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Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach.

ABSTRACT: In this communication, based upon the stochastic Gompertz law of population growth, we have reformulated the Leaky Competing Accumulator (LCA) model with multiple alternatives such that the positive-definiteness of evidence accumulation is automatically satisfied. By exploiting the Lie symmetry of the backward Kolmogorov equation (or Fokker-Planck equation) assoicated with the modified model and applying the Wei-Norman theorem, we have succeeded in deriving the N-dimensional joint probability density function (p.d.f.) and marginal p.d.f. for each alternative in closed form. With this joint p.d.f., a likelihood function can be constructed and thus model-fitting procedures become feasible. We have also demonstrated that the calibration of model parameters based upon the Monte Carlo simulated time series is indeed both efficient and accurate. Moreover, it should be noted that the proposed Lie-algebraic approach can also be applied to tackle the modified LCA model with time-varying parameters.

SUBMITTER: Lo CF

PROVIDER: S-EPMC8149408 | biostudies-literature | 2021 May

REPOSITORIES: biostudies-literature

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Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach.

Lo Chi-Fai CF Ip Ho-Yan HY

Scientific reports 20210525 1

In this communication, based upon the stochastic Gompertz law of population growth, we have reformulated the Leaky Competing Accumulator (LCA) model with multiple alternatives such that the positive-definiteness of evidence accumulation is automatically satisfied. By exploiting the Lie symmetry of the backward Kolmogorov equation (or Fokker-Planck equation) assoicated with the modified model and applying the Wei-Norman theorem, we have succeeded in deriving the N-dimensional joint probability de ...[more]

PMID: 34035348

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Project description:Background:Despite similar survival rates, breast-conserving therapy (BCT) remains a distant second choice after simple mastectomy for patients with early-stage breast cancer in Singapore. Uptake of reconstruction after mastectomy is also low (18 per cent). The aim of this study was to explore the factors influencing a patient's choice for mastectomy when eligible for BCT, and why patients decline reconstruction after mastectomy. Methods:Patients from the National Cancer Centre Singapore, who were eligible for BCT but chose mastectomy without reconstruction, between December 2014 and December 2015 were included. An interviewer-administered questionnaire focusing on patients' reasons for choosing mastectomy over BCT and not opting for immediate breast reconstruction after mastectomy was used. Tumour characteristics were retrieved from medical records. Spearman's rank correlation coefficient, Mann-Whitney U and Kruskal-Wallis tests were used to analyse the correlation between the patient's self-rated influential factors and variables. Statistical significance was taken as P < 0·050. Results:Ninety-one patients were included (90·1 per cent response rate). The main reasons for choosing mastectomy over BCT were: fear of cancer recurrence (considered very important in 74 per cent), the perception that health outweighs breast retention (49 per cent) and the possibility of second surgery for margins (40 per cent). Key factors for rejecting immediate reconstruction after mastectomy were: patient-perceived 'old age' (very important in 53 per cent), concern about two sites of surgery (42 per cent) and financial cost (29 per cent). Given a second chance, 19·8 per cent of patients would undergo BCT instead of mastectomy. Conclusion:This study has identified the considerations that women in Singapore have when deciding on breast cancer surgery. Some perceptions need to be addressed for women to make a fully informed decision, especially as one-fifth regret their initial choice.

Dataset Information

Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach.

Publications

Modified leaky competing accumulator model of decision making with multiple alternatives: the Lie-algebraic approach.

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