As I read papers in invertebrate pathology (my specialty) I frequently find a fundamental statistics  error in several papers. Time and again, in both published papers and unpublished manuscripts submitted for review, I see probit analysis used to (inappropriately) calculate an LT50, which is itself a misnomer, but more on that later.

According to Finney as well as subsequent authors, probit/logit analysis requires observation of independent cohorts of insects at each time interval, NOT  observation of the same cohort during a post-treatment observation period. Probit does work to give nice numbers but is invalid.  The appropriate analytical tools are Kaplan Meier Survivorship analysis with some sort of log rank or similar test.

Furthermore, Use of the term LT50 is not appropriate. From the Glossary of Invertebrate Pathology, 3rd Edition.

Median lethal time (LT50) In a time-dependent biological assay procedure, this is the period of exposure to a pathogenic (including toxicological) stimulus which will produce death in half the test subjects. The length of exposure is a direct measure of dosage, and an increase in the period of exposure results in an increase in uptake and true dose in the same ratio. Its symbol is LT50, not to be confused with the Median Survival time (ST50). (Estimation of this parameter by probit analysis, general linear models, and certain other statistical methods is generally invalid because the data are usually censored [see "censored data" in relevant statistical references] and assumptions of independence and normal distribution of data are almost always violated.) Median survival time is a restricted concept of median effective time. The time at which death occurs in half the test subjects after exposure to a pathogenic (including toxicological) stimulus. Its symbol is ST50 or MST, not a direct measure of dosage, and it is not to be confused with the Median Lethal Time (LT50), which is a direct measure of dosage.

Also, when Kaplan Meier is properly used, I often see one or two decimal places for the MST.  If observations are made on a once a day basis, an MST is expressed in whole number of days; if the insects are examined for mortality every 12 hours, then one could get away with one decimal place. Only if mortality observations are made 4+ times a day, can one be justified in 2 decimal places for an MST, as I often see too many times. Most Kaplan Meier programs I have used only give whole number of days as the MST and 95% Confidence Limits. So, with the exception of the last method, two decimal places is spurious precision.

A less important point is Average Survival Time (AST) versus Median Survival time. MST vs AST

Median Survival Time: This is the time from diagnosis or treatment [whichever is taken as the beginning point] to the point at which half [50%] of the group had died. It is another way to evaluate treatment of a group, and another way to indicate seriousness of a condition. Mean (Average)  Survival Time: This is the AVERAGE survival time of the members of a group. The Mean and the Average are the same. This is the time from diagnosis or treatment [whichever is taken as the beginning point] until death, for each member of the group, added up, and then divided by the number of members of the group. In order to have a Mean Survival Time statistic, all of the members of the group must be dead, i.e., final mortality observation must be 100%. Mean Survival Time is often used to evaluate studies where very sick people with very advanced cancers are treated, thus 100% mortality. Advantages of Using the Median instead of the Mean There are certain advantages in using Median Survival Time as a statistic. 1. You don't have to wait for the entire group to die before getting a statistical idea of effectiveness. 2. Averages can be influenced strongly by one or two way-out atypical scores. Medians essentially indicate the fiftieth percentile of a group. Medians are not so easily biased by an atypical data point.

I also recommend: ONOFRI A, CARBONELL EA, PIEPHO H-P, MORTIMER AM & COUSENS RD (2010). Current statistical issues in Weed Research. Weed Research 50, 5–24. Weed research, yes, but the issues are in common with entomology.

So please, those who should read this diatribe, keep my points in mind, and tell your colleagues who might be doing bioassays.

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