Methods for setting thresholds in time series analysis - Revision history

Bosmana fem at 20:23, 22 March 2023

2023-03-22T20:23:02Z

← Older revision		Revision as of 20:23, 22 March 2023
Line 48:		Line 48:
	* Vladimir Prikazsky		* Vladimir Prikazsky
	* Lisa Lazareck		* Lisa Lazareck

			[[Category:Analysis by time characteristics]]

Bosmana fem: /* Comparing numbers, proportional morbidity, or rates with similar periods in the past. */

2022-12-18T15:14:38Z

Comparing numbers, proportional morbidity, or rates with similar periods in the past.

Bosmana fem: /* Doubling or tripling the absolute number of cases over a given time period */

2022-12-18T15:13:19Z

Doubling or tripling the absolute number of cases over a given time period

← Older revision		Revision as of 15:13, 18 December 2022
Line 12:		Line 12:
	==Doubling or tripling the absolute number of cases over a given time period==		==Doubling or tripling the absolute number of cases over a given time period==
	Although simple, this method is crude because it does not consider the number of cases on which the increase is calculated. Doubling the number of cases from 10 to 20 carries a greater statistical significance than doubling the number from 3 to 6. As an alternative, to enhance the method, a Poisson test can be applied to express the departure from previous period values (figure 2). For example, the averaged value observed in the previous 5 weeks is the parameter expected in the Poisson test. The test returns the probability of observing the number of cases, or more, for the week to test, assuming the average value is expected. For example, if three cases, on average, have been notified weekly in the past five weeks, the probability of notifying six cases or more is 0.084 (8.4%) using a Poisson test. This means such an observation may occur by chance once every 12 weeks. Applying the same approach to 20 cases when only 10 are expected yields a probability of 0.0035 (0.35%), potentially occurring by chance only once every 6 years.		Although simple, this method is crude because it does not consider the number of cases on which the increase is calculated. Doubling the number of cases from 10 to 20 carries a greater statistical significance than doubling the number from 3 to 6. As an alternative, to enhance the method, a Poisson test can be applied to express the departure from previous period values (figure 2). For example, the averaged value observed in the previous 5 weeks is the parameter expected in the Poisson test. The test returns the probability of observing the number of cases, or more, for the week to test, assuming the average value is expected. For example, if three cases, on average, have been notified weekly in the past five weeks, the probability of notifying six cases or more is 0.084 (8.4%) using a Poisson test. This means such an observation may occur by chance once every 12 weeks. Applying the same approach to 20 cases when only 10 are expected yields a probability of 0.0035 (0.35%), potentially occurring by chance only once every 6 years.

	Figure 2: Using a Poisson test to detect unexpected changes		Figure 2: Using a Poisson test to detect unexpected changes
	[[File:Poissontest.png\|600px\|frame\|none]]		[[File:Poissontest.png\|600px\|frame\|none]]


	==Comparing numbers, proportional morbidity, or rates with similar periods in the past.==		==Comparing numbers, proportional morbidity, or rates with similar periods in the past.==

Bosmana fem at 15:10, 18 December 2022

2022-12-18T15:10:29Z

← Older revision		Revision as of 15:10, 18 December 2022
Line 1:		Line 1:
	~~Temporal~~ analysis ~~consists in identifying~~ abnormal events in ~~the~~ temporal distribution ~~of a disease~~. This can be straightforward for rare diseases requiring immediate notification, but often requires ~~the use of~~ statistical methods to differentiate abnormal events from the expected fluctuation in notifications for diseases occurring at a baseline level in the community.		The temporal analysis identifies abnormal events in a disease's temporal distribution. This can be straightforward for rare diseases requiring immediate notification but often requires statistical methods to differentiate abnormal events from the expected fluctuation in notifications for diseases occurring at a baseline level in the community.

