Probit Analysis of bioassays: Sure, you are seriously talking about it

 

 

After reviewing a manuscript, I thought of talking to my friend who works in the prestigious Government institution to know as to how he estimates various parameters of toxicity like LC50, fiducial limits [FL] or Confidence intervals [CI], intercept. And this reminded me of my days as a M.Sc. student when I would do these calculations using a Facit® manual calculator on a tabulated sheet that our insect toxicology teacher, Dr. B.S. Atri would provide us. It was tedious work involving filling of columns like concentrations, log concentrations, % mortality, their transformation into probits, weighting coefficients, empirical probits, expected probits, working probits and other parameters meticulously up to three decimal points until we came to an equation, y=a+bx, where y is 5.0, a, an intercept and b, a slope and x (log LC50) is what we will calculate. For 95% FL, we used two equations, m1=m-1.96√V and m2=m+.6√V where m1, m2, lower and upper FLs of LC50, √ square root of variance and 1.96 being log value of 95%. I was not good at these calculations. Two books came handy-one entitled “Probit Analysis” by D.J. Finney and another,” A Critical Review of Techniques for Testing Insecticides” by J.R. Busvine. Although Finney’s book was ‘Bible’ for estimating toxicity parameters, I found the latter easy to understand as it dealt with toxicity experiments and was less cluttered with statistics and a bit ease with probit analysis. Later, Dr. A. Regupathy of TNAU too dealt with this topic to explain the probit analysis in as easily as possible.

Although Busvine’s book 2^nd edition published in 1971 makes a mention of digital computer for estimating LC50 and other parameters referring to Sokal’s 1958 paper entitled “Probit Analysis by computer” (in J. Econ. Ent. 51,738); we never got a way forward to the use of computer until mid-1980s. In the meantime, we missed this important landmark paper of 1958 and all that what computer has to do with our lives until late 1980s and early 1990s.

It so happened that in late 1980s, my Ph.D. Guru, Dr. K.N. Mehrotra got a maximum likelihood programme (Ross, G.E.S. (1987) Maximum likelihood programme. The numerical Algorithms Group, Rothamsted Experimental Station, Harpenden, UK) and I was hooked on to it until my retirement in 2015. MLP was robust and sensitive even using limited concentrations for bioassays, and gave extra estimates like LC95, LC99 along with graphical representation. I had never before imagined an ease with which we got various estimates while entering values of doses/concentrations, insects treated and insects killed, and const for % mortality in control, that saved many hours of toil in doing analytical work as before. It also helped to forget the basics.

I had used Indostat Services, Hyderabad (M M Khetan)’s Entomology pack that provided probit analysis in early 2000s which was equally good. Khetan was very unassuming person who would visit us on his own while in Delhi just to check if his software is working well. He would be ever ready to guide us whenever we had problem.

Both of these programmes were priced, but the former was ex-gratis gift to our Guru who passed it on to us and even being used by others almost two decades later.

Although I knew of SPSS package, I did not use it as it was very costly. Later, it was subscribed by our institute, but we remained loyal to the MLP.

While reviewing a manuscript, I stumbled upon the negative FL and that revived my memories of using MLP and requesting help for software and/or for estimating toxicity parameters for the imaginary dose-mortality data. In the meantime, I got to know of R-programme (https://cran.r-project.org/web/packages/ecotoxicology/index.html) which is freely available (while reviewing another manuscript). Dr. Daisy Salifu of ICIPE, Kenya helped with instructions to use this programme. My senior Dr. H Rao would often tell that there are many softwares freely available on the internet and are as good as the commercially available ones. This further led to me to look for more of such softwares. One that I got recently is from Prof. Hsin Chi, Chung Hsing University, Taiwan. I am yet to use it.

I also got to know about POLO Plus software that was developed by Robertson et al. of USDA-Forest Service in early 1980s. Currently this software is marketed by LeOra Software Company. This software is based upon use of logit as well as probit values similar to R-programme.

I thought of imaginary dose-mortality data for estimating various parameters of toxicity estimations. I am helped in this by my colleagues who used their own softwares.

  

Table 1: Data set 1

No of conc. mg/l: 0, 1, 3, 5, 7,10,15; No of insects treated: 30,30,30,30,30,30,30

No of insects killed: 1,5,10,13,18,26,30

	LC50	C.I. 95%	Intercept with s.e.	Slope with s.e.	Chi-square$ [d.f.];   sign.	Remarks
SPSS	4.107	1.793-7.162	-1.16	1.86 [Work probit vs log conc]	11.025 [4]; 0.026#	#heterogeneity factor used for C. I. estimation
R-program	5.50	4.67-6.41	-1.39± 0.185	0.252± 0.0311	2.69[5]; 0.748	Probit,logit and DRC estimates same
POLO@	x	x	-1.386	2.63± 0.496	10.237	Simple, but not versatile
POLO Suite	5.61	0.862-7.815		3.99± 0.92	6.98	P 0.137ns
SAS	5.163	3.517- 6.290	-2.551± 0.744	3.578± 0.847	6.405[4]
MLP
Sheoran*	4.428	2.840-6.906	-1.501	2.322[exp probit + 5 vs log conc]	8.971[4]; 0.062
GBabu**	4.29	3.855-4.775	0.012	0.772 [proportion probit vs log conc]	7.049[4]	Goodness of fit p value-0.735

@unable to estimate LC50 & others in view of high chi sq & heterogeneity values.

