Cumulative Temporal Patterns

Introduction

Cumulative temporal patterns are produced by applying the incidence-prevalence analytical method run over several years, beginning with 1-year, and ending with n-years.

Two major statistical rules tend to demonstrate through this form of analyses.

  1. Rule 1 states that a regression to the means is assumed to be the case for the series of analyses that are made.  In other words, as Population 1 with size n increases by increments of n, the results are assumed to represent closer and closer outcomes to the true end results.  Restating this in an opposing fashion, it is assumed that each new population that is larger is more representative of th true outcome, meaning that the first population selected was not a perfect match of the entire population thereby producing perfect results.
  2. Rule 2 states that if Population 1 is truly a representative sample of the entire population, and the number of individuals in Population 1 is n, then an evaluation of Population n in the sequence of 1n, 2n, 3n, 4n, 5n should result in an outcome very close to the true and expected values for the larger population.  This is the regression to the means expected with increased sampling sizes for sequential studies.  Examples of applications of this form of evaluation, tested in past analyses of long term studies are as follows.

Example 

Population size n is evaluated.  Population 1 consists of everyone participating in a study during the first month of that study.  This population has to undergo a pre-post test evaluation to determine the learning experience associated with a new educational [program.  You wish to know if this population represents the results for an entire 12 months of repeating this same study on similar populations for the next 11 months.  You decide to monitor the results monthly as well as cumulatively, and measure the statistical significance of any changes in results seen in the pre versus post responses indicative of the learning experience.  Your begin with the assumption that Month 1 may be a bad sample, and expect to see truer results in Month 2 followed by even better results in Month 3.  This should result in an improvement in the scores over time, meaning that later cumulative tests will be more indicative of the overall impact of this progam consisting of 12 months of teaching, to new students each month.    This ‘regression to the means’ assumption also means that your results should first show a trend in outcomes for cumulative scores, and that newer outcomes are going to more than likely look like the final outcomes.

The greatest difference in monthly results statistically has the greatest likelihood of impacting overall scores, so much that they are vastly different from the final scores based on statistical significance test outcomes, occurs only between months 1 and 2, when these two are compared with each other, followed by months 2 and 3, when the 3 months cumulative is compared with the 2 months cumulative.  This is due to the greatest change in n tested and the impact of that n of overall cumulative scores.  In Month 1, you have for example 50 people, and in month 2 you have 100 people to assess for the cumulative score.   This represents a 100% increase in population size, which has a significant impact on the statistical equations being used.  For Month 3, you have 150 people, and this new population constitutes only one-third of the total test population.  This group can only influence the results by one-third, assuming this Month 3 population is riddled with outliers.  Since the outliers problem is rarely the case, the most likely outcome the Month 3 yest will have is to stabilize the overall outcomes of the program.  It is not unusual for a series of monthly tests to show a very good result for Month 1 which is statistically significant, only to be followed by a test result that is not significantly different for Month 2 participants, even though the population and its scores appear to be somewhat similar.  By adding the Month 3 participants to the test population, there is a reversal of the changes seen for Month 1 to Month 2 changes.  The only question remaining is ‘will this tendency for the score and its statistical significance to improve and be more truthful on a monthly basis also present for Month 4?’ 

For Month 4, you repeat the procecss and add the results to your cumulative score evaluation.  The population size has by now increased by only 25%, and the impacts of this new n on the total N lessened considerable compared to the previous two month-to-month change comparisons.  But this larger number has now stabilized your formula used to evaluate statistical significance.  Assuming true samples were presented with each month, and Month 1 population ~ Month 2 ~ Month 3 ~ Month 4, in terms of representing the entire population of expected participants, this 4 month analysis is required to stabilzie results and then confirm this stabilization of the outcomes by engaging in overall statistical significance measures.  Month 5 is the number of studies needed to confirm that sampling and outcomes are what results of Month 3 and 4 suggest.  If this population was pretty much representative of overall population expected and anticipated for 12 months,  if the results are statistically significant at Month 5, the overall program is significant, and the expectation is that on Month 12, these results will remain true to form so long as other outlying changes do not take place.

