Meta-analysis of venom toxicity of 167 most lethal ophidian species provides a basis for estimating human lethal doses

Background: This is the first meta-analysis to characterize intra-ophidian-species variation in whole venom. The largest possible meta-analysis possible at this time, it encompasses all known records of animal lethality studies over the past 100 years. These results are not artifacts of resistant test-animal-species, and show orders of magnitude beyond the 1.6 logs (40 fold change) range of lethal dose documented in literature between amphibians, lizards and mice. Methods: 1198 lethal dose study results for 167 of the most lethal venomous ophidian species in the world are analyzed. Results: LDLo does not differentiate from LD50 across studies, indicating the true range of toxicity is probably larger. The belief that for route of inoculation, IC<IV<IP<IM<SC has good support (R 2 = 0.90). However, 5% of ICs were the highest dose, and 7% of SC inoculations were the lowest dose. Within the mouse test species, for one route of inoculation, the widest LD range is 3 logs (1000 fold change, N = 14). Within mouse, for multiple routes of inoculation, the widest LD range is 3.6 logs (4,150 fold change), N = 20, SC/IM. The strongest correlate for range of lethal dose results is the number of studies (R 2 = 0.56); followed by the number of test-animal-species (R 2 = 0.55); then by the number of routes of inoculation (R 2 = 0.43). Conclusions: Scientists working with humans should use combined LDLo and LD50 meta-datasets for all data and calculate: mean, median, minimum, range, and standard deviations. Standard deviation multiples will provide desired coverage. For estimating LD50 range and minimum lethal dose for species with little data, I recommend curating a meta-dataset of related snakes, and computational research to strengthen this.

Introduction duck or frog, and there might be some venom component sensitivity variances. However, no literature indicates variances of more than 1 order of magnitude between test-animalspecies, and one would not expect exotic monkeys, ducks or frogs to be tested. For part of this analysis, "mammal" and "bird" are treated as separate species. In most cases the designation of mammal would be a rat or a mouse. And most birds would be pigeons or chickens. As will be seen, using only mouse data did not change results.
These studies were mostly performed in the 20th century, with the peak from 1975 to 1979 (Fig. 1). This suggests that venom science may not believe that further studies are necessary or useful. As will be seen, this does not appear to be the case.

Methods
The analysis had several questions. First, does ophidian venom variance fall within the literature documented parameter of 1.6 logs (40X fold change) between mice and frogs test-animal-species? Second, to what extent did the assumption that IC < IV < IP < IM < SC hold? Third, what correlates are there to dose range, and how much of a contribution could be assigned to each factor? For this analysis, null hypotheses conform to what is available in published literature. To make data comparable between ophidian species, normalization was performed based on the range of values present. These normalization steps created fractions of the total range, or the fold change of the highest value over the lowest value.

Null hypotheses
The minimum lethal dose for single ophidian species has a factor of 40 or less fold change variation (log of 1.6). This statement captures the idea that across test-animal-species and inoculation methods, while there is variance, it should not exceed what has been reported in literature. (e.g. 4X and 10X, for a total of 40X) Within a single test-animal-species for a single ophidian species, there is a factor of 2 or less range of lethal doses between studies (log approximately 0.3).
LDLo values cluster below LD50 values such that the mean of the respective fractions of the range differ from each other by more than one standard deviation, or, barring this, by standard error.
LDLo values will not be maximum lethal doses reported across studies.
The lethal dose varies by route of inoculation such that IC < IV < IP < IM < SC for 90% or more of venomous ophidian species across studies.

Primary views of data
This meta-analysis examined 3 primary views of the data with subset views: 1.) Minimum lethal dose (LDmin) and maximum lethal dose (LDmax) for each ophidian species; 2.) The range fold changes for: all data (LD-ADrf), single test species (LD-SSrf), single test species -single route of administration (LD-SRrf), for each ophidian species; 3.) The fraction of the range within one ophidian species that each DB entry represented, expressed as a percentage, explained below.
Range fold change is Rmax ÷ Rmin where Rmax is the highest LD for the species, and Rmin is the lowest LD for that ophidian species. (LD can be LDLo or LD50.) LDmin is the lowest lethal dose reported for an ophidian species. LDmin can be either an LD50 or an LDLo. LDmax is the highest lethal dose reported across ophidian species, and similarly, can be either an LD50 or an LDLo.
The lethal dose range fold change is the LDmax divided by the LDmin (LDmax ÷ LDmin) for an ophidian species. The fraction of the range for an entry is LDentry ÷ LDrange, where LDrange = LDmax -Ldmin.
There are three LD range fold changes: All data (LD-ADrf), single species (LD-SSrf), and single species, single route (LD-SRrf). LD-ADrf means DB entries for all test-animal-species were used. LD-SSrf means that the widest range fold change within one test-animalspecies for an ophidian species was used. LD-SRrf means that the widest range fold change within one test-animal-species that was administered by the same route was used.
(e.g. use the highest and lowest LD for IC, IV, IP, IM, and SC, and take the largest range multiple for one of the routes of inoculation.) After curation, the data was sorted by species and then by lethal dose. It was further segregated by species family, finding 1 Atractaspid, The LD-SRrf difference between Elapids and Viperids did not appear to be significant. (Not shown.) The coefficient of determination, R 2 , is the primary measure of significance used in this meta-analysis. Best fit regressions were exponential curves of the form y = C•x m , with one exception, which was a linear fit.

