results from Huang et al. (2004)²⁹. Huang et al. (2004)²⁹ used multiple levels of family history with and without APOE4 to find relative risk and we calculated the odds ratio of dementia for 0 and 2-or-more risk groups using these, assuming 6 years of follow-up to match. While the comparison is limited since the covariates could not be adjusted, the odds ratios from Huang et al are in the range of 0.74 to 1.46 for the group having APOE4 or family history, and 1.65 to 3.16 for the group having both APOE4 and family history, which is somewhat consistent with odds ratio 1.59 (0 vs 1 risk group) and 2.50 (0 vs 2-risks group) from our model.

Follow-up time and Odds Ratio

Enough observation time was crucial to observe serious cognitive impairment; however, longer observation did not guarantee lower p-value and higher odds ratio. For instance, the odds ratios comparing the 1-risk group to the 0-risk group for clinical MCI or dementia are 0.98, 1.93, 1.96, 1.81, and 1.83 (at 5, 10, 15, 20, and 25-year dataset, respectively). Similarly, the odds ratios for the 2-risks group compared to the 0-risk group are 2.21, 2.77, 2.99, 3.69, and 2.97, with corresponding p-values of 0.0304, 0.0215, 0.0179, 0.0046, and 0.0288. Both odds ratios exhibit an increasing trend followed by a peak and a subsequent decrease. Notably, the 0-risk group demonstrates slower cognitive decline compared to the other groups, resulting in changing incident ratios among the groups over time.

Estimation of Cumulative Incidence Function

Our approach involves estimating the number of transitions at each follow-up year by fitting the data across all possible follow-up years, and predicting the chance of serious cognitive impairments for the given follow-up year. The cumulative incidence function is obtained when the predictions are plotted by follow-up years for the given risk group. Figures 2 and 3 illustrate the cumulative number of transitions to dementia and clinical MCI assuming 100 participants were recruited in each specific risk group and age at entry.

Figure 3:

Predicted Cumulative Number of Conversions to Dementia & Clinical MCI by Follow-up year among 100 Participants Recruited at Age 80

The cumulative plots presented demonstrate the sub-distribution or cumulative incidence function of cognitive transitions, which provides the expected observation time for these events. Table 4 demonstrates the average observation time for cognitive event transitions to occur in adequate numbers to allow accurate risk assessment.

Estimation of Observation Time for Cognitive Impairments

Studying cognitive transitions requires a lengthy follow-up period, making it challenging to adjust to inclusion/exclusion criteria once the study is underway. Therefore, understanding risk factors and predicting incidence rates and their observation time are crucial when recruiting participants to an observational longitudinal cohort.

The incidence rate can be inferred from the cumulative incidence function we derived. In the present study, we present Figures 2 and 3 along with Table 4, illustrating the expected number of transitions to MCI or dementia assuming 100 participants were recruited. The plots and Table 4 can help estimate the required observation time to observe a specific number of transitions. For instance, if 100 individuals with one risk factor are recruited at age 70, approximately 17 transitions for males, and 16 transitions for females are expected after a 10-year follow-up, and 30 events for males and 31 for females after a 15-year follow-up (Figure 2).

The mean observation time for the conversion can also be estimated using the cumulative incidence function. On average, it takes about 10.6 years to observe a transition to a seriously impaired cognitive state for a 70-year-old female participant with 0 risk factors, whereas it takes 9.7 years for males (Table 5). Figures 2 and 3 and Table 4 demonstrate that the observation time for cognitive transitions tends to be shorter when participants are recruited at a later age or possess more risk factors, and more transitions occur for the 1 or more risks groups compared to the 0-risk group. The observation time needed to study transition to clinical MCI or dementia is about 2 years shorter for 65- to 70-year-old female and 65-year-old male participants compared to 5-year older participants. For the rest, the difference was smaller. Table 5 shows that it takes approximately 9 to 15% longer to observe a transition to dementia for the 0-risk group compared to the 2-risk group except for the 85-year-old group. The time difference was larger for the female group. Observation time is longer for the study of transition to dementia compared to clinical MCI or dementia; however, Table 5 demonstrates a need for longer observation times in order to study clinical MCI or dementia for the female 1-risk group between age 65 and 70. This effect is due to participants transitioning to clinical MCI and dying without dementia in later life. Figures 2 and 3 also show that the cumulative incidence of cognitive transitions is 2.3 to 2.7 times higher for the 2-risk group compared to the 0-risk group.