	Such statistical methods include, from the simplest to the most sophisticated:		Such statistical methods include, from the simplest to the most sophisticated:

			==Crossing a predefined threshold==
	Crossing a predefined threshold, as for meningitis in the meningitis African belt (> 5 cases/100,000/week, Figure 1)		Crossing a predefined threshold, as for meningitis in the meningitis African belt (> 5 cases/100,000/week, Figure 1)

	Figure 1: Using a pre-defined threshold to detect unexpected changes		Figure 1: Using a pre-defined threshold to detect unexpected changes
			[[File:MeningitisbyweekBK.png\|600px\|frame\|none]]


			==Doubling or tripling the absolute number of cases over a given time period==
	Doubling or tripling of the absolute number of cases over a given time period.		Although simple, this method is crude because it does not consider the number of cases on which the increase is calculated. Doubling the number of cases from 10 to 20 carries a greater statistical significance than doubling the number from 3 to 6. As an alternative, to enhance the method, a Poisson test can be applied to express the departure from previous period values (figure 2). For example, the averaged value observed in the previous 5 weeks is the parameter expected in the Poisson test. The test returns the probability of observing the number of cases, or more, for the week to test, assuming the average value is expected. For example, if three cases, on average, have been notified weekly in the past five weeks, the probability of notifying six cases or more is 0.084 (8.4%) using a Poisson test. This means such an observation may occur by chance once every 12 weeks. Applying the same approach to 20 cases when only 10 are expected yields a probability of 0.0035 (0.35%), potentially occurring by chance only once every 6 years.
	~~This method, although~~ simple, is crude because it does not ~~take into consideration~~ the number of cases on which the increase is calculated. Doubling the number of cases from 10 to 20 carries a greater statistical significance than doubling the number ~~of cases~~ from 3 to 6. As an alternative, to enhance the method, a Poisson test can be applied to express the departure from previous period values (figure 2). For example, the averaged value observed in the previous 5 weeks is ~~used as~~ the expected ~~value parameter~~ in the Poisson test. The test returns the probability of observing the number of cases or more, for the week to test, assuming the ~~averaged~~ value is expected. For example if three cases, on an average, have been notified weekly in the past five weeks, the probability of notifying six cases or more is 0.084 (8.4%) using a Poisson test. This means ~~that~~ such an observation may occur by chance once every 12 weeks. Applying same approach to 20 cases when only 10 are expected yields a probability of 0.0035 (0.35%), potentially occurring by chance only once every 6 years.
	Figure 2: Using a Poisson test to detect unexpected changes		Figure 2: Using a Poisson test to detect unexpected changes
			[[File:Poissontest.png\|600px\|frame\|none]]


			==Comparing numbers, proportional morbidity, or rates with similar periods in the past.==
	Comparing ~~number~~, proportional morbidity or rates with similar periods in the past.		The mean or median of the number of cases observed on weeks from previous years, centered around the current week, are used as a basis for comparison (for example, five weeks for the past five years resulting in a historical distribution of 25 weeks). The departure from the historical mean is measured by comparing it to the standard deviation of the historical distribution. When the median is used, thresholds for the unusual patterns are defined by the value of the 90% or 95% percentile of the historical distribution (figure 3). This approach considers the seasonal variations by restricting the analysis to similar periods from past years but should not be applied to series presenting a significant trend.
	The mean or median of the number of cases observed on weeks from previous years, centered around the current week, are used as a basis for comparison (for example five weeks for the past five years resulting in an historical distribution of 25 weeks). The departure from the historical mean is measured by comparing it to the standard deviation of the historical distribution. When the median is used, thresholds for unusual ~~pattern~~ are defined by the value of the 90% or 95% percentile of the historical distribution (figure 3). This approach ~~takes into account~~ the seasonal variations by restricting the analysis to similar periods from past years but should not be applied to series presenting ~~with~~ a significant trend.
	Figure 3: Using historical median and percentiles to detect unexpected changes		Figure 3: Using historical median and percentiles to detect unexpected changes

			[[File:Historialmedian.png\|600px\|frame\|none]]

	Modeling historical data by time series analysis techniques that will account for trends and seasonality in the data.		Modeling historical data by time series analysis techniques that will account for trends and seasonality in the data.
	Regression techniques ~~are used to~~ account for ~~trend~~ and seasons by fitting lines and sine curves to the data (figure 4). The confidence interval for detecting unusual events relies on calculating the dispersion of the residuals and applying a statistical threshold (95% confidence interval). More advanced techniques using seasonal autoregressive and moving average models (SARIMA) on differentiated data are indicated for diseases with unstable historical patterns but are rarely used in routine surveillance (figure 5).		Regression techniques account for trends and seasons by fitting lines and sine curves to the data (figure 4). The confidence interval for detecting unusual events relies on calculating the dispersion of the residuals and applying a statistical threshold (95% confidence interval). More advanced techniques using seasonal autoregressive and moving average models (SARIMA) on differentiated data are indicated for diseases with unstable historical patterns but are rarely used in routine surveillance (figure 5).
	Figure 4: Using periodic regression modeling to detect unexpected changes		Figure 4: Using periodic regression modeling to detect unexpected changes

