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About Healthcare Delays: Clarifications by a New Incidence Rate Restricted Bivariate Geometric Distribution

Ramalingam Shanmugam

Abstract



Healthcare professionals warn that a delayed diagnosis and/or treatment delays could be a life and death issue. Probing delays and interpreting them are worthwhile. For a sample, refer Tate et al.’s (2009) data on the number days delayed in the diagnosis and treatment of ovarian cancer cases. Their data hint that the delays differ from a symptom to another as much as in a stage to another in the medical treatment process. The symptoms are abdominal pain (AP), urogenital (U), abdominal distension (AD), bowel habits (BH), abdominal mass (AM), indigestion (I), nausea vomiting (NV), back pain (BP), breathing issues (BI), appetite weight (AW), tiredness (T), pelvic pain (PP). The stages are referral (R), preexisting (PE), ambiguous (A), and definite diagnosis (DD) before the cure. Motivated to comprehend and interpret their frequency patterns and inter-correlations, this article introduces an incidence rate restricted bivariate geometric distribution (IRRBG) with its statistical properties, develops and illustrates a new statistical methodology to explain the impacts of medical delays. In specific, expressions for probabilities for no delay scenario to exist, inter-correlation of delays within a group of symptoms and within a group of treatment stages, the jump ratios (see its definition in section 2), frailties, expected excessive delays, and tail value at risk are derived, computed and interpreted in the ovarian cancer cases. The maximum likelihood estimate (MLE) of the delay incidence and its restriction parameters are obtained. A hypothesis testing procedure for the significance the MLE of the restriction parameter is developed, illustrated, and discussed. Both scope and limitations of our contribution are summarized. Recommendations are stated in the end for further future research work in the end.

Keywords


Correlation, p-value, statistical power, conditional mean and variance, odds ratio, risk

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