Table 5:

Computed Average Observation Time to Observe a Serious Cognitive Impairment as a Function of Age at Entry and the Number of Risks for Two different Definitions of Serious Cognitive Impairment

		Observation Time to Serious Cognitive Impairment (years)
		Clinical MCI or Dementia		Dementia
Age at Entry	Number of Risks	Female	Male	Female	Male
65	0	12.8	11.6	14.3	15.1
	1	12.6	11.3	11.5	12.7
	2	11.7	11.5	12.5	13.6
70	0	10.6	9.7	12.4	13.4
	1	10.3	9.4	9.8	11.2
	2	9.5	9.5	10.8	12.3
75	0	8.2	8.8	10.5	12.0
	1	8.0	8.3	9.4	10.1
	2	7.6	8.4	9.2	11.0
80	0	6.9	7.7	8.7	10.7
	1	6.9	7.6	8.6	8.7
	2	6.3	7.5	7.9	9.7
85	0	5.8	6.2	7.2	9.7
	1	6.6	7.1	8.1	7.4
	2	7.0	8.5	7.0	8.4

Family history

Although many studies have explored the impact of family history on transition to cognitive impairment from a cognitively unimpaired status while controlling for APOE4, family history has received less attention compared to APOE4. In the UK-ADRC cohort, we found that family history increased the risk of transition to cognitive impairment when controlling for APOE4. In the subgroup lacking the APOE4 allele, 37.5% of individuals without a family history transitioned to clinical MCI or dementia, compared to 44.4% for those with a positive family history. Among individuals with one APOE4 allele, 46.9% of those without family history transitioned to clinical MCI or dementia, while the figure rose to 57.5% for the other group. This observation highlights the importance of considering family history as a relevant factor in assessing the risk of dementia in observational cohorts of cognitively unimpaired persons.

Discussion

Applications and findings

Given the gradual progression of cognitive decline resulting in transition events and the extended observation period required to capture such transitions in longitudinal studies, understanding key factors that may optimize the design of an observational risk cohort can have a significant impact on study outcomes. In this manuscript, we examined these key factors and presented the expected cumulative incidence rates over varying follow-up times.

Additionally, we presented the predicted number of transitions at each follow-up year by analyzing the data of 1 to 25 year incidence (Figures 2 and 3), and the average observation time to see a cognitive transition (Table 4). The figures and tables demonstrate that the observation time tends to be shorter when the participants have more risk factors or are recruited at a later age, when a greater number of transitions occur for these higher-risk groups.

Factors Related to Cognitive Events

The present findings suggest that the APOE4 allele alone may not always fully explain the risk in isolation; the goodness-of-fit and the significance of the model improved by pooling the possession of APOE4 and family history into groups compared to including them separately. This is consistent with Seto et al. (2024)¹⁵, who demonstrated a significantly higher association between amyloid-β accumulation and family history when controlling for APOE4. However, Gleason et al. (2019)³⁰ demonstrated an opposing influence of family history, indicating that when a participant reports a family history of dementia, it suggests the participant has access to care and diagnostic information, thereby reducing the risk. This emphasizes the importance of considering family history alongside APOE4 when assessing heritability risks in observational cohorts, particularly when the cohort has a limited sample size.

Nonlinearity of Age

Initially, we assumed a linear relationship between age at entry and its effect. However, as suggested by Treves and Korczyn (2012)³¹, the association between incident dementia and age might not be linear, particularly beyond the age of 90. In the UK-ADRC cohort, there is a noticeable increase in the incidence of death with advancing age at entry, whereas the proportion of persons with MCI declines after the early 80s. Additionally, when stratified by the number of risks, the competing risk of death notably increases for the 0-risk group, especially after an entry age of 77. In addition to the non-linearity of the relationship, only 2.16% (14 participants) of the UK-ADRC cohort entered the study after the age of 90. Hence, risk for individuals aged 90 and older at entry, especially those with 0 risks, should be inferred with caution.

We did not include the age-by-APOE interaction in the final model. The rate of cognitive decline might be different by age and APOE alleles as stated by Vasiljevic et al. (2020)³². The interaction term did not improve the UK-ADRC model and decreased the p-value of the goodness-of-fit test. Since our focus was to fit the conversion of the cognitive status, once the participants were categorized, we stopped collecting data. Therefore, we do not have the finer details on cognitive decline. That is different from Vasiljevic et al. (2020)³², which uses cognitive scores and amyloid-β accumulation as response variables. We suspect that is why we do not see the interaction term as significant.

