ProbitAnalysis

Toxicity Testing cont’d• Toxicology is Easy - Discussion• Shape of Dose-Response Curve

– Linear vs Sigmoid– Steep vs Flat

• Why LC50?• Acute Toxicity Test Design• Probit Analysis

Shape of the Dose-Response Relationship

Why LC50?

Concentration (or Dose)

Res

pons

e

Low High

0%

100%

Acute Toxicity Test Design

1. Test Material (toxicant)• Pure• Commercial formulation• Mixtures of known concentration• Carriers/solvents• Unknown mixtures (eg. sediment,effluent)

2. Test Organism• Most sensitive• Most representative• Wild species• Rear in lab• Known physiology• Bred for uniformity• Certified disease free• Known susceptible

strain

Ex: Daphnia

Fathead minnows

Rats/Mice

Animal Cell cultures

Algal cell cultures

Duckweed

Mealworms

Earthworms

Frogs/tadpoles

3. Exposure Method/Apparatus

• Oral dose/gavage• Diet• Intraperitoneal injection• Inhalant• Dermal• Dry vial• Static vs Flow-thru aquaria

4. Experimental Design

• Sample size• Unbiased allocation of subjects• Test environment (temp, 02, pH, light cycle, food, etc)• Negative controls (untreated, solvent/carrier)• Positive controls (toxin with well known effect)• Baseline measurements (size, test envt, etc)

5. Range-Finding Test

• 10X progression of toxin concentration• 3-5 individuals per concentration• 5 concentrations plus control(s)

6. Definitive Test

• Expand on meaningful conc. From range test• 5+ conc. Plus control(s)• Geometric progression of conc. (2X or higher)• 1 conc. Kills < 35%; 1 conc. Kills > 65%• 10+ individuals per concentration• Replicates?• 96h, no food

7. Endpoint (what response to measure?)

• Death (LC50, LD50)• Paralysis, loss of equilibrium (EC50)• Other sub-lethal endpoints (EC50)

Pop. growth rate

Indiv. growth rate

Foraging behavior

Escape behavior

Learning/cognitive

Bone formation

Protein production

Enzyme activity

Chromosome breakage

RNA synthesis

8. Calculations•Plot %mortality vs log conc. (or dose)

•Do not include control data in curve fit

•If control mortality exceeds 10%, correct w/ Abbotts formula•Do probit analysis for accurate LC50

•Calc. 95% confidence intervals

(Lindane)

Diff. toxicity to diff. spp.Diff. Toxicity via diff routes of exposure – why?

Yikes! – those are my tax dollars!

What about transgenerational effects??

Increasing realityIncreasing costIncreasing uncertainty

Scale of Toxicological Endpoints

Probit Analysis

• Turn a curve into a lineCan connect dots more accuratelyAllows accurate “inverse prediction”Allows statistical analysis using regression/linear

models

• Probit = probability unit% of population responding as a function of standard deviation units from the mean

Tolerance

Dose-Response

No.

of I

ndiv

idua

ls

No.

of I

ndiv

idua

ls

Cum

ulat

ive

Perc

ent

Cum

ulat

ive

Perc

ent

Log of Concentration

Log of Concentration

Concentration

Concentration

Result = ‘nearly’ straight line

Normal Distribution Mean50%

Std Dev Units

1. What % of observations fall with each SD unit?

2. Express % from above as cumulative percent.

3. Assign probits to cumulative %.


Std Dev Units




2.5 2.534.2 34.213.3 13.3


Std Dev Units




2.5

15.8 84.2 97.52.5

2.534.2 34.213.3 13.3


Std Dev Units




2.5

15.8 84.2 97.52.5

2.534.2 34.213.3 13.3

2.5

2.5

15.8 84.2 97.5

Log Probit6.181.009

6.18

1.009

Log LC84= 0.93; LC84= 8.51

Log LC16 = 0.43; LC16 = 2.69

Log LC50 = 0.68; LC50 = 4.79

“Inverse Prediction”

Why calc. 95% C.L.? How?

Calculating 95% Confidence Limits of LC50's(source: F. Matsumura. 1985. Toxicology of Insecticides, 2nd Ed., Plenum, pp.14-16)Example Worksheet - Rotenone toxicity to Macrosphoniella sanborni

1. Use inverse prediction from the graph to estimate the Log 10 of the LC84, LC16, and LC50 then “un-log” the values and express as mg/L.

Log10 Conc. Conc.(mg/L)eg: LC84 = LC16 =

LC50 =

2. Calculate S and Log10 (S) (use the 'un-logged' dose/conc. values).

LC84 LC50 S = LC50 __ LC16

2S = Log10 (S) =

Calculating 95% Confidence Limits of LC50's(source: F. Matsumura. 1985. Toxicology of Insecticides, 2nd Ed., Plenum, pp.14-16)Example Worksheet - Rotenone toxicity to Macrosphoniella sanborni

1. Use inverse prediction from the graph to estimate the Log 10 of the LC84, LC16, and LC50 then “un-log” the values and express as mg/L.

Log10 Conc. Conc. (mg/L)eg: LC84 = .93 8.51 LC16 = .43 2.69

LC50 = .68 4.79

2. Calculate S and Log10 (S) (use the 'un-logged' dose/conc. values).

LC84 LC50 8.51 4.79S = LC50 __ LC16 4.79 2.69

2 2S = 1.78 Log10 (S) = 0.250

+ +

3. Determine NN = the total number of individuals tested between the range of dosages that correspond to the LC16 to the LC84.

N =

4. Calculate Log10(f) and f. 2.77

Log10(f) = N x Log10 (S)

Log10(f) = f =

5. Calculate Upper and Lower 95% Confidence Limits (multiply or divide 'unlogged'conc/dose values by f):

Upper Limit = LC50 x f =

Lower Limit = LC50 / f =


N = 49 + 46 + 48 = 143

4. Calculate Log10(f) and f. 2.77Log10(f) = N x Log10 (S)

Log10(f) = f =




=


N = 49 + 46 + 48 = 143

4. Calculate Log10(f) and f. 2.77 2.77Log10(f) = N x Log10 (S) 143 x 0.250

Log10(f) = 0.058 f = 1.143




=


N = 49 + 46 + 48 = 143

4. Calculate Log10(f) and f. 2.77 2.77Log10(f) = N x Log10 (S) 143 x 0.250

Log10(f) = 0.058 f = 1.143


Upper Limit = LC50 x f = 4.79 x 1.143 = 5.47

Lower Limit = LC50 / f = 4.79 / 1.143 = 4.19

=

LC50 = 4.79 mg/L (4.19 – 5.47; 95% C.L.)

Log scale

ProbitAnalysis

Documents

Transcript of ProbitAnalysis