Doseresponse relationships Tjalling Jager Theoretical Biology Doseresponse analysis
Dose-response relationships Tjalling Jager Theoretical Biology
Dose-response analysis This morning: 1. Introduction in effects assessment 2. Analysis of survival data 3. Analysis of continuous data 4. Problems with these methods 5. An alternative approach
Why effects assessment? How toxic is chemical X? – for RA of the production or use of X – for ranking chemicals (compare X to Y) – for environmental quality standards Need measure of toxicity that is: – good indicator for environment – comparable between chemicals
Test organisms (aquatic)
Standardisation Toxicity tests are highly standardised (OECD, ISO, etc. ): – – species exposure time endpoints test medium, temperature etc.
Types of tests ‘Acute’ – short-term – usually mortality or immobility – quantal or discrete response ‘Chronic’ – long-term – usually sub-lethal endpoint – graded or continuous response
Standard test set-up
Survival test
Survival test
After 2 days …
Reproduction test
Reproduction test
After 21 days …
Range of Concentrations
Plot response vs. dose Response What pattern to expect? log concentration
Response Linear? log concentration
Response Threshold, linear? log concentration
Response Threshold, curve? log concentration
Response S-shape? log concentration
Response Hormesis? log concentration
Response Essential chemical? log concentration
Standard approaches 1. Statistical testing 2. Curve fitting Contr. Response NOEC * LOEC assumes threshold log concentration
Standard approaches Response 1. Statistical testing 2. Curve fitting EC 50 usually no threshold log concentration
Standard summary statistics NOEC Ø highest tested concentration where effect is not significantly different from control EC 50 or LC 50 Ø the estimated concentration for 50% effect, compared to control
Dose-response analysis This morning: 1. Introduction in effects assessment 2. Analysis of survival data 3. Analysis of continuous data 4. Problems with these methods 5. An alternative approach
Available data Ø Number of live animals after fixed exposure period Ø Example: Daphnia exposed to nonylphenol mg/L 0 h 24 h 48 h 0. 004 20 20 20 0. 032 20 20 20 0. 056 20 20 20 0. 100 20 20 20 0. 180 20 20 16 0. 320 20 13 2 0. 560 20 2 0
Plot dose-response curve Procedure – plot fraction survival after 48 h – concentration on log scale Objective first: parametric analysis 100 survival (%) – derive LC 50 – (seldom NOEC) 80 60 40 20 0 0. 001 0. 1 concentration (mg/L) 1
What model? Requirements – start at 100% and decrease to zero – inverse cumulative distribution? survival (%) 100 80 60 40 20 0 0. 001 0. 1 concentration (mg/L) 1
Cumulative distributions E. g. the normal distribution … cumulative density probability density 1
Distribution of what? Assumptions – animal dies instantly when exposure exceeds ‘threshold’ – threshold varies between individuals – spread of distribution indicates individual variation
Concept of “tolerance” 20% mortality cumulative density 1 20% mortality
What is the LC 50? ? cumulative density 1 50% mortality
Graphical method Probit transformation std. normal distribution + 5 mortality (%) 100 80 60 40 20 data 0 0. 001 0. 1 concentration (mg/L) 1 2 3 4 5 6 7 8 9 probits Linear regression on probits versus log concentration
Fit model, least squares? survival (%) 100 80 60 Error is not normal: – discrete numbers of survivors – response must be between 0 -100% 40 20 0 0. 001 0. 1 concentration (mg/L) 1
How to fit the model Ø Result at each concentration as binomial trial Ø Probability to survive is p, to die 1 -p Ø Predicted p = f(c) Ø Estimate parameters of the model f – maximum likelihood estimation – weighted least-squares … – chi-square for goodness of fit … 1
Fit model, least squares? survival (%) 100 80 60 40 20 0 0. 001 0. 1 concentration (mg/L) 1
Max. likelihood estimation survival (%) 100 80 60 40 20 0 0. 001 0. 1 concentration (mg/L) 1
Which distribution? Popular distributions – log-normal (probit) – log-logistic (logit) – Weibull ISO/OECD guidance document A statistical regression model itself does not have any meaning, and the choice of the model is largely arbitrary.
