Distracted multinomial model for corona screening at entry ports

Background: On 24 January 2020, 1287 corona cases were noticed in Wuhan, China, causing 41 deaths. Its incubation period is at least 14 days. Now, this deadly virus has spread to other foreign countries. The prevalence of corona cases is changing daily. See www.who.org for daily reports. The corona cases are mystic and nightmare to the public, health professionals, and governing agencies globally.Methods: The Center for Disease Control (CDC) compiled in their webpage (www.cdc.org) the number of confirmed, number of healthy, and the number of pending cases at the port of entries in United States of America (USA). These numbers are perhaps under-estimates because of inappropriate diagnostics and imprecise incubation period. To resolve the under estimating, this article, introduces a distracted multinomial model to refine the imprecise corona screening process and interpret the probability of detecting a corona case in US entry gates.Results: An alternate expression (2) for the correlation between the corona ill and corona free cases at the USA ports of entry reveals that it was rising since 31st January 2020, reached its maximum on 5th February 2020, then declined to hit a bottom on 7th February 2020 only to rise again.Conclusions: Most desirable is an accurate predictability of a traveller with the corona virus at the portal entry to minimize its spread. To make such prediction, a regression is necessary with involvement of covariates like age, body’s immunity level, comorbidity, and precise understanding of its incubation period. The model in this article is the starting point for further future research work.

Learning from an early start but late end epidemics via an incidence rate restricted bivariate distribution and data analysis.

Background: An ideal expectation of public health administrators or field medical workers is to have a late start and quick ending of any epidemic. Instead, when an epidemic starts early but ends late, it is where much can be learned from the incidences. A case in point for discussion in this article is the pattern of 2009 H1N1 epidemic. Methods: With a parameter to portray an existing health environment as a deterrent for an epidemic like H1N1 to outbreak in any location at a week, a bivariate distribution is created and is used to analyze the data for a learning so that it helps to prevent a too long prevailing future epidemic. This new distribution is named Incidence Rate Restricted Bivariate Distribution (IRRBGD). Statistical properties of IRRBGD are derived and illustrated using 2009 H1N1 incidences in all five continental regions (Africa, Asia, Europe, Americas, and Oceanic) across on earth. Results: The Asian continent, compared to other four continental regions, had most vulnerability for H1N1 incidences. The odds for no H1N1 to occur is lowest only in Oceanic among the four continental regions, namely Africa, Europe, Americas, and Oceanic. Since the beginning of the year 2009 with 52 weeks, the week number, Y in which the H1N1 appeared first and the number, X of weeks the H1N1 continued on in a region are consistently highly correlated in all five continental regions. Conclusions: From the data analyses of 2009 H1N1 incidences, no continental region is risk free with respect another round of H1N1 epidemic in future. The medical community and public healthcare administrators ought to identify the common and region specific unique deterrents of the epidemic like H1N1. The impact of such deterrents to H1N1 is captured in our model and analysis. By increasing the deterrent level, the outbreak of an epidemic like H1N1 could be delayed, according to our model and data information.

Never, once, and repeated illness: a geometric view for insights and interpretations.

Background: Medical/health researchers depend on data evidence for knowledge discovery. At times, data analysis to capture the data evidence is overwhelming and the process becomes too tedious to give up the attempt. A prudent thing to do is to seek out a simpler visual approach to obtain insights. One visual approach is devised in this article to understand what the data are really revealing to either get an insight first or then confirm what is intuitively configured by the medical concepts. This visual approach is geometric concepts based. In specific, triangle is employed in this new and novel approach. Methods: A successful treatment of any illness is a consequence of knowledge build-up arising from data mining about the never, once, or repeated episode of a disease incidence in a patient. This article investigates and illustrates a novel and pioneering geometric approach, especially based on the properties of triangle, to extract hidden evidence in the data. New probabilistic expressions are derived utilizing trigonometric relations among the corner points of a triangle. The conceptual contents of this article are versatile enough for different medical/health data analysis. Results: For illustration here, the medical binomial data in Hopper et al. (Genetic Epidemiology, 1990) on the occurrence of asthma or hay fever among the four groups: (1) monozygotic females (MZF), (2) monozygotic males (MZM), (3) di-zygotic females (DZF), and (4) di-zygotic males (DZM) are considered and triangularly interpreted. The results indicate that the angle in the vertex representing one episode is the largest compared to the other two angles in the vertices representing never or repeated episode of an illness among a random sample of twins from these four groups with respect to getting asthma or hay fever. This geometric finding implies that the event of never and the event of repeated incidence of the illness have farthest Euclidean distance in probability sense. In other words, the never and repeated incidences are not in close proximity as probable. Conclusions: This geometric view of this article is versatile enough to be useful in other research studies in drug assessment, clinical trial outcomes, business, marketing, finance, economics, engineering and public health whether the data are Poisson or inverse binomial type as well.

