Odds to Quicken Reporting Already Delayed Cases: Acquired Immune Deficiency Syndrome Incidences are Illustrated

Delayed reporting in a medical system complicates efforts to estimate the number of cases that occurred in a time period. A case in point is the government’s difficulty to estimate the number of Acquired Immune Deficiency Syndrome (AIDS) cases. The reporting delays are not intentional but are ongoing due to changing Federal regulations or medical definitions of the case like AIDS. To simplify the complications, this article approaches by modifying the geometric distribution. To be specific, let 0<1-θ<1 is a chance for a case (like AIDS) to be reported in the same time period of its occurrence to a (Federal or other) agency. If the reporting is missed in its occurrence time period, the case gets reported in a next or later time period. Let Y be the number of time periods skipped until its reporting. In this process, the reporting probability in a current period is chained with that of past period with an "odds of quickening" to report. The implication and significance of "quickening odds" are investigated and explained in this article, using the AIDS data with delayed reporting.