Categories
General Statistical Applications Podcasts (audio)

Why Predictions of Surgery-Duration are So Poor, and a Possible Remedy (Podcast)

Accurate prediction of surgery-duration is key to optimal utilization of operating theatres. Yet, current predictions, based on best available statistical and AI techniques, are highly inaccurate. This causes operating rooms worldwide to operate in a sub-optimal mode. Based on personal experience, supported by recently published three peer-reviewed articles, we believe that the poor state-of-the-art of current predictive methods for surgery-duration is traceable to a single cause. What is it? What is the remedy?

Literature

[1] Shore, H (1986). An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres. J. Statist. Com. Simul. 1986; 23:157-81. Available on Shore’s ResearchGate page.

[2] Shore, H (2020). An explanatory bi-variate model for surgery-duration and its empirical validation, Communications in Statistics: Case Studies, Data Analysis and Applications, 6:2, 142-166, DOI: 10.1080/23737484.2020.1740066 .

[3] Shore, H (2021a). SPC scheme to monitor surgery-duration. Qual Reliab Eng Int. 37: 1561– 1577. DOI: 10.1002/qre.2813 .

[4] Shore, H (2021b). Estimating operating room utilisation rate for differently distributed surgery times. International Journal of Production Research. DOI: 10.1080/00207543.2021.2009141

[5] Shore, H (2021c). “Predictive Methods for Surgery Duation”Wikipedia. April 16, 2021.

Categories
General Statistical Applications

Why Surgery-Duration Predictions are So Poor, and a Possible Remedy

Operating theatres are the most expensive resource at the disposal of hospitals. This renders optimizing scheduling of surgeries to operating rooms a top priority. A pre-condition to optimal scheduling is that accurate predictions of surgery-duration be available. Much research effort has in recent years been invested to develop methods that improve the accuracy of surgery-duration predictions. This ongoing effort includes both traditional statistical methods and newer Artificial Intelligence (AI) methods. The state-of-the-art of these methods, with relevant peer-reviewed literature, have recently been summarized by us in a new entry on Wikipedia, titled “Predictive Methods for Surgery Duation”.     

Personally, I was first exposed to the problem of predicting surgery-duration over thirty years ago, when I was involved in a large-scale project encompassing all governmental hospitals in Israel (at the time). Partial results of this effort had been reported in my published paper of 1986, and further details can be found in my more recent paper of 2020. Both articles are listed in the literature section at the end of this post (for podcast listeners, this list may be found on haimshore.blog).

My second involvement in developing predictive methods for surgery-duration was in more recent years, culminating in three peer-reviewed published papers (Shore 2020, 2021 ab; see references below).

Surgery-duration is known to be very highly volatile. The larger the variability between surgeries, the less accurate the prediction may be expected to be. To reduce this variability, newly devised predictive methods for surgery-duration tend to concentrate on subsets of surgeries, classified according to some classification system. It is assumed that via this classification, prediction accuracy may be enhanced. A common method to classify surgeries, implemented worldwide, is Current Procedural Terminology (CPT®). This coding system delivers, in a hierarchical fashion, particular codes to subsets of surgeries. In doing so, variability between surgeries sharing same CPT code is expected to be reduced, allowing for better prediction accuracy.

A second effort to increase accuracy is to include, in the predictive method, certain factors, known prior to surgery, which deliver variability to surgery-duration. It is hoped that by taking account of these factors, in the predictive method, unexplained variability in surgery-duration will be reduced, thereby enhancing prediction accuracy (examples will soon be given).

A third factor that influence accuracy is the amount of reliable data, used to generate predictions. Given recent developments in our ability to process large amounts of data, commonly known as Big Data, Artificial Intelligence (AI) methods have been summoned to assist in predicting surgery times.

These new methods and others are surveyed more thoroughly in the aforementioned entry on Wikipedia.

The new methods notwithstanding, current predictive methods for surgery-duration still deliver unsatisfactory accuracy.

Why is that so?