How do queuing concepts and tools help to efficiently manage hospitals when the patients are impatient? A demonstration.

Background: Due to severe pain, patients are impatient in several wings sporadically and more frequently in emergency wing of the hospitals. To efficiently administer in such environment and the hospital management seeks helpful strategies. The queuing concepts and related methodologies can help as this article has demonstrated by an analysis and interpretation of real data from a hospital in Malta. Methods: The queuing concepts are probabilistic and statistical ideas based approach. They require configuration of the rate and pattern of arriving patients, the rate and pattern of the service, the number of channels serving, the capacity of the waiting room, and the criterion for selecting patients for service etc. New ideas are presented in this article to manage in various scenarios of real life emergency operations. The pertinent queuing concepts and tools are made easier for the readers to comprehend and practice in their own situations in which they notice that the patients are impatient in their waiting. Results: Using the new ideas and formulas of this article, the data in the emergency wing of a hospital in Malta (a largest island of an archipelago situated in the center of the Mediterranean with a total population of a million) are analyzed and interpreted. The results clearly explain why there were a prolonged waiting times at the emergency department creating public dissatisfaction and patients were leaving without waiting to be seen. The total time spent by non-urgent patients with nurse and casualty officer is more in the second shift and lesser and lesser in the third and fourth shifts. The interactive time with a nurse by patient is statistically same in all three types: life-threatening, non-life threatening but urgent, and non-urgent. Very strikingly, the patients in all three groups wait longer to be seen by the nurse in shift three and lesser time in shifts two or four. Conclusion: In 21st century with flourishing globalized medical tourism, a standardized approach to minimize efficiently the waiting time in emergency and other wings of the hospitals in developing as much as in developed nations is a necessity as this auricle has pointed out. The impediments and the remedies for an efficient standardization are overdue.

Revelation of shrunken or stretched binomial dispersion and public perception of situations which might spread AIDS or HIV.

Background: In 1985, the center for disease control coined the name: “Acquired Immune Deficiency Syndrome (AIDS)” to refer a deadly illness. The World Health Organization (WHO) estimated that about 33.4 million people were suffering with AIDS and two million people (including 330,000 children) died in 2009 alone in many parts of the world. A scary fact is that the public worry about situations which might spread AIDS according to reported survey result in Meulders et al. (2001). This article develops and illustrates an appropriate statistical methodology to understand the meanings of the data. Methods: While the binomial model is a suitable underlying model for their responses, the data mean and dispersion violates the model’s required functional balance between them. This violation is called over-under dispersion. This article creates an innovative approach to assess whether the functional imbalance is too strong to reject the binomial model for the data. In a case of rejecting the model, what is a correct way of warning the public about the spreads of AIDS in a specified situation? This question is answered. Results: In the survey data about how AIDS/HIV might spread according to fifty respondents in thirteen nations, the functional balance exists only in three cases: “needle”, “blood” and “sex” justifying using the usual binomial model (1). In all other seven cases: “glass”, “eating”, “object”, “toilet”, “hands”, “kissing”, and “care” of an AIDS or HIV patient, there is a significant imbalance between the dispersion and its functional equivalence in terms of the mean suggesting that the new binomial called imbalanced binomial distribution (6) of this article should be used. The statistical power of this methodology is indeed excellent and hence the practitioners should make use of it. Conclusion: The new model called imbalanced binomial distribution (6) of this article is versatile enough to be useful in other research topics in the disciplines such as medicine, drug assessment, clinical trial outcomes, business, marketing, finance, economics, engineering and public health.