			[[File:Periodicregression.png\|600px\|frame\|none]]

	Figure 5: Using SARIMA modeling to detect unexpected changes		Figure 5: Using SARIMA modeling to detect unexpected changes

			[[File:Sarima.png\|600px\|frame\|none]]

	Weekly notification of typhoid and paratyphoid fever in France, 1992-1996		Weekly notification of typhoid and paratyphoid fever in France, 1992-1996
	The selection of the most appropriate method for analysis of time ~~characteristic~~ must take into account:		The selection of the most appropriate method for the analysis of time characteristics must take into account:

	The nature of the alert to detect, in relation ~~with~~ the type of transmission		The nature of the alert to detect in relation to the type of transmission
	The availability of historical data. In a new system, historical comparisons can only be performed on the most recent periods, and may not account for seasonality.		The availability of historical data. In a new system, historical comparisons can only be performed on the most recent periods and may not account for seasonality.
	The existing statistical resources and software		The existing statistical resources and software

Bosmana fem: Created page with "Temporal analysis consists in identifying abnormal events in the temporal distribution of a disease. This can be straightforward for rare diseases requiring immediate notifica..."

2022-12-18T15:03:43Z

Created page with "Temporal analysis consists in identifying abnormal events in the temporal distribution of a disease. This can be straightforward for rare diseases requiring immediate notifica..."

New page

Temporal analysis consists in identifying abnormal events in the temporal distribution of a disease. This can be straightforward for rare diseases requiring immediate notification, but often requires the use of statistical methods to differentiate abnormal events from the expected fluctuation in notifications for diseases occurring at a baseline level in the community.

Such statistical methods include, from the simplest to the most sophisticated:

Crossing a predefined threshold, as for meningitis in the meningitis African belt (> 5 cases/100,000/week, Figure 1)
Figure 1: Using a pre-defined threshold to detect unexpected changes

Doubling or tripling of the absolute number of cases over a given time period.
This method, although simple, is crude because it does not take into consideration the number of cases on which the increase is calculated. Doubling the number of cases from 10 to 20 carries a greater statistical significance than doubling the number of cases from 3 to 6. As an alternative, to enhance the method, a Poisson test can be applied to express the departure from previous period values (figure 2). For example, the averaged value observed in the previous 5 weeks is used as the expected value parameter in the Poisson test. The test returns the probability of observing the number of cases or more, for the week to test, assuming the averaged value is expected. For example if three cases, on an average, have been notified weekly in the past five weeks, the probability of notifying six cases or more is 0.084 (8.4%) using a Poisson test. This means that such an observation may occur by chance once every 12 weeks. Applying same approach to 20 cases when only 10 are expected yields a probability of 0.0035 (0.35%), potentially occurring by chance only once every 6 years.
Figure 2: Using a Poisson test to detect unexpected changes

Comparing number, proportional morbidity or rates with similar periods in the past.
The mean or median of the number of cases observed on weeks from previous years, centered around the current week, are used as a basis for comparison (for example five weeks for the past five years resulting in an historical distribution of 25 weeks). The departure from the historical mean is measured by comparing it to the standard deviation of the historical distribution. When the median is used, thresholds for unusual pattern are defined by the value of the 90% or 95% percentile of the historical distribution (figure 3). This approach takes into account the seasonal variations by restricting the analysis to similar periods from past years but should not be applied to series presenting with a significant trend.
Figure 3: Using historical median and percentiles to detect unexpected changes

Modeling historical data by time series analysis techniques that will account for trends and seasonality in the data.
Regression techniques are used to account for trend and seasons by fitting lines and sine curves to the data (figure 4). The confidence interval for detecting unusual events relies on calculating the dispersion of the residuals and applying a statistical threshold (95% confidence interval). More advanced techniques using seasonal autoregressive and moving average models (SARIMA) on differentiated data are indicated for diseases with unstable historical patterns but are rarely used in routine surveillance (figure 5).
Figure 4: Using periodic regression modeling to detect unexpected changes

