Alzheimer’s disease is an incurable disorder that accounts for up to 70% of all dementia cases. While the prevalence of Alzheimer’s disease and other types of dementia has increased by more than 160% in the last 30 years, the rates of undetected cases remain critically high. The present work aims to address the underdetection of Alzheimer’s disease by proposing four logistic regression models that can be used as a foundation for community-based screening tools that do not require the participation of medical professionals. Our models make use of individual clock drawing errors as well as complementary patient data that is highly available and easily collectible. All models were controlled for age, education, and gender. The discriminative ability of the models was evaluated by area under the receiver operating characteristic curve (AUC), the Hosmer-Lemeshow test, and calibration plots were used to assess calibration. Finally, decision curve analysis was used to quantify clinical utility. We found that among 10 possible CDT errors, only 3 were informative for the detection of Alzheimer’s disease. Our base regression model, containing only control variables and clock drawing errors, produced an AUC of 0.825. The other three models were built as extensions of the base model with the step-wise addition of three groups of complementary data, namely cognitive features (semantic fluency score), genetic predisposition (family history of dementia), and cardio-vascular features (BMI, blood pressure). The addition of verbal fluency scores significantly improved the AUC compared to the base model (0.91 AUC). However, further additions did not make a notable difference in discriminatory power. All models showed good calibration. In terms of clinical utility, the derived models scored similarly and greatly outperformed the base model. Our results suggest that the combination of clock symmetry and clock time errors plus verbal fluency scores may be a suitable candidate for developing accessible screening tools for Alzheimer’s disease. However, future work should validate our findings in larger and more diverse datasets.