We believe that a major factor for the poor performance of current predictive methods is lack of essential understanding of what constitute major sources of variability to surgery-duration. Based on our own personal experience, as alluded to earlier, and also on our professional background as industrial engineers, specializing in analysis of work processes (of which surgeries are an example), we believe that there are two sets of factors that generate variability in surgery-duration: A set of major factors and a set of secondary factors. We denote these Set 1 and Set 2 (henceforth, we refer only to variability between surgeries within a subset of same code):

Set 1 — Two Major Factors:

  • Factor I. Work-content instability (possibly affected by variability in patient condition);
  • Factor II. Error variability.

Set 2 — Multiple Secondary Factors, like: patient age, professional experience and size of medical team, number of surgeries a surgeon has to perform in a shift, type of anaesthetic administered. 

Let us explain why, in contrast to current practices, we believe that work-content instability has critical effect on prediction accuracy, and why accounting for it, in the predictive method, is crucial to improving current accuracy, obtained via traditional methods.

To prepare predictions for any random phenomenon, assumed to be in steady-state, the best approach is to define its statistical distribution and estimate its parameters, based on real data. Once the distribution is completely defined, various statements about the conduct of the random phenomenon (like surgery-duration) can be made.

For example:

  • What is the most likely realization (given by distribution’s mode);
  • What is the middle value, which delivers equal probabilities, for any realization, to be larger or smaller than that value (expressed by distribution’s median);
  • What is the probability that any realization of the random phenomenon exceeds a specified value (calculated by the cumulative density function, CDF)?

Understanding that complete definition of the distribution is the best approach to predict surgery-duration, let us next explain what type of distributions can one expect in the two extreme states, regarding the two major factors of Set 1:

State 1. There is no variability in work-content (there is only error variability);

State 2. There is no error (error variability is zero; there is only work-content variability).

The two states define two different distributions for surgery-duration.

The first state, State 1, implies that the only source of variability is error. This incurs the normal distribution, for an additive error, or the log-normal distribution, for a multiplicative error (namely, error expressed as a percentage).

State 2, lack of error variability, by definition can only materialize when there is no typical value (like the mode), on which error can be defined. Since no definition of error is feasible, error variability becomes zero. For work-processes, like surgery, this can happen only when there is no typical work-content. In statistical terms, this is a state of lack-of-memory. An example is the duration of repair jobs at a car garage, relating to all types of repair. The distribution typical to such situations is the memoryless exponential.

We learn from this discussion, that any statistical model of surgery-duration, from which its distribution may be derived, needs to include, as extreme cases, both the normal/lognormal distributions and the exponential distribution.

This is a major constraint on any model for the distribution of surgery-duration. It has so far eluded individuals engaged in developing predictive methods for surgery-duration. Lack of knowledge of basic principles of industrial engineering, as well as total ignorance regarding how instability in work-content of a work process (like surgery) influences the form of the distribution, these probably constitute the major culprit for the poor current state-of-the-art of predicting surgery-duration.

In Shore (2020), we have developed a bi-variate model for surgery-duration, which delivers not only the distributions of surgery-duration in the extreme states (State 1 and State 2), but also the distributions of intermediate states, residing between the two extreme states. The two components of the bi-variate model represent work-content and error as two multiplicative random variables, with relative variabilities (standard deviations) that gradually change as surgery-duration moves from State 1 (normal/lognormal case) to State 2 (exponential case).

What do we hope to achieve with publishing of this post (and the accompanying podcast)?

We hope that individuals, engaged in developing predictive methods for surgery-duration, internalize the grim reality that:

  1. Unless their predictive method allows for the normal/lognormal and for the exponential to serve as exact distributions of surgery-duration at the extreme states;
  2. Unless their predictive method allows intermediate states, spanned on a continuous spectrum between the two extreme states, to converge smoothly to these states (as in Shore, 2020),

unless these two conditions be met, the likelihood for the accuracy of predictive methods for surgery-duration to improve anytime soon, this likelihood would remain, as it is today, extremely slim.

