{"id":633,"date":"2015-10-24T08:43:38","date_gmt":"2015-10-24T08:43:38","guid":{"rendered":"http:\/\/idealhealthcare.net\/?p=633"},"modified":"2015-12-01T06:16:51","modified_gmt":"2015-12-01T06:16:51","slug":"mathematics-behind-this-blog","status":"publish","type":"post","link":"http:\/\/idealhealthcare.net\/index.php\/2015\/10\/24\/mathematics-behind-this-blog\/","title":{"rendered":"Mathematics Behind this Blog"},"content":{"rendered":"

\n

Abstract<\/p>
\n

This post develops the simple mathematics necessary to (1) compute the relative importance of each of the six attributes of an ideal healthcare system based on public databases and (2) construct the 6P scoring system.<\/p>
\n

Together these will (1) measure a given country\u2019s healthcare system\u2019s divergence from achieving an ideal healthcare system, (2) rank countries by how close they are to an ideal healthcare system and (3) guide allocation of healthcare budgets to resources that will help most in achieving an ideal healthcare system.

\n<\/div><\/div>\n

Simple Mathematics Proposed in this Blog<\/h1>\n

This blog proposes a mathematical basis for measuring a country\u2019s proximity to a goal of achieving an ideal healthcare system. For this purpose, this blog proposes a scoring\u00a0system called the 6P score. In addition, it proposes a multivariate regression that will establish the relative importance of each of the six principles describing an ideal healthcare system through the computation of regression coefficients. These will help policymakers guide investments in healthcare to derive the best bang for the buck so that at the margin, each dollar is spent on a variable that yields the best improvement in HALE<\/a>.<\/p>\n

In summary,<\/p>\n

1. We start with 6 basic variables that define an ideal healthcare system.<\/p>\n

2. We collect data on these 6 variables from established WHO databases.<\/p>\n

3. We collect data on HALE<\/a>.<\/p>\n

There are several epidemiological variables other than these six that may affect HALE for a country. For example, if the average age of the population is advanced, the HALE by definition, would be skewed accordingly as the elderly may have shorter intervals of healthy periods of life compared to a decidedly younger population. Second, the presence of a sweeping disease epidemic in a country would alter HALE. Third, the presence of wars or catastrophic events can also alter reported HALE.<\/p>\n

<\/a><\/p>\n

If for every country denoted by \"J\", each attribute denoted by \"i\" is allotted a weight of \"w_{i}\" such that \"\sum_{i=1}^{6} (w_{i})=1\". The weight \"w_{i}\" is the same across all countries \"J\". Let the value of each attribute \"i\" for country \"J\" be\u00a0\"v_{iJ}\". This value \"v_{iJ}\" is the amount each country \"J\" has invested in the attribute \"i\". \u00a0\"v_{iJ}\" may be a PPP dollar amount or a rank order or a binary yes\/no variable. Then the weighted average 6P score \"P_{J}\" is:<\/p>\n

<\/a><\/p>\n

(1) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

How to estimate the relative attribute weights \"w_{i}\"? – A multivariate regression<\/span><\/strong><\/h3>\n

The weights \"w_{i}\" are estimated using current data on these attributes. A multivariate regression can be\u00a0run with the six attributes and three epidemiological variables as the independent variables and, say, HALE\u00a0as the dependent variable. The resulting coefficients, for the six variables normalized to a total of 1 become the weights.<\/p>\n

The regression equation would then be:<\/p>\n

\"\vspace{5 pt}HALE =\newline<\/p>\n

where \"w_i\" are the respective coefficients.<\/p>\n

No human investigation can claim to be scientific
\nif it doesn't pass the test of mathematical proof.<\/em><\/p>\n

-Leonardo Da Vinci<\/h2><\/div><\/div>