Resulting fits: close-up fraction surviving 1 LC 50 -log lik. 0. 9 Log-logistic 0. 225 16. 681 0. 8 Log-normal 0. 226 16. 541 0. 7 Weibull 0. 242 16. 876 0. 6 Gamma 0. 230 16. 582 0. 5 0. 4 0. 3 0. 2 0. 1 0 data log-logistic log-normal Weibull gamma -1 10 concentration
Non-parametric analysis Spearman-Kärber: wted. average of midpoints survival (%) 100 Ø weights is number of deaths in interval Ø only for symmetrical distributions 80 60 40 20 0 0. 001 0. 1 log concentration (mg/L) 1
“Trimmed” Spearman-Kärber survival (%) 100 Interpolate at 95% 80 60 40 20 0 0. 001 Interpolate at 5% 0. 01 0. 1 log concentration (mg/L) 1
Summary: survival Ø Survival data are quantal data, reported as fraction responding individuals Ø Analysis types – parametric (tolerance distribution) – non-parametric (trimmed Spearman-Kärber) Ø Model hardly affects LC 50 Ø Error is ‘multinomial’
Dose-response analysis This morning: 1. Introduction in effects assessment 2. Analysis of survival data 3. Analysis of continuous data 4. Problems with these methods 5. An alternative approach
Difference graded-quantal Quantal: fraction of animals responding – e. g. 8 out of 20 = 0. 4 – always between 0% and 100% – no standard deviations Graded: degree of response of the animal – e. g. 85 eggs or body weight of 23 g – usually between 0 and infinite – standard deviations when >1 animal
Analysis of continuous data Endpoints – In ecotoxicology, usually growth (fish) and reproduction (Daphnia) Two approaches – NOEC and LOEC (statistical testing) – ECx (regression modelling)
Derive NOEC Contr. Response NOEC * LOEC log concentration
Derivation NOEC ØANOVA: are responses in all groups equal? H 0: R(1) = R(2) = R(3) … Post test: multiple comparisons to control, e. g. : – – t-test with e. g. Bonferroni correction Dunnett’s test Fisher’s exact test with correction Mann-Whitney test with correction ØTrend tests – stepwise: remove highest dose until no sign. trend is left
What’s wrong? Ø Inefficient use of data (most data are ignored) Ø No statistically significant effect does not mean no effect – large effects (>50%) may occur at the NOEC – large variability leads to high NOECs Ø However, NOEC is still used! See e. g. , Laskowski (1995), Crane & Newman (2000)
Regression modelling Select model – log-logistic (ecotoxicology) – anything that fits (mainly toxicology) • straight line • exponential curve • polynomial
Least-squares estimation reproduction (#eggs) 100 80 60 40 Note: lsq is equivalent to max. likelihood, assuming normallydistributed errors 20 0 0. 001 0. 1 concentration (mg/L) 1
Example: Daphnia repro test Standard protocol – take juveniles <24 h old – expose to chemical for 21 days – count number of offspring daily – use total number of offspring after 21 days – calculate NOEC and EC 50
Example: Daphnia and Cd NOEC is (probably) zero 100 90 # juv. /female 80 70 60 50 40 30 20 10 0 0 0. 2 0. 4 0. 6 0. 8 1 1. 2 1. 4 concentration 1. 6 1. 8 2
Example: Daphnia repro Put data on log-scale and fit sigmoid curve 100 EC 10 0. 13 m. M (0. 077 -0. 19) 90 # juv. /female 80 70 60 EC 50 0. 41 m. M (0. 33 -0. 49) 50 40 30 20 10 0 -2 10 -1 10 0 10 concentration 1 10
Regression modelling Advantage – use more of the data – ECx is estimated with confidence interval – poor data lead to large confidence intervals Model is purely empirical – no understanding of the process – extrapolation is dangerous!