Literature

[1] Shore, H (1986). An approximation for the inverse distribution function of a combination of random variables, with an application to operating theatres. J. Statist. Com. Simul. 1986; 23:157-81. Available on Shore’s ResearchGate page.

[2] Shore, H (2020). An explanatory bi-variate model for surgery-duration and its empirical validation, Communications in Statistics: Case Studies, Data Analysis and Applications, 6:2, 142-166, DOI: 10.1080/23737484.2020.1740066 .

[3] Shore, H (2021a). SPC scheme to monitor surgery-duration. Qual Reliab Eng Int. 37: 1561– 1577. DOI: 10.1002/qre.2813 .

[4] Shore, H (2021b). Estimating operating room utilisation rate for differently distributed surgery times. International Journal of Production Research. DOI: 10.1080/00207543.2021.2009141

[5] Shore, H (2021c). “Predictive Methods for Surgery Duation”. Wikipedia. April 16, 2021.

Categories
My Research on the Bible and Biblical Hebrew Podcasts (audio)

Agag, Haman the Agagite, Gog, Magog, Gag — What binds them all together? (Podcast)

On the general concept of “Roof” in the Hebrew Bible, and what does it really signify:

Categories
Historical Coincidences My Research on the Bible and Biblical Hebrew

Agag, Haman the Agagite, Gog, Magog, Gag — What binds them all together?

Gag in Hebrew is roof. For example:

“I lie awake; I have become like a bird on the roof (Gag)” (Psalm 102:8; 102:7, in some English translations).

Agag was king of Amalek. The latter, throughout the Bible, serves as epitome for the disconnect between the Heaven and the Earth (Genesis 1:1). Therefore, the Israelites are explicitly commanded, in no ambiguous terms:

“Remember what Amalek had done to you on the way, when you came out of Egypt…you shall blot out the memory of Amalek from under the sky; thou shall not forget” (Deuteronomy 25:17,19).

The Bible tells us about king Saul, and what he did to Agag, king of Amalek:

“He took Agag king of Amalek alive, and utterly destroyed all the people with the sword” (1 Samuel 15:8).

Haman, a central figure in the Book of Esther, was the first historic figure to conceive and then attempt to implement a “Final Solution” on the Jewish people (during the reign of the Persian Empire, as expounded in detail in the Book of Esther). Haman was a descendent of Agag, namely, of Amalek seed:

“Esther again pleaded with the king, falling at his feet and weeping. She begged him to put an end to the evil plan of Haman the Agagite, which he devised against the Jews” (Esther 8:3).

Gog and Magog are well-known names, central to Ezekiel’s prophecy of End-Time final war:

“Son of man, set your face against Gog, of the land of Magog, the chief prince of Meshech and Tubal, and prophesy against him” (Ezekiel 38:2).

What binds together all these names?

Answer: The double appearance of a single letter of the Hebrew Alphabet, the third letter, Gimel (corresponding to the English g).

In Biblical Hebrew, as well as in modern Hebrew, a double appearance of Gimel forms the Hebrew word Gag (written with two Gimels, גג). This combination has a single meaning — “Roof”.

The roof is that part of a house, which protects its residents from harm that may befall them from the sky.

In biblical terms, the roof attains a much wider meaning, indeed a gigantic symbolic significance:

As a roof of a house disconnects earth from sky, the biblical “Roof” symbolizes disconnect between “The Heaven” and “The Earth”, as these are alluded to in the first verse of Genesis:

“In the beginning Elohim created the heaven and the earth” (Genesis 1:1).

The most concrete biblical allusion to this interpretation is given by the command, given to the Israelites, to build booths (Sukot) during the Feast of Tabernacles:

“You shall dwell in booths for seven days; All native-born Israelites are to live in booths so that your descendants will know that I made the Israelites live in booths when I brought them out of Egypt. I am the Lord your God” (Leviticus 23:42).