Since this is a method used to measure learning, and the materials taught are usually new results or innovations, a study of 6 months generally is the longest period you want to perform such a measure.  During the second half of a year, the diffusion of knowledge tends to occur and any new lessons promoted by that program, espeically when it comes to new forms of medical care, become common knowledge, so the learning response decreases by the end of a year.  This is because a new drug, new method of treatment, etc. has undergone published professional criticisms and reviews, meaning that more and more people will commence the educational series knowing this information as soon as they initiate the program.  This means that pre-post test results, in terms of changes in response will lesson. 

The second problem with a 6 versus 12 month approach to reviewing a program is related to the statistical formulas themselves.  For a population os size n, a population of equal size is needed to perform the analysis and have a significant likelihood of changing your averages in some statistically significant fashion.  Averages routinely change from population to population, but statistical significance doesn’t.  One has to double a popular to improve upon a given study type.  For example, were you to study 100 diabetes patients and thought that by adding another 25 you might improve upon your results in terms of them being more like a total population review, you haven’t doubled your original n and have little chance of demonstrating improvements in your response patterns.  You must double the population to accomplish this.  (This is why many national studies involve 250 to 1500 respondents, usually favoring 256 to 512 (i.e. HEDIS); to produce a more accurate study for HEDIS, you would have to double your 516, plus add the other possible candidates, about 80, in case of later disqualification from the HEDIS review).    

Applying this to the above pre-post styudy method, once you’ve completed a 6-month study, with each nerw passing Month, your averages might change, but there will be no more statistical change, since regression to the means is now preventing you from finding statistically signifncat changes in response patterns.  After 6 months, due to new knowledge being disseminated outside the classroom training environment, the pre-test education scores better than during the first few months, and the overall changes pre-post are reduced.  This rarely reduced your scores, except when a particular program goes on too long (>15 mos), resulting in intermediate experience people taking the program during the later months.  

ICD Applications

In terms of statisitical significance measures attached to a study, a 1 month  requries a 2 month, followed by a 4, and then an 8 month to produce statistically significant change.  In terms of performing long term studies such as these studies of ICDs, a 5 year study demonstrates the required regression to the means required for most rare disease types.

For ICDs, a 1-year study usually suffices in n and frequency of that ICD is large enough.  For studies of very rare incidence-prevalence ICDs, the critical n is reached at 3 years of cumulative analysis, surpassed with 4 years, made more reliable with 5 years of studies.  Any subsequent studies for the most part just change the peaks and depressions in the graph, but do very little to impact statistical significance. 

A number of studies demonstrate this behavior using one series of a very rare culturally-derived ICD and three isolated ICDs types that demonstate strong culturally-bound tendencies.  Even though relative few patients, these patients are expected to be cases  representing high percentage groups.  When age grouping occurs in even very rare disease or condition diagnoses, the human tendency is to have these events take place in normal sequence.  Assuming Expectancy of n tested ~ Normal expectancy, with SD = normal values [p ~ 0.05 –> 95%] as well and equally distributed, the most likely ages these events are to occur, do occur, for 90-95% or more of the time with the initial tallies of new cases.  This behavior recurs when you review the same model again the following year, for 90-95% of the time.

These same behaviors were seen for other rare ICDs, such as the following reviewed briefly on the sociocultural page:

  1. 429.83 Takotsubo
  2. 425.3 Obscure African Cardiomyopathy
  3. 300.16 Factitious Disorder
  4. 692.2*  Female Genetic Mutilations
    • 629.20 Unspecified
    • 629.21 Type 1 – Clitorectomy
    • 629.22 Type 2 – Labia minora excision
    • 629.23 Infibulation Status
    • 629.29 Other Mutilation

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