Analysis
LDLo does not differentiate from LD50 across studies. 64 out of 167 ophidian species had at least one LDLo value. These 64 ophidian species had 243 LDLo values, and 532 LD50 values. In the meta-dataset, 26 of these 64 ophidian species (~ 40%) had an LDmin that was, indeed, an LDLo. However, 24 of the 64 ophidian species (~ 37.5%) had LDLo values that were the meta-study LDmax, which was against expectations.
For Figs. 2 and 3, the range fraction is determined by Eq. 1. This way, relative toxicity between ophidian species is normalized, and comparison of variation can be done between ophidian species. In Fig. 2, the mean of the LDLo fractions is 28.3%, and the mean of the LD50 fractions is 27.2%. The standard deviation of the LDLo fractions mean is 29.4%, and standard error is 3.7%. The standard deviation of the LD50 fractions mean is 22.4%, and standard error is 2.8%. Even by the less stringent method of standard error, this is insignificant. Thus, the mean of the LDLo and LD50 range fractions for the 64 out of 167 are not meaningfully differentiated.
However, one might argue that significant difference might be seen in LDLo values for single test-animal-species, as shown in Fig. 3. Here, as above, the data does not show this. Instead it shows that for 4 out of 11 test-animal-species, mean LDLo is higher than LD50, and exceeds standard error. (Mouse, guinea pig, dog, frog. Monkey was excluded due to low N for LD50.) Note that this also occurs for the highest N dataset (mouse). There is only 1 test-animal-species (rabbit) where mean LD50 is higher than LDLo and exceeds standard error as expected. However, rabbit has a low N and this disappears when median is used. (Standard error not shown for median.) Only the mouse test-animal-species exceeds standard error if median is used, and it still shows LDLo higher than LD50.
Strengthening this point, for 10 ophidian species, both LDmin and LDmax were LDLo's. The median number of DB entries for an ophidian species with one or more LDLo values was 4.
Consequently, because LDLo did not differentiate significantly from LD50 when examined across studies, LDLo designations were categorized together with LD50 for the rest of this meta-analysis.

Route of inoculation minimum and maximum lethal dose
In Fig. 4, there is good support for the concept that IC (intra-cerebral) < IV (intra-venous) < IP (intra-peritoneal) < IM (intra-muscular) < SC (subcutaneous). This is the only hypothesis not falsified in this analysis. However there are contradictory instances.
Out of 29 intracerebral injections (IC), 16 were LDmin values, which is as expected. So, approximately half the time, an IC injection was the minimum, and the N should be meaningful at 29. Using a synthetic x-axis the 0.9062 R 2 coefficient of determination suggests that approximately 91% of the distribution fits the assumption that route of inoculation varies as IC < IV < IP < IM < SC. The curve fit for LDmax shows the opposite trend, with a good R 2 suggesting 75% of results can be attributed to route of inoculation distributed in this manner. This latter R 2 being lower agrees with LDmax having higher variance (not shown).
However, 13 out of 249 of the subcutaneous injections were LDmin values, which makes this, unexpectedly the route of highest toxicity for 7.8% of the 167 ophidian species. Out of these 13, there were 4 venoms with strong hemotoxic or nephrotoxic effects, the other 9 were neurotoxic.
Of the intracerebral inoculations, 2 were LDmax, the opposite of expectations, (Notechis scutatus and Naja atra), which is 1.2% of the 167 ophidian species. Notechis scutatus and Naja atra contain both pre and post synaptic neurotoxins. Notechis scutatus had 26 DB entries and Naja atra had 17, so this should probably not be an artifact of a low number of studies performed for each. The percentages of these paradoxical SC and IC inverted cases are about the same, at 7% and 5% of their respective route of inoculation.