Planning Cohort Considering Risk factors and Observation Time

In designing a prevention clinical trial, it is desirable to shorten the observation time. It is essential to know the trajectory of the number of cognitive transitions in order to optimize the duration of the observational time frame. Table 5 highlights the average observation time to collect sufficient cognitive transitions, revealing a noticeable decrease in observation time among higher-risk groups. Specifically, the female 0-risk group experienced approximately 7.9% to 11.6% longer observation times for transitions to clinical MCI or dementia compared to participants with two or more risks whereas the difference was 0.9% to 4.8% for males. Moreover, the female 0-risk group required an approximately 10% to 14.8% longer observation time for transition to dementia compared to participants with two or more risks; for males, it took 8.9% to 11.0% longer.

Risk factors and Proportion of Cognitive Impairment

In addition to observation time, the number of risk factors plays a critical role in the proportion of cognitive impairment that may be observed. When two or more risk factors are present, the long-term incidence of dementia is 2.1 to 2.7 times higher than that of the 0-risk group, whereas the long-term incidence of clinical MCI and dementia is 2.3 to 2.7 times higher than that of the 0-risk group.

Variability in Estimation of Cumulative Incidence Function

While the cumulative incident plots (Figures 2 and 3) offer detailed predictions of cognitive events, they exhibit variations characterized by small ups and downs, deviating from a strictly increasing function over follow-up years. This variability arises from fitting models using datasets with different follow-up times, with each point in the cumulative incidence plots representing estimates that incorporate the inherent variabilities of the data into the predictions.

Limitation

Sample bias: Higher Education

The UK-ADRC cohort is a community-based sample that overly represents highly educated individuals. Since higher education is considered protective against conversion to dementia³³, the probability of cognitive impairment at ten years of follow-up might be biased downward. There is an insufficient number of participants with twelve or fewer years of education in this cohort to address this issue.

Limits on UK-ADRC Data and its Implication in Estimation

The analysis set of the UK-ADRC cohort includes 100 subjects with two or more of the risks studied. Considering the age at entry, the occurrence of events within this cohort appeared sporadic and noisy, posing challenges for reliable analysis. For instance, among those with two or more risks, 30% of participants transitioned to dementia in the age range of 70 to 75, but no incident dementia was observed in the 75 to 80 age group; 30% transitioned to dementia between 80 and 85, yet no incident dementia was seen for participants older than 85. Despite the higher propensity for dementia, this variability made it difficult to identify a clear trend of risk associated with age at entry.

Lack of Genetic Information

We acknowledge that this study does not regard genetic information beyond APOE gene. Including a covariate such as Polygenic risk scores (PRS), or investigating interactions between other genetic information and APOE4 could provide valuable insights into the progression of dementia; however, the absence of such data prevented us from incorporating these aspects into our analysis.

Table 3.

Estimated Odds Ratio and 95% Confidence Intervals for Clinical MCI or Dementia as Serious Cognitive Impairment

Follow-up time	Odds Ratio (95% Profile likelihood CI) & p-value
	0 vs 1-risk	0 vs 2+ risks
5 years	0.98 (0.51, 1.90) 0.1913	2.21 (1.00, 4.85) 0.0304
10 years	1.93 (1.15, 3.23) 0.5419	2.77 (1.44, 5.36) 0.0215
15 years	1.96 (1.14, 3.39) 0.6169	2.99 (1.49, 5.99) 0.0179
20 years	1.81 (1.00, 3.27) 0.8330	3.69 (1.70, 8.00) 0.0046
25 years	1.83 (0.99, 3.39) 0.8329	2.97 (1.35, 6.51) 0.0288

Appendix

Table 6.

Participants APOE alleles in the UK-ADRC cohort data (n=649)

		Family history
Apolipoprotein	All	Positive	Negative
ϵ4ϵ4	9 (1.4%)	6 (2.4%)	3 (0.8%)
ϵ4ϵ2	14 (2.2%)	7 (2.8%)	7 (1.8%)
ϵ2ϵ2 or ϵ2ϵ3	97 (14.9%)	31 (12.4%)	66 (16.6%)
ϵ3ϵ4	174 (26.8%)	84 (33.5%)	90 (22.6%)
ϵ3ϵ3	355 (54.7%)	123 (49.0%)	232 (58.3%)
Total	649 (100.0%)	251 (100.0%)	398 (100.0%)

Figure 4:

Predicted Cumulative Number Conversions to Dementia by Follow-up years among 100 Participants Recruited at Age 70

Figure 5:

Predicted Cumulative Number Conversions to Dementia by Follow-up years among 100 Participants Recruited at Age 80

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.