Figure 5: Using SARIMA modeling to detect unexpected changes

Weekly notification of typhoid and paratyphoid fever in France, 1992-1996
The selection of the most appropriate method for analysis of time characteristic must take into account:

The nature of the alert to detect, in relation with the type of transmission
The availability of historical data. In a new system, historical comparisons can only be performed on the most recent periods, and may not account for seasonality.
The existing statistical resources and software

===FEM Editor 2007===
* Denis Coulombier
===Original FEM Authors===
* Christophe Paquet
* Arnold Tarantola
* Philippe Quenel
* Nada Ghosn
===FEM Contributors===
* Denis Coulombier
* Vladimir Prikazsky
* Lisa Lazareck

← Older revision		Revision as of 15:14, 18 December 2022
Line 18:		Line 18:
	==Comparing numbers, proportional morbidity, or rates with similar periods in the past.==		==Comparing numbers, proportional morbidity, or rates with similar periods in the past.==
	The mean or median of the number of cases observed on weeks from previous years, centered around the current week, are used as a basis for comparison (for example, five weeks for the past five years resulting in a historical distribution of 25 weeks). The departure from the historical mean is measured by comparing it to the standard deviation of the historical distribution. When the median is used, thresholds for the unusual patterns are defined by the value of the 90% or 95% percentile of the historical distribution (figure 3). This approach considers the seasonal variations by restricting the analysis to similar periods from past years but should not be applied to series presenting a significant trend.		The mean or median of the number of cases observed on weeks from previous years, centered around the current week, are used as a basis for comparison (for example, five weeks for the past five years resulting in a historical distribution of 25 weeks). The departure from the historical mean is measured by comparing it to the standard deviation of the historical distribution. When the median is used, thresholds for the unusual patterns are defined by the value of the 90% or 95% percentile of the historical distribution (figure 3). This approach considers the seasonal variations by restricting the analysis to similar periods from past years but should not be applied to series presenting a significant trend.

	Figure 3: Using historical median and percentiles to detect unexpected changes		Figure 3: Using historical median and percentiles to detect unexpected changes

	[[File:Historialmedian.png\|600px\|frame\|none]]		[[File:Historialmedian.png\|600px\|frame\|none]]

	Modeling historical data by time series analysis techniques that will account for trends and seasonality in the data.		==Modeling historical data by time series analysis techniques that will account for trends and seasonality in the data.==
	Regression techniques account for trends and seasons by fitting lines and sine curves to the data (figure 4). The confidence interval for detecting unusual events relies on calculating the dispersion of the residuals and applying a statistical threshold (95% confidence interval). More advanced techniques using seasonal autoregressive and moving average models (SARIMA) on differentiated data are indicated for diseases with unstable historical patterns but are rarely used in routine surveillance (figure 5).		Regression techniques account for trends and seasons by fitting lines and sine curves to the data (figure 4). The confidence interval for detecting unusual events relies on calculating the dispersion of the residuals and applying a statistical threshold (95% confidence interval). More advanced techniques using seasonal autoregressive and moving average models (SARIMA) on differentiated data are indicated for diseases with unstable historical patterns but are rarely used in routine surveillance (figure 5).

	Figure 4: Using periodic regression modeling to detect unexpected changes		Figure 4: Using periodic regression modeling to detect unexpected changes

	[[File:Periodicregression.png\|600px\|frame\|none]]		[[File:Periodicregression.png\|600px\|frame\|none]]

	Figure 5: Using SARIMA modeling to detect unexpected changes		Figure 5: Using SARIMA modeling to detect unexpected changes

	[[File:Sarima.png\|600px\|frame\|none]]		[[File:Sarima.png\|600px\|frame\|none]]

	Weekly notification of typhoid and paratyphoid fever in France, 1992-1996		==Weekly notification of typhoid and paratyphoid fever in France, 1992-1996==
	The selection of the most appropriate method for the analysis of time characteristics must take into account:		The selection of the most appropriate method for the analysis of time characteristics must take into account:
			* The nature of the alert to detect in relation to the type of transmission
	The nature of the alert to detect in relation to the type of transmission		* The availability of historical data. In a new system, historical comparisons can only be performed on the most recent periods and may not account for seasonality.
	The availability of historical data. In a new system, historical comparisons can only be performed on the most recent periods and may not account for seasonality.		* The existing statistical resources and software
	The existing statistical resources and software

	===FEM Editor 2007===		===FEM Editor 2007===