Hazard Analysis

This analysis calculates a hazard function – the conditional probability of a spike at time t0+t on the condition that there is a spike at time t0 and there are no spikes in the interval [t0, t0+t).

Parameters

Parameter	Description
Max IIH Interval (sec)	Maximum interspike interval used in calculation of interspike interval histogram (see Algorithm below).
Hazard Time Max (sec)	Time axis maximum in seconds. This parameter is expected to be smaller than Max IIH Interval (sec). See Algorithm below.
Bin	Bin size in seconds.
Select Data	If Select Data is From Time Range, only the data from the specified (by Select Data From and Select Data To parameters) time range will be used in analysis. See also Data Selection Options.
Select Data From	Start of the time range in seconds.
Select Data To	End of the time range in seconds.
Int. filter type	Specifies if the analysis will use a single or multiple interval filters.
Interval filter	Specifies the interval filter(s) that will be used to preselect data before analysis. See also Data Selection Options.
Create filter on-the-fly	Specifies if a temporary interval filter needs to be created (and used to preselect data).
Create filter around	Specifies an event that will be used to create a temporary filter.
Start offset	Offset (in seconds, relative to the event specified in Create filter around parameter) for the start of interval for the temporary filter.
End offset	Offset (in seconds, relative to the event specified in Create filter around parameter) for the end of interval for the temporary filter.
Fix overlaps	An option to automatically merge the overlapping intervals in the temporary filter.
Overlay Graphs	An option to draw several histograms in each graph. This option requires that Int. filter type specifies that multiple interval filters will be used (either Table (row) or Table (col)).
Smooth	Option to smooth the histogram after the calculation. See Post-Processing Options for details.
Smooth Filter Width	The width of the smooth filter. See Post-Processing Options for details.
Add to Results / Bin left	An option to add an additional vector (containing a left edge of each bin) to the matrix of numerical results.
Add to Results / Bin middle	An option to add an additional vector (containing a middle point of each bin) to the matrix of numerical results.
Add to Results / Bin right	An option to add an additional vector (containing a right edge of each bin) to the matrix of numerical results.
Send to Matlab	An option to send the matrix of numerical results to Matlab. See also Matlab Options.
Matrix Name	Specifies the name of the results matrix in Matlab workspace.
Matlab command	Specifies a Matlab command that is executed after the numerical results are sent to Matlab.
Send to Excel	An option to send numerical results or summary of numerical results to Excel. See also Excel Options.
Sheet Name	The name of the worksheet in Excel where to copy the numerical results.
TopLeft	Specifies the Excel cell where the results are copied. Should be in the form CR where C is Excel column name, R is the row number. For example, A1 is the top-left cell in the worksheet.

Summary of Numerical Results

The following information is available in the Summary of Numerical Results

Column	Description
Variable	Variable name.
YMin	Hazard minimum.
YMax	Hazard maximum.
Spikes	The number of spikes used in calculation.
Filter Length	The length of all the intervals of the interval filter (if a filter was used) or the length or the recording session (in seconds)
Mean Freq.	Mean firing rate (Spikes/Filter_Length).
Mean Hazard.	The mean of the hazard values.

Algorithm

First, the program calculates the interspike interval histogram using interspike intervals that are less than Max IIH Interval.

The hazard function is then calculated according to the following formula (see Reference below):

(hazard in bin [t, t+dt]) = (number of intervals in bin [t,t+dt])/(number of intervals of length > t)

where dt is the bin size.

Hazard Time Max (which specifies the last bin of the hazard function) is expected to be smaller than Max IIH Interval.

If Hazard Time Max = Max IIH Interval, the hazard value for the last bin is always 1. Then the maximum of Y axis is set to 1 and smaller hazard values are scaled down. To avoid this scaling down, specify a smaller value of Hazard Time Max.

Reference

N.Sabatier, et.al., Phasic spike patterning in rat supraoptic neurones in vivo and in vitro, J. Physiol. 558.1 (2004) pp 161-180.