DOWNLOAD LD50/LC50 CALCULATOR HERE
Median lethal dose or concentration is the dose or concentration of the compound that produces 50% mortality in the exposed population. Estimation of LD or LC provides a measure of acute toxicity of the compound and is used for comparing the toxicities of two compounds.
The following steps are used in the calculation of LD or LC in this spread sheet
1. Converting doses to log (10) doses (x)
2. Converting mortality to proportions
3. The proportions are corrected for control mortality if its is more than 10% using Schneider-Orelli’s (1947) formula:
% Responded – % Responded in Control
Corrected mortality (p) = ________________________________ x 100
100 - Responded % in Control
4. Converting corrected proportions (p) to empirical probits (y).
5. A dose response curve is drawn using the log(10) doses (x) and empirical probits (y) and the regression equation is derived. Empirical probits less than 1 and more than 7 are ignored as they have little and no significance in the estimation of LD or LC (Hayes, 2014).
y=5+(x-µ)/σ
6. From the equation of the curve and log10 doses, the expected probits (Yi) are derived
7. From the expected probits (Yi), expected mortality proportion followed by expected no.of animals are derived
8. The original mortality (Observed) and derived mortality (Expected) are used to calculate the Chi-Square test with (No. of log doses used -2) degrees of freedom. If the Chi-square test is non-significant, it indicates good curve fitting.
9. Z value is derived using the formula
Z=1/(√2π)e(-1/2(Yi-5)^2)
where Yi = Expected probits
9. The weighting coefficents (W) are derived using the formula
W=Z^(2 )/PQ,
where P = Expected proportion
Q=(1-P)
10. The weighted coefficients were used to calculate the standard error
SE= σ/√ƩnW
where σ = Standard deviation (1/slope)
n= number of animals in each group
W= Weighting coefficient
11. Working probits (Yw) are derived from the regression equation as follows
Yw = Yi-(P/Z)-p/Z
Y = Expected probits
P = Expected Proportion
p = Observed proportion
11. The LD or LC values are derived from the curve drawn using working probits and log doses. Antilog of the dose corresponding to respective probit value.
12. 95% Fiducial confidence limits are calculated using the formula
Fiducial Limits =Antilog (Log10 Dose ± 1.96 (SE)
(Your comments and corrections are welcome to make this spread sheet better: alpharajm@gmail.com)
References
Busvine J.r. 1971. A critical review of the techniques for testing insecticides. Commonwealth Agricultural
Bureaux, London, ISBN 0851980309
Finney, D. J., Ed. (1952). Probit Analysis. Cambridge, England, Cambridge University Press.
Finney, D. J. and W. L. Stevens (1948). "A table for the calculation of working probits and weights in probit analysis." Biometrika 35(1-2): 191-201.
Greenberg, B. G. (1980). "Chester I. Bliss, 1899-1979." International Statistical Review / Revue Internationale de Statistique 8(1): 135-136.
Hayes, W. J. and C. L.Kruger(eds).2014 Handbook of Haye's principles and methods of toxicology, 6th Edition, CRC Press, Boca Raton, NY
(Please Note:
- This calculator is based on the method of Finney (1952). [D.J.Finney (1952) Probit Analysis (2nd Ed), Journal of the Institute of Actuaries, 78 (3): 388-390]
- This calculator works with Excel 2010 or higher. There are issues with lower versions due to array formulas.
- This calculator ignores Probits less that one and more than seven for calculating LD/LC values as they have little bearing (Hayes & Kruger, 2014 - Principles & Methods of Toxicology )
- In earlier version (before 25/01/2016) the intercept was displayed in probits. Now it is changed to Log10
Median lethal dose or concentration is the dose or concentration of the compound that produces 50% mortality in the exposed population. Estimation of LD or LC provides a measure of acute toxicity of the compound and is used for comparing the toxicities of two compounds.
The LD or LC values are calculated using 'Probit Analysis', which was initially developed by D.J. Finney (1971) and later discussed in detail elsewhere (Finney, 1978; Robertson et al., 2007). In general, the data from bioassays ( mortality proportions and corresponding doses) gives an S shape curve. In order to make this curve linear, the proportions are transformed to probits and doses to log10. The LD or LC values are estimated using regression analysis (Busvine 1971).
Several computer programmes (SAS, SPSS,POLO, LeOra etc) accurately calculate LD or LC values but these programmes are not free and requires knowledge of using them. Furthermore, these programmes do not provide real time results (time required for entering commands and processing). Hence, in this blog an user-friendly, free, dynamic EXCEL spread sheet is provided for estimating LD or LC values.
The following steps are used in the calculation of LD or LC in this spread sheet
1. Converting doses to log (10) doses (x)
2. Converting mortality to proportions
3. The proportions are corrected for control mortality if its is more than 10% using Schneider-Orelli’s (1947) formula:
% Responded – % Responded in Control
Corrected mortality (p) = ________________________________ x 100
100 - Responded % in Control
4. Converting corrected proportions (p) to empirical probits (y).
5. A dose response curve is drawn using the log(10) doses (x) and empirical probits (y) and the regression equation is derived. Empirical probits less than 1 and more than 7 are ignored as they have little and no significance in the estimation of LD or LC (Hayes, 2014).
y=5+(x-µ)/σ
6. From the equation of the curve and log10 doses, the expected probits (Yi) are derived
7. From the expected probits (Yi), expected mortality proportion followed by expected no.of animals are derived
8. The original mortality (Observed) and derived mortality (Expected) are used to calculate the Chi-Square test with (No. of log doses used -2) degrees of freedom. If the Chi-square test is non-significant, it indicates good curve fitting.
9. Z value is derived using the formula
Z=1/(√2π)e(-1/2(Yi-5)^2)
where Yi = Expected probits
9. The weighting coefficents (W) are derived using the formula
W=Z^(2 )/PQ,
where P = Expected proportion
Q=(1-P)
10. The weighted coefficients were used to calculate the standard error
SE= σ/√ƩnW
where σ = Standard deviation (1/slope)
n= number of animals in each group
W= Weighting coefficient
11. Working probits (Yw) are derived from the regression equation as follows
Yw = Yi-(P/Z)-p/Z
Y = Expected probits
P = Expected Proportion
p = Observed proportion
11. The LD or LC values are derived from the curve drawn using working probits and log doses. Antilog of the dose corresponding to respective probit value.
12. 95% Fiducial confidence limits are calculated using the formula
Fiducial Limits =Antilog (Log10 Dose ± 1.96 (SE)
(Your comments and corrections are welcome to make this spread sheet better: alpharajm@gmail.com)
References
Busvine J.r. 1971. A critical review of the techniques for testing insecticides. Commonwealth Agricultural
Bureaux, London, ISBN 0851980309
Finney, D. J., Ed. (1952). Probit Analysis. Cambridge, England, Cambridge University Press.
Finney, D. J. and W. L. Stevens (1948). "A table for the calculation of working probits and weights in probit analysis." Biometrika 35(1-2): 191-201.
Greenberg, B. G. (1980). "Chester I. Bliss, 1899-1979." International Statistical Review / Revue Internationale de Statistique 8(1): 135-136.
Hayes, W. J. and C. L.Kruger(eds).2014 Handbook of Haye's principles and methods of toxicology, 6th Edition, CRC Press, Boca Raton, NY
