Present data come from the longitudinal “Non-demented patients with Parkinson’s disease with and without low Amyloid-beta 1–42 in cerebrospinal fluid” (ABC-PD longitudinal) study, focusing on the predictive value of Aβ42 pathology for cognitive worsening. The study was approved by the local ethics committee (686/2013BO1). Participants were recruited via the outpatient PD clinic or the ward at Tübingen University Hospital’s neurology department. Patients received monetary compensation for travel expenses, and were assessed in the “on-state” with regular dopaminergic medication.

100 non-demented PD patients were selected by pre-screening neurological function confirming PD diagnosis following United Kingdom Brain-Bank criteria (Hughes et al., 1992). All patients received a lumbar puncture at least six weeks before the baseline visit and were between 50 and 85 years old. Patients were able to communicate well with the investigator, understand study requirements and give written informed consent. Diagnosis of PDD according to the Movement Disorder Society (MDS) Task Force criteria (Emre et al., 2007), other concomitant neurodegenerative diseases as well as substance abuse (except nicotine) led to participant exclusion.

Patients’ CSF Aβ42 status was determined using commercially available ELISA kits (INNOTEST; Fujirebio Germany GmbH, Hannover, Germany, RRID: AB_2797385). Patients were divided into two equal sized (n = 50) groups: Aβ42+ (<600 pg/mL) and Aβ42– (≥600 pg/mL). Groups were matched according to age, gender and educational status. For the present analysis, PD-MCI was diagnosed according to the Level I MDS Task Force criteria (Litvan et al., 2012). All 100 patients were included in the analyses.

Testing took place in Tübingen University Hospital. Patients gave written informed consent and were assessed for eligibility based on the in- and exclusion criteria. Additionally to study assessments, most patients had appointments in the Parkinson’s disease outpatient clinic before or after the study visit. Therefore, the order of clinical assessment varied between patients.

Assessments were analyzed manually and data was managed using REDCap electronic data capture tools (Harris et al., 2009; RRID: SCR_003445). Statistical analyses were conducted with R version 4.0.3 (R Core Team, 2014; RRID: SCR_001905) and JASP version 0.13.1 (JASP Team, 2018; RRID: SCR_015823). Due to the small patient samples, Gaussian distribution of data was not assumed resulting in analyses using median, range, Mann-Whitney U tests, χ²-tests, Brunner-Munzel tests (non-parametric trend test with p^″ = test statistic of stochastic equality; Brunner and Munzel, 2000), and binary logistic regressions. Confounders for the logistic regressions were chosen based on significantly differing variables between groups with and without arithmetic errors in financial contexts. Multicollinearity between predictors of the regression models was assessed based on a variance inflation factor (VIF) criterion above 10, not met by any predictor. For inferential statistics, an α-level of 0.05 was applied.

Analyses were conducted with the entire sample. Due to the over-representation of Aβ42+ patients, analyses were repeated with a subsample (N = 63) including all Aβ42- patients (n = 50) and a proportion of 20% Aβ42+ patients (n = 13). This reflects the estimated empirical distribution with a prevalence of AD pathology (Aβ42+, Tau, phosphorylated Tau) in approximately 30 to 40% of predominantly demented PD patients with non-demented PD patients falling considerably below this rate (Boller et al., 1980; Blennow and Hampel, 2003; Braak et al., 2005; Siderowf et al., 2010; Irwin et al., 2012). Unless indicated otherwise, outcomes did not differ between overall and representative sample (see Supplementary Material).

The total sample included 42% PD-MCI patients. Overall, 18% of PD patients (PD-NC and PD-MCI) showed arithmetic errors in at least one of the two financial items. PD-MCI patients showed 1 or 2 errors more frequently (26.2%) than PD-NC patients (12.1%), however, this difference did not reach significance, p^″ = 1.74, p = 0.09. For the Aβ42 groups, 16.0% of positive and 20.0% of negative patients showed arithmetic errors; this was not statistically significant χ²(1) = 0.27, p = 0.60.

The amount of errors differed marginally significantly between PD-NC (0 errors: 87.9%, 1 error: 8.6%, 2 errors: 3.4%) and PD-MCI (0 errors: 73.8%, 1 error: 4.8%, 2 errors: 21.4%), p^″ = −1.92, p = 0.059. The binary logistic regression correcting for the influence of gender, disease duration, and depression [χ²(94) = 11.92, p = 0.018, RMcFadden2 = 0.088, Area under the curve (AUC) = 0.695] revealed the amount of errors was the only significant predictor of cognitive status, with PD-MCI displaying more errors than PD-NC (p = 0.004). This model did not reach significance with the reduced representative sample (see Supplementary Material A). For analyses of RBANS subtests see Supplementary Material B (gender, depression, story memory predict arithmetic errors; differences between arithmetic groups: digit span, list learning, list recognition, picture naming, semantic fluency, line orientation).