Venom toxicity range fold change
The range of venom toxicity per ophidian species within the mouse test species has a mean average of 2.22 logs (168 fold change) within a single test-animal-species, as shown in Fig. 5. This is 4.2 times the 1.6 logs (40 fold change) documented in literature for toxicity difference between test-animal-species, as discussed above. For all test-animalspecies together, the mean range is 3.2 logs (1597 fold change), which is 40 times what current literature indicates.
The largest range fold change seen for an ophidian species tested in mouse for one route of inoculation is Boiga irregularis, 3 logs (1000 fold change), N(studies) = 14. The largest range fold change for an ophidian species tested only in mouse for all routes of inoculation is Crotalus horridus, 3.6 logs (4,150 fold change), N(studies) = 20, routes of inoculation: SC/IM. For one ophidian species data for all test-animal-species, including all routes of inoculation, the largest range fold change is Naja nivea, 4.46 logs (28,571 fold change), N (studies) = 22, N (test-animal-species) = 9, routes of inoculation: SC/IV between frog (LDmax) and rabbit (LDmin). These are among the highest N studies counts for ophidian species. Note that a specific ophidian species mentioned does not mean this species has been determined to be the most venomous, or the widest range of all.
One might ask whether the range fold change increasing holds up when a single species and single route of inoculation is examined. We see this in Fig. 6, where the range fold change is plotted against the number of studies. No curve fit is shown because there is insufficient data for determination. However, by inspection, one can see that the range fold change does appear to increase as the number of different studies rises. Figure 7, which looks at single test species for multiple routes of inoculation, shows a linear regression trend that reaches significance for the range fold change increasing as the N for number of studies gets larger. This graph appears to signal the same thing that a set of ecological diversity transects continuing to increase would. It indicates that to fully characterize ophidian venom lethal doses, probably requires more than 50 different studies.

Regressions of LDmin
Null hypotheses for minimum lethal dose A.) Minimum lethal dose within each ophidian species varies by less than a factor of 2. B.) The minimum lethal dose does not correlate with the number of times the lethal dose has been tested (e.g. the number of LD DB entries).

Alternate hypothesis
Minimum lethal dose varies by more than a factor of 2, and minimum lethal dose correlates with the number of times dose has been tested. Table 1 Regressions curve fit summary for LDmin, rounded.

Number of routes of inoculation correlation to LDmin
In Fig. 8, as the number of routes of inoculation increases, the likelihood of having more test-animal-species for the ophidian species also increases. The fitted curve is probably determined by the probability of inclusion of a lower lethal dose value rising as the number of inoculation routes goes to 5, because, as was seen above, IC < IV < IP < IM < SC does tend to hold true.
The N for the number of routes of inoculation 1 to 5 are, respectively: 30, 36, 61, 33, and 7.

Number of test-animal-species per ophidian species correlation to LDmin
Here in Fig. 9 the apparent drop visible in the fitted curve is 1.5 logs, a fold change of 32X. Similarly to the above, it should be expected that lethal dose would drop some with larger numbers of test-animal-species, because literature indicates that some animals are up to 1.6 logs (fold change of 40X) more susceptible to certain venoms than others, and there is some frog data in the dataset.
Additionally, the more test-animal-species there are for one ophidian species, the more likely it is that there will be more routes of inoculation. However, in the dataset, there are multiple instances of the same test-animal-species occupying LDmin and LDmax, and quite a few are very close to this state, which suggests that, indeed, the number of times an ophidian species is tested is a major factor.
Number of DB entries (studies reported) per ophidian species correlation to LDmin In Fig. 10

Discussion Of Possible Confounders
There may be errors in database record entries, or some papers or books got the numbers wrong. However, Sascha Steinhoff has made strenuous efforts to validate the data entries as evidenced by the sourcing of each one, and I have discussed this with him in personal communications as well. I do not believe that this is a significant source of error.
Biomedical science in general has a reproducibility problem [29]. However, venom LD50 and LDLo studies are straightforward to perform and the reproducibility issues in bioscience tend to be in more complex work. Against that, after multiple discussions with animal handlers and scientists practiced at injections, some plausible sources of error emerged. It is conceivable that an intracerebral injection was performed incorrectly sometimes, as this procedure is arguably more difficult than the others. It is plausible that injections into animals are more difficult to standardize than believed, particularly small animals. For instance, subcutaneous injections may be done in different locations on the animal, and some of these may be more effective spots than others. It could happen that a subcutaneous injection hits a vein more often than thought. Similarly, veins may be missed and either become subcutaneous injections or intramuscular injections. In animals such as mice, muscles can be missed.
However, for this study, there is no way to know what issues there may be, and rejecting data post hoc because it doesn't fit preconceptions, particularly when no injection method appears to fit those preconceptions better, is hard to support. I do not have a basis for quantifying the degree to which these data might represent a window into the rate of bench error in venom lethality studies nor the rate of such error.
Another plausible influence on the dataset could be that the ophidian species that kill humans get tested more, and so those species that do get tested more have a wider range fold change of LDmax ÷ LDmin. To test this hypothesis, several methods were used. The

Ecological Transects And Venom Variation
An ecological transect is a survey line of some length laid out in an area. Along that line, to some distance on each side, a survey is conducted to count the number of species. The transect is divided into segments, and each segment is a sampling of the species along the transect. As one progresses along the transect, the new species discovery rate will decline. Based on that slowing discovery rate, one can fit a curve, and using this, estimate the number of species in the area of the transect [30,31].