Table 2: Data set 2

No of conc mg/l: 0, 1, 3, 5, 7,10,15; No of insects treated: 30,30,30,30,30, 30,30

No of insects killed: 3,7,15,23,25,30,30

	LC50	FL95%	Intercept with s.e.	Slope with s.e.	Chi-square [d.f.]; sign.	Remarks
SPSS	2.397	1.798-2.986	-0.79	2.05	5.410[4]; 0.248	No need of heterogeneity factor
R-program	3.27	2.58-3.95	-1.11± 0.187	0.340± 0.044	2.48[5]; 0.782	Probit,logit and DRC estimates same
POLO@	3.017	1.353-4.136		3.161± 0.630	4.282
POLO Suite	3.49	0.340- 4.820		3.84± 1.12	4.04 [4]	P value 0.4006ns
SAS	3.488	1.651- 4.479	-2.083± 0.874	3.839± 1.119	4.036 [4]
MLP
Sheoran*	2.880	1.875-4.425	-1.217	2.649	2.293[4]; 0.682
GBabu**	2.952	2.736-3.184	0.127	0.794	6.648	Goodness of fit p value-0.995

@K Subaharan, NBAIR, Bangalore;

*Although probit vs log conc is based upon working probit+5, for this equation Y=a+bx, Y value will be 0 & not 5 for LC50; & Y will vary for diff LCs as per tabulated value in the programme. *,** are python-based. $ Table value of chi sq at p 0.05 is 9.5 [d.f. 4] and11.1 at [d.f.5].

Table 3: Fiducial limits at different levels of probability

	LC50	FL 95%	FL90%	FL80%
Analysis with GBabu
Data set 1	4.29	3.855-4.775	3.922-4.694	4.000-4.602
Data set 2	2.952	2.736-3.184	2.769-3.146	2.809-3.101
Analysis with POLO Plus
Data set 1	4.107	1.793-7.162	2.438-6.117	NA
Analysis with SAS
Data set 1	5.163	3.517-6.290	NA	4.205-5.917
Data set  2	3.488	1.651-4.479	NA	2.466-4.178

 

Discussion

Differences in results between softwares: These differences exist due to various regression models that involve transformation of % mortality data vis-à-vis log concentration.

Evaluation of these softwares for data set 1 shows significant differences in chi square values, in some cases higher than the table values at p 0.05, which means the observed mortalities are significantly different from the expected ones. Only, SPSS programme is reported to take this in to consideration and applies a heterogeneity factor to estimate FL at 95%.

In comparison to data set 1, data set 2 shows that chi square values are below the table values at p 0.05 for all analyses. In other words, all softwares show that there is homogeneity in data, as expected and observed mortalities are not significantly different.

Since different regression models are used for plotting curves between transformed mortalities and log concentration, there is a wide variation in intercept as well as slope value.

Differences in results between two data sets: Only two softwares viz., R-programme and GBabu clearly show that these two data sets are significantly different, as 95% FL of their LC50 do not overlap. All other softwares show overlapping 95%FL for both data sets. SAS did not show significant differences between these two LC50 at 95%FL, but surely at 80%FL.

Conclusion

1.     Both data sets are imaginary with mortality data dispersed with intent that these are evenly [later turned out to be false assumption] distributed in the first set, and sigmoidally distributed with 100% mortalities at the last two concentrations in the second set, with expectation of significant difference in their LC50s.  Only two softwares, R-program and GBabu met this expectation.

2.     POLO Plus was found simple, but not versatile as it required a near fit of dependable variable Y over independent variable X axis. POLO Suite appeared to be much better in handling heterogenous data and its results were close to R-programme

3.     SPSS and POLO Suite both showed a wide range of 95%FL for LC50s.

4.     Slope values differ in many softwares, suggesting importance of mention of dependable variable vs independent variable which is invariably log concentration.

5.     R-program and SAS gave details of estimates of probit analysis-max likelihood.

6.     CI or FL are wide at 95% and relatively narrow at 80%. CI or FL at 95% is widely used.

7.     Which one is best? It is a difficult question. Ideally, all softwares may work best if the data are the best fit line of Y vs X variables. However, for the researchers, repeating bioassays for this aim may not be always possible in view of many uncertainties. The best software will be one which is versatile, easy and full of features.

PS: An idea of probit analysis published in 1938 was of C I Bliss who worked as an entomologist at Connecticut Ag Exp Stn.

 

 

Acknowledgements: Thanks are due to Drs Daisy Salifu, ICIPE, Kenya; A Dhandapani, NAARM, Hyd; Gajendra Babu, Chloropy, Hyd; K Subaharan and Ramya NBAIR, Bangaluru; Shankarganesh, CICR, Coimbatore; O P Sheoran, HAU, Hisar; Y Andi Trisyono, UGM, Indonesia; PK Chhuneja & Satnam Singh, PAU, Ludhiana; Archana and Suresh Nebapure, IARI, New Delhi and Z R Khan, ICIPE, Kenya for their help in estimation and discussion.