probitanalysis
TRANSCRIPT
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 %.
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 %.
2.5 2.534.2 34.213.3 13.3
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 %.
2.5
15.8 84.2 97.52.5
2.534.2 34.213.3 13.3
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 %.
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 =
3. Determine NN = the total number of individuals tested between the range of dosages that correspond to the LC16 to the LC84.
N = 49 + 46 + 48 = 143
4. Calculate Log10(f) and f. 2.77Log10(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 =
=
3. Determine NN = the total number of individuals tested between the range of dosages that correspond to the LC16 to the LC84.
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
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 =
=
3. Determine NN = the total number of individuals tested between the range of dosages that correspond to the LC16 to the LC84.
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
5. Calculate Upper and Lower 95% Confidence Limits (multiply or divide 'unlogged'conc/dose values by f):
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