There is no solid protective roof for the booths, where the Feast of Tabernacles is celebrated. Traditionally, the roof must be made from natural elements that have grown from the ground. Most people use either palm fronds or bamboo with wooden beams as support. The roof also must be thick enough to provide significant shade, but thin enough to let the stars shine through.

Why does the Sukkah not have a solid roof? What does this signify?

The answer is simple: Lack of solid roof signifies complete faith in Divine Providence, in Divine protection against harm that may befall us. Conversely, relying on the symbolic “physical roof” as protection, perhaps sole protection, signifies a deep faith that “The Earth” (Genesis 1:1) is all that there is. There is no heaven. There is no God.

The roof of a house generates a disconnect from the sky. Symbolically, sitting in the booth during the Feast of Tabernacles, while removing the roof, signifies faith in Divine protection that would protect against any harm (from the sky or otherwise). And more generally, complete faith in the connection between “the heaven” and “the earth”.

Amalek embodies the opposite: There is no heaven, no system of Divine justice, no God. There is only “the earth” (the observable physical reality, ruled by law of nature). Everything else, which looks random, is indeed random. There is no Divine Providence.

Agag, Haman the Agagite, Gog, Magog — they all represent the Amalekite philosophy of life: “No God, no heaven, all is coincidental”. The biblical concept of “Roof” symbolizes exclusive reliance on our own ability (and capability) to understand nature, rule nature, and construct the needed “Roof” that would protect us.

“Roof”, consistently throughout the Bible, is an integral part of names of historic figures, past (Agag) or future (Gog), and of names of lands (like the mysterious Magog), which represent a philosophy diagonally opposite to that of the Bible, a philosophy central to current Western Civilization (see here) — the Amalekite philosophy of life.

Surprisingly and unexpectedly, all these names include the Hebrew “Gag” (Roof).

And how will the future Gog and Magog war end?

Quote from prophet Zechariah:

“And it shall come to pass, that every one that is left of all the nations, which have come against Jerusalem, shall go up, every single year, to bow before the King, the Lord of hosts, and to celebrate the Feast of Tabernacles” (Zechariah 14:16).

Personal confession: Amazing!!

Comment.

The Israelites, on their way to the promised land, committed two major sins, both being testimony to lack of faith in Divine protection:

  • The sin of the Golden Calf (in Hebrew, sin of the Egel);
  • The sin of the spies (sin of the Meraglim).

Both sins are considered, in Jewish tradition, to have fateful consequences to Jewish history.

The first sin caused Moses to smash the first tablets with the Ten Commandments. This required of Moses going up Mount Sinai to receive the tablets the second time.

The second sin occurred, in Jewish tradition, on the ninth of the month of Av. In Jewish tradition, this was the date when the two temples in Jerusalem had been destroyed. Other catastrophes in Jewish history are also known to occur on that same date.

Surprisingly, Hebrew names of both sins have, as their middle letter, the second most rare letter in biblical Hebrew, the letter Gimel.

With these two sins, combined, the Israelites, on their way to the promised land, formed their own particular version of GAG (“Roof”).

 

Categories
My Research on the Bible and Biblical Hebrew Podcasts (audio)

Is Torah Divinely Inspired? (Podcast)

Three research efforts that have found shared patterns between scientific models of physical reality, the Hebrew Bible and biblical Hebrew.

How are these associated with the critical question of whether Torah is divinely inspired?

YouTube addresses of all three videos are given below (on haimshore.blog):

Fibonacci Numbers in Biblical Hebrew

Physical Properties in Biblical Hebrew Words

Genesis 1:1 and Pi

Categories
My Research on the Bible and Biblical Hebrew Shorties Videos

Is Torah Divinely Inspired?

The first verse of Genesis reads:

“In the beginning Elohim created the heaven and the earth”.

This means that there are two worlds apart: The heaven and the earth.

Two cultures prevail over Planet Earth:

Culture 1: There is only “The earth” (namely, the observable physical world). There is no heaven.