Conclusion
The import of this meta-analysis is several. First, the correlation between number of times a venomous ophidian's lethal dose is studied and the range of lethal dose indicates there is quite a bit of room for exploring lethal dose range, and that to properly characterize toxicity of whole ophidian venom is a large meta-project.
Second, the inability to differentiate between LDLo and LD50, and the preponderance of subsets where LDLo is higher than LD50, indicates that the N required to fully characterize venom is beyond what current studies have collected. This indicates, in turn, that the range of toxicity results for whole venom should be less reliable than they appear to be here, even for those ophidian species with the highest number of studies reported. In ecological parlance, the transect is at the beginning of its discoveries.
Beyond this, there are several areas that this analysis has bearing on: How to best estimate LD50 given current limitations; confirmations and caution relative to existing medical practice; and further research.

LD50 estimations
The correct way to define LD50 at this time is to use a meta-dataset. Treat LDLo the same as LD50, and provide LD mean, median, minimum, range, and standard deviation, along with the N for number of studies per test species used. Safety could be estimated by specifying from 1 up to 6 standard deviations (6 sigma) depending on desired safety margin. If an LDLo value is desired, this is simply the minimum lethal dose in the metadataset, and should be referred to that way (e.g. LDmin) to avoid confusion. This can be done separately for each route of inoculation.

Human LD50 estimations
The ethical problems of determining human dose-response force us to develop methods of estimation based on animal data. Yet, the human dose-response may be different than other animals, including monkeys.
It may be reasonable to consider exclusion of amphibian, bird and reptile data if there is sufficient N from mammals, where N is the number of studies conducted. However, from this meta-analysis it appears that a sufficient N is more than 50 different studies, and this is unlikely to happen soon. Also, there are multiple instances in larger ophidian datasets where non-mammal data is bracketed within mammalian data. Consequently, the most reasonable general course is to use aggregate data for all species, and compute as discussed above for the general case.
It has been argued that humans cannot receive IP or IC inoculations, except in the case of infants. However, there are cases of bites to the thorax in adults that appear to progress more quickly which may be similar enough to include it for that instance. Estimation of margin of error for this proposed algorithm will require non-trivial development and validation against existing datasets such as the one used for this metaanalysis, and represents an area of computational research.

Human bite treatment: confirmations and caution
This meta-dataset tells us that, controlling for dose, envenomation effect can vary by over 28,000 times within one species. Adding uncontrolled venom dose into the equation indicates that medicine is probably dealing with effective dose ranges spanning up to 1 million times. Consequently, physicians treating patients with snakebite cannot presume that because they saw 10, or even 50 cases for one species, that this will necessarily tell them what will happen on the next bite. This is true even if they have gotten good at estimating the size of the animal from the distance between the fang puncture marks. This analysis confirms that snakebite treatment should always be treated symptomatically, and that this should be done aggressively, because sooner or later an outlier should appear.
These results also confirm that antivenom manufacturers should use mixtures from a variety of snakes of the same species for immunization of animals.

Author contributions
This single author publication is entirely the work of the author.

Competing interests
The author declares that he has no competing interests.

Consent for Publication
Not applicable.
Ethics approval and consent to participate Not applicable.     Route of inoculation distribution: minimum and maximum lethal doses.

Figure 5
Mouse vs all test species LDmin and averages. Standard error of the means is shown as solid or dashed bars above and below mean average lines.  Venom range fold change for single test-animal-species and multiple routes of inoculation. N = 167 ophidian species with 2 or more reports for the same test species. There is a strong linear trend of increase in the range as the number of studies rises. In this graph, within each ophidian species, for test species with 2 or more entries, the test species with the largest fold change is shown.

Figure 8
Minimum lethal dose vs number of routes of inoculation. (Table 1, first entry,).
The N for the number of routes of inoculation 1 to 5 are, respectively: 30, 36, 61, 33, and 7. (Ophidian species N = 167). What is visible by inspection is that when data is filtered to only include mouse studies, the curve fit for mouse data is a near exact match, it is just truncated because of fewer ophidian species with higher number of DB entries.

Supplementary Files
This is a list of supplementary files associated with the primary manuscript. Click to download. Steinhoffs-DB-Selected-Venoms-curated-dataset-v1.xlsx