P- Reviewer: Bharaj P, Ghiringhelli PD S- Editor: Ji FF L- Editor: A E- Editor: Lu YJ
Published online May 12, 2016. doi: 10.5501/wjv.v5.i2.85
Peer-review started: January 10, 2016
First decision: March 1, 2016
Revised: March 2, 2016
Accepted: March 17, 2016
Article in press: March 19, 2016
Published online: May 12, 2016
Two commonly used methods for calculating 50% endpoint using serial dilutions are Spearman-Karber method and Reed and Muench method. To understand/apply the above formulas, moderate statistical/mathematical skills are necessary. In this paper, a simple formula/method for calculating 50% endpoints has been proposed. The formula yields essentially similar results as those of the Spearman-Karber method. The formula has been rigorously evaluated with several samples.
Core tip: The formula described in this manuscript can be used to calculate 50% endpoint titre such as TCID50%, LD50, TD50, etc., in addition to the currently existing methods. The proposed formula can be applied without the help of calculator or computer.
Citation: Ramakrishnan MA. Determination of 50% endpoint titer using a simple formula. World J Virol 2016; 5(2): 85-86
Currently, there are two methods (formulas) viz., Reed and Muench and Spearman-Karber[2,3] are commonly employed for the calculation of 50% endpoint by serial dilution. To understand/apply these methods, moderate mathematical skills along with calculator or computer are essential. Here, I have proposed a simple formula to calculate the 50% endpoint titre and this formula can be used in addition to Reed and Muench or Spearman-Karber, methods but not exclusively at this point. In the following section, the newly proposed method is compared with two commonly used methods viz., Reed and Muench and Spearman-Karber.
log10 50% end point dilution = log10 of dilution showing a mortality next above 50% - (difference of logarithms × logarithm of dilution factor).
Generally, the following formula is used to calculate “difference of logarithms” (difference of logarithms is also known as “proportionate distance” or “interpolated value”): Difference of logarithms = [(mortality at dilution next above 50%)-50%]/[(mortality next above 50%)-(mortality next below 50%)].
log10 50% end point dilution = - (x0 - d/2 + d ∑ ri/ni)
x0 = log10 of the reciprocal of the highest dilution (lowest concentration) at which all animals are positive;
d = log10 of the dilution factor;
ni = number of animals used in each individual dilution (after discounting accidental deaths);
ri = number of positive animals (out of ni).
Summation is started at dilution x0.
log10 50% end point dilution = -[(total number of animals died/number of animals inoculated per dilution) + 0.5] × log dilution factor.
Formula 2 (if any accidental death occurred):
log10 50% end point dilution = -(total death score + 0.5) × log dilution factor.
Comparison of the newly proposed and existing methods with an example of virus titration in mice: For simplicity, it is assumed that 1 mL of each dilution was inoculated (Table 1, Table 2 and Table 3).
|Log10 virus dilution||Mice||Cumulative total||Percent mortality|
|-1||10||0||57||0||57||57/57 × 100 = 100|
|-2||10||0||47||0||47||47/47 × 100 = 100|
|-3||10||0||37||0||37||37/37 × 100 = 100|
|-4||10||0||27||0||27||27/27 × 100 = 100|
|-5||10||0||17||0||17||17/17 × 100 = 100|
|-6||6||4||7||4||11||7/11 × 100 = 63|
|-7||1||9||1||13||14||1/14 × 100 = 7|
|Log10 virus dilution||Mice|
|Log10 virus dilution||Mice||Death score|
|-1||10||10||10/10 = 1|
|-2||10||10||10/10 = 1|
|-3||10||10||10/10 = 1|
|-4||10||10||10/10 = 1|
|-5||10||10||10/10 = 1|
|-6||6||10||6/10 = 0.6|
|-7||1||10||1/10 = 0.1|
The newly proposed formula has been intensively validated with several samples and essentially yields the same results as those by the Spearman-Karber method. Therefore, the newly proposed method can be used in addition to the existing methods but not exclusively at this point.
|1.||Reed LJ, Muench H. A simple method of estimating fifty per cent endpoints. Am J Hyg. 1938;27:493-497.|
|2.||Kärber G. Beitrag zur kollektiven Behandlung pharmakologischer Reihenversuche. Archiv f experiment Pathol u Pharmakol. 1931;162:480-483. [DOI]|
|3.||Spearman C. The Method of “Right and Wrong Cases” (Constant Stimuli) without Gauss’s Formula. Br J Psychol. 1908;2:227-242. [DOI]|