Patients with arithmetic errors differed from those without regarding gender (more females), disease duration (longer), depression (lower BDI-II scores), and global cognition (lower MoCA total and RBANS total scale scores, see Table 2). On average, females (0 error: 63.6%, 1 error: 12.1%, 2 errors: 24.2%) committed more errors than males (0 error: 91%, 1 error: 4.5%, 2 errors: 4.5%), p^″ = 3.01, p = 0.004. Effects were the same in the representative sample, except for groups not differing statistically regarding disease duration and depression (Supplementary Material, Table A1).

Results of the binary logistic regression indicated a significant association of gender, disease duration, depression, and all RBANS domain scores with the presence of arithmetic errors, χ²(90) = 51.12, p < 0.001, RMcFadden2 = 0.545, AUC = 0.941. Female gender, long disease duration, low depression scores, impaired attention and visuo-spatial/constructional deficits significantly predicted arithmetic errors (see Table 3). In the representative sample, only attention was a significant predictor for study group (see Supplementary Material, Table A2). In a second binary logistic regression model, confounding variables (gender, disease duration, depression) influenced presence of arithmetic errors χ²(94) = 22.00, p < 0.001, RMcFadden2 = 0.234, AUC = 0.822, while the FAQ score did not (see Table 3). This model was not stable in the representative sample (see Supplementary Material A).

Arithmetic tasks differed regarding error categories in the entire patient sample. For the 5 cent task, place-value integration errors were most frequent (54.5%), followed by procedural (9.1%) and other errors (9.1%). In the 50 cent task, most errors could not be categorized (33.3%) or were magnitude-related (33.3%), followed by procedural (11.1%) and place-value integration errors (5.6%). Importantly, 27.3% (5 cent) and 16.7% (50 cent) of cases were NAs. The proportion of error categories did not differ between cognitive groups or by gender, but descriptively, more place-value integration errors occurred in the 5 cent task compared to the 50 cent task (see Table 4).

The overall frequency of arithmetic errors of 18% in two simple tasks supports the need for further systematic investigation. When correcting for clinical confounders, the amount of errors was able to correctly predict cognitive status where higher errors were indicative of PD-MCI. However, some PD-NC patients also showed arithmetic errors, similar to previous AD studies finding dyscalculia in early stages (Parlato et al., 1992; Martin et al., 2003). Therefore, PD patients showing heterogeneous arithmetic impairments even in early stages and its association to specific cognitive profiles demands further examination. The model using the representative sample did not reach significance, which needs to be interpreted with care due to: a smaller sample (63 instead of 100 patients), an associated decrease in arithmetic errors, a greater tendency to ceiling effects, and a smaller amount of explained variance. Based on the current findings, it is impossible to infer on global financial capacities, as these are defined multidimensionally and exceed arithmetic function alone. However, showing a difference in arithmetic errors between PD-NC and PD-MCI indicates an association of PD disease severity and the likelihood of arithmetic errors in financial contexts.

Profiles of PD patients with arithmetic errors were female, longer disease duration, less depression, and more cognitively impaired. Total MoCA and RBANS scale scores differed significantly between arithmetic groups, suggesting an association between arithmetic errors and cognition in PD. As PD-MCI and longer disease duration predict PDD (Aarsland et al., 2017), our data suggest that arithmetic errors occur within the frame of heterogeneous progressive cognitive deterioration.

When analyzing the proportion of errors (0,1,2), a systematic effect of gender (women made more errors) and cognitive status (PD-MCI patients made more errors) was observed, even after correcting for confounders. However, when error frequency was aggregated (1 or 2 errors in one category), when confounders were not considered, or when a smaller sample was used with a proportion of Aβ42+, differences between PD-NC and PD-MCI were only trends. We attribute this lack of significance when error categories are grouped to a statistical power issue due to sample sizes, tendency toward ceiling effects in the more representative sample, or decreased explained variance. While these results suggest more severe arithmetic errors in more cognitively impaired PD patients, they also advise for a future more systematic assessment.