Summary: continuous data Repro/growth data are ‘graded’ responses – look at average response of animals – not fraction of animals responding! Thus: no ‘tolerance distribution’! Analysis types – statistical testing (e. g. , ANOVA) NOEC – regression (e. g. , log-logistic) ECx
Dose-response analysis This morning: 1. Introduction in effects assessment 2. Analysis of survival data 3. Analysis of continuous data 4. Problems with these methods 5. An alternative approach
Problems Dilemma of risk assessment Available data Protection goal • different exposure time • different temperature • different species • time-variable conditions • limiting food supplies • interactions between species • …
single time point single endpoint Response Extrapolation? LC 50 ECx NOEC log concentration Available data Assessment factor Three LC 50 s 1000 One NOEC 100 Two NOECs 50 Three NOECs 10 ‘Safe’ level for field system
Where’s the science? No attempt to understand process of toxicity Ø Dose-response approaches are descriptive Ø Extrapolation through arbitrary ‘assessment factors’ Ø Ignores that LC 50/ECx/NOEC change in time
Effects change in time 1 0. 9 fraction surviving 0. 8 LC 50 s. d. tolerance 24 hours 0. 370 0. 306 48 hours 0. 226 0. 267 0. 6 0. 5 24 hours 0. 4 0. 3 48 hours 0. 2 0. 1 0 0 0. 1 0. 2 0. 3 0. 4 concentration 0. 5 0. 6 0. 7
Toxicokinetics Why does LC 50 decrease in time? Partly: internal concentration Change in time depends on 1. chemical 2. test species internal concentration – effects are related to internal concentrations – accumulation takes time Daphnia chemical B chemical small fish. A large fish C chemical time
Chronic tests With time, control response increases and all parameters may change … 100 increasing time (t = 9 -21 d) 90 # juv. /female 80 70 60 50 40 30 20 10 0 -2 10 -1 10 0 10 concentration 1 10
EC 10 in time survival Alda Álvarez et al. (2006) body length cumul. reproduction carbendazim 2. 5 pentachlorobenzene 140 120 2 100 1. 5 80 60 1 40 0. 5 20 0 0 5 10 time (days) 15 20 0 0 2 4 6 8 10 time (days) 12 14 16
Toxicity is a process in time Ø Effects change in time, how depends on: – endpoint chosen – species tested – chemical tested Ø Ignored by standardising exposure time Ø No such thing as the ECx/LC 50/NOEC – difficult to compare chemicals, species, endpoints
Dose-response analysis This morning: 1. Introduction in effects assessment 2. Analysis of survival data 3. Analysis of continuous data 4. Problems with these methods 5. An alternative approach
Biology-based modelling Make explicit (but simple) assumptions on mechanisms of toxicity internal concentration in time external concentration (in time) toxicokinetics toxicodynamics effects in time
Toxicokinetics internal concentration Ø Simplest form: 1 -compartment model Ø More detail in Module 2 … n tio a n te ra i lim e time
Why do animals die? Instant death at certain threshold? lethal exposure ? ? Newman & Mc. Closkey (2000)
Hazard modelling Ø Chemical increases probability to die Ø Effect depends on internal concentration hazard rate 1 comp. kinetics NEC hazard rate blank value internal concentration survival in time
Example DEBtox
Results Parameters are • time-independent • comparable between species and chemicals Use parameters to predict effects • on different time-scale • of time-varying exposure • of different size animals • of different chemicals • …
Sub-lethal effects
Sub-lethal effects
Sub-lethal effects toxicant
Sub-lethal effects
Dynamic Energy Budgets assimilation reproduction maintenance growth
DEBtox basics Ø Effect depends on internal concentration Ø Chemical changes parameter in DEB model toxicokinetics DEB growth and repro in time
Example DEBtox
Results Parameters are • time-independent • comparable between species and chemicals Use parameters to predict effects • on different time-scale • of time-varying exposure • of different size animals • at population level • …
Life-cycle data Ø Follow growth/repro/survival over large part of the life cycle Ø Example: – nematode Acrobeloides nanus – exposed to cadmium in agar for 35 days – body size, eggs and survival determined regularly Alda Álvarez et al. (2006)
Example: A. nanus and Cd Mode of action: costs for growth Parameters: 7 for basic life history 7 for chemical behaviour Alda Álvarez et al. (2006)
Alternative approach Ø Biology-based methods (DEBtox) – – make explicit assumptions on processes analyse all data in time parameters do not change in time basis for extrapolations
Summary
Remember Survival Ø Usually acute Growth / repro Ø Usually (sub)chronic
Remember Survival Ø Usually acute Ø Quantal response (dead or alive) Growth / repro Ø Usually (sub)chronic Ø Graded response (#eggs, size)
Remember Survival Ø Usually acute