Culture 2: There are two worlds, and our duty is to connect the two.

The first, Culture 1, prevails in current Western Civilization.

Culture 2 is cornerstone in Judaism, and probably also in other monotheistic faiths.

The question of whether Torah is divinely inspired is tightly linked to the choice between the two cultures (as succinctly outlined above):

According to Culture 2, Torah is divinely inspired. Therefore, it represents the Divine moral code, the spiritual dimension of our physical existence on Planet Earth, with the Ten Commandments at its center, and details scattered throughout the Five Books of Moses (Torah). If Torah is divinely inspired, we are here to connect the heaven and the earth.

According to Culture 1, Torah is a historic relic of human writings from ancient times. In view of the scientific progress, made over recent centuries, in understanding how the physical world is structured and how it is functioning, Torah is no more relevant to our lives. Torah can only serve in academia as a subject of scientific research of ancient cultures.

How do we decide between the two cultures?

How can we lend scientific validity to the truth of one culture over the other?

In other words: How do we scientifically prove, or disprove, that Torah is divinely inspired?

Numerous words and lectures, nowadays also videos, have been produced to address this extremely critical question. Endless number of words of persuasion, one way or another, have been put forward.

We believe that there is a single method to scientifically address this question:

To find out whether certain patterns, recently discovered by science to widely prevail in scientific models of the physical world, whether these same patterns also prevail in Torah and in its original language, namely, biblical Hebrew.

Can we scientifically demonstrate that, indeed, “In the beginning, God created the heaven and the earth”?

Three such research efforts have been carried out in recent years (expounded in three meticulously-produced videos by Oren Evron):

  • Rav Ginsburgh, on Fibonacci numbers in biblical Hebrew (Hebrew; English subtitles, please activate):
  • Professor Haim Shore (me), on the reflection of numeric values of physical reality in corresponding biblical Hebrew words (English):
  • Oren Evron, on the associations between numbers, relating to the first verse of Genesis (in its original biblical Hebrew) and constant Pi, cornerstone and frequent-visitor in numerous scientific models of physical reality (English):
Categories
My Research on the Bible and Biblical Hebrew Shorties

Values of Hebrew Day-Names in Genesis 1 Represent Ordinal Positions

All week-days in Genesis 1 have specific names.

These are (Hebrew, left to right):

Echad (“One”; Sunday); Sheni (“Second”; Monday); Shlishi (“Third”; Tuesday); Reviee (“Fourth”; Wed.); Chamishi (“Fifth”; Thurs.); Yom Ha-Shishi (“The Sixth Day”; Friday); Yom Ha-Sheviee (“The Seventh Day”; Sat.) or Shabbat (Sabbath).

Each of these biblical Hebrew names has a specific numerical value, the sum total of the numeric values of the Hebrew letters comprising the name.

Do these values represent the ordinal position of the days they represent?

Pursuing the same method used by me throughout my research of the Bible and biblical Hebrew (namely, “linear plot indicates same set of values, represented by two different scales”), the attached plot, with the explanatory comments that follow, seem to support the claim expressed in the title of this post:

,

Categories
Podcasts (audio)

Punishment vs. Guidance — Explaining Adverse Outcome of Well-intentioned Behavior (Podcast)

“Why Bad Things Happen to Good People?”

A somewhat original insight to an age-old mystery:

 

Categories
General Podcasts (audio)

How Israel Transformed from a Land of Common-Sense to a Bastion of Formalities (Podcast)

A magnifying glass directed at the fundamental transformation that the Israeli society is going through, shifting personal responsibility, mandated by free-will, to the responsibility of court of law:

Categories
Podcasts (audio)

Why Trust Bible Prophets?? (Podcast)

(Find complete post at: Why do I Trust the Biblical Prophets??)

Israelite prophets, whose prophecies are everywhere in the Jewish Bible, right left and center, explicitly stated that God, the creator of “The Heaven and The Earth”, had spoken to them.

Should we trust them?