The binary logistic regressions showed attention, visuo-spatial/constructional function, and story memory predicted arithmetic errors, suggesting degeneration in these domains at least partly causing arithmetic deficits. Current research in PD also discusses the importance of attention and visuo-spatial function for cognitive status und progression to PDD, introducing these domains as candidates for early biomarkers (Lopes et al., 2017; Becker et al., 2020). Associations between visuo-spatial/constructional functions and numerosity in healthy adults are in line with finding visuo-spatial/constructional functions to predict arithmetic errors in the current study (Lammertyn et al., 2002; Thompson et al., 2013). Furthermore, retrieving arithmetic facts requires an intact verbal memory (Dehaene and Cohen, 1997). Interestingly, females showed worse arithmetic performance than males. The gender differences in favor of men are in line with findings by Delazer et al. (2013) and Arcara et al. (2019). They explain advantages of elderly men in arithmetic and financial capabilities with employment in mathematics-related fields, higher level of education (paralleling generational effects) and mathematical interests. The arithmetic advantage for men is remarkable as gender effects usually dissociate from men showing stronger global cognitive decline but indicate differentiated visuo-spatial and verbal memory deficits in female PD patients (Fengler et al., 2016; Bakeberg et al., 2021). Therefore, the current association of visuo-spatial/constructional functions and story memory with arithmetic deficits is in line with finding more arithmetic deficits in female patients.

We also found that patients with arithmetic errors were, on average, less depressed than those without. This contradicts research on numeracy skills negatively affecting mental health in elderly (Fastame et al., 2019), and depression impairing cognitive performance in PD (Alzahrani and Venneri, 2015). As the difference in arithmetic does not seem to be PD-specific or directly related to cognition, the association with gender and education should be addressed to differentiate a coincidental finding from a systematic effect of depression on arithmetic in PD.

The binary logistic regression including ADL explained no more than a small amount of variance in arithmetic errors. The insignificant effect might be explained by patients in the current study being less heavily impacted on ADL, with ADL impairment occurring later in the process of transition from PD-MCI to PDD (Becker et al., 2020).

Most observed errors were place-value integration errors, followed by magnitude-related or procedural errors. Therefore, our data provide first evidence that not all numerical representations are impaired alike in PD. Future research should examine the validity of these results in a systematic methodological setup, with multi-digit and complex arithmetic tasks, enough items for a broader investigation of errors, and enough statistical power to identify PD-specific error categories and differences between cognitive statuses.

The current exploratory study indicates the presence of particular arithmetic error types in financial contexts in PD, which – in some analyses – seem to associate with cognitive decline. These findings are novel in a hitherto neglected research field. However, this study has a couple of limitations, requiring consideration in follow-up studies.

First, the comparison with a healthy elderly group is missing to estimate the extent of impairments. However, finding arithmetic errors in both groups of PD-NC and PD-MCI with arithmetic errors to increase alongside progression of cognitive status indicates differing arithmetic impairments in discrete PD stages. Future studies should include healthy controls for comparisons between PD and the general population as well as more cognitively nuanced PD groups. Second, the methodological approach is not sufficient to provide generalizable inferences on arithmetic errors in financial contexts in PD with a rate of 18%. Yet, these errors are not negligible, but are absent in the diagnostic criteria for cognitive deficits in PD. Third, there were only two items and one type of arithmetic problem. Future studies should employ more systematic and broader assessments (e.g., different operations, different magnitudes, different place-value processing procedures, verbal and non-verbal tasks, symbolic and non-symbolic tasks) to obtain a more comprehensive overview on which errors are PD-specific and how pronounced they are for different numerical representations and processes. Fourth, this study is cross-sectional; however, longitudinal studies, informative for characterizing neurodegenerative processes when appropriately correcting for practice effects and selective attrition (Moody et al., 2017; Tucker-Drob, 2019), are missing. These designs can identify person-to-person heterogeneity in trajectories of lifespan cognitive developments being specific for the respective cognitive ability and interdependent for individuals (see Tucker-Drob, 2019). Heterogeneous arithmetic deficits found in AD (Girelli and Delazer, 2001) stress the need for differential investigations in PD.

In conclusion, while the current study reports first interesting data about arithmetic errors in financial contexts in PD, it is a mere starting point and inspiration to investigate such errors more systematically in the future. The current study suggests: (1) PD patients show arithmetic errors in financial contexts which seem to be more pronounced with cognitive impairment, (2) error type does not seem to be arbitrary but hints at a predominantly impaired place-value processing, and (3) apart from PD-MCI status there is heterogeneity within the groups and distinct attributes such as attention, visuo-spatial/constructional function, gender, or disease duration influence the likelihood of arithmetic errors, (4) The male advantage in arithmetic processing in PD contrasts men’s larger global cognitive decline but follows female visuo-spatial and story memory disadvantages. In sum, we believe that these results suggest arithmetic performance in financial contexts to be a problem in PD-MCI, deserving future attention.