An assessment of nurses' sufficient immunity when treating infectious patients using bumped-up binomial model.

Background: In times of an outbreak of a contagious deadly epidemic1-4 such as severe acute respiratory syndrome (SARS), the patients are quarantined and rushed to an emergency department of a hospital for treatment. Paradoxically, the nurses who treat them to become healthy get infected in spite of the nurses’ precautionary defensive alertness. This is so unfortunate because the nurses might not have been in close contact with the virus otherwise in their life. The nurses’ sufficient immunity level is a key factor to avert hospital site infection. Is it possible to quantify informatics about the nurses’ immunity from the virus? Methods: The above question is answered with a development of an appropriate new model and methodology. This new frequency trend is named Bumped-up Binomial Distribution (BBD). Several useful properties of the BBD are derived, applied, and explained using SARS data5 in the literature. Though SARS data are considered in the illustration, the contents of the article are versatile enough to analyze and interpret data from other contagious diseases. Results: With the help of BBD (3) and the Toronto data in Table 1, we have identified the informatics about the attending nurses’ sufficient immunity level. There were 32 nurses providing 16 patient care services. Though the nurses were precautionary to avoid infection, not all of them were immune to infection in those activities. Using the new methodology of this article, their sufficient immunity level is estimated to be only 0.25 in a scale of zero to one with a p-value of 0.001. It suggests that the nurses’ sufficient immunity level is statistically significant. The power of accepting the true alternative hypothesis of 0.50 immunity level, if it occurs, is calculated to be 0.948 in a scale of zero to one. It suggests that the methodology is powerful. Conclusions: The estimate of nurse’s sufficient immunity level is a helpful factor for the hospital administrators in the time of making work schedules and assignments of the nurses to highly contagious patients who come in to the emergency or regular wings of the hospital for treatment. When the approach and methodology of this article are applied, it would reduce if not a total elimination of the hospital site infections among the nurses and physicians.

Does smoking delay pregnancy? Data analysis by a tweaked geometric distribution answers.

Background: Smoking is generally known to be carcinogenic and health hazardous. What is not clear is whether the smoking impacts on the woman’s reproductive process. There have been medical debates on whether a woman in the child bearing age may delay her pregnancy due to smoking. A definitive conclusion on this issue has not been reached perhaps due to a lack of appropriate data evidence. The missing link to answer the question might be exercising a suitable model to extract the pertinent data information on the number of missed menstrual cycles by smoking women versus non-smoking women. This article develops and demonstrates a statistical methodology to answer the question. Methods: To construct such a needed methodology, a new statistical distribution is introduced as an underlying model for the data on the number of missed menstrual cycles by women who smoke. This new distribution is named Tweaked Geometric Distribution (TGD). Several useful properties of the TGD are derived and explained using a historical data in the literature. Results: In the data of 100 smokers and 486 non-smokers, on the average, smoking women missed 3.22 menstrual cycles and non-smoking women missed only 1.96 menstrual cycles before becoming pregnant. The smoking women exhibited more variation than the non-smoking women and it suggests that the non-smoking women are more homogeneous while the smoking women are more heterogeneous. Furthermore, the impairment level to pregnancy due to smoking among the 486 women is estimated to be 5% in a possible scale of zero to one. The 5% impairment level appears like a small amount, but its impact can be felt once it is cast in terms of fecundity. What is fecundity? The terminology fecundity refers the chance for a woman to become pregnant. The fecundity is 0.24 for smoking woman while it is 0.34 for non-smoking woman. The fecundity of a non-smoking woman is more than twice the fecundity of a smoking woman. Conclusion: The smoking is really disadvantageous to any one in general and particularly to a woman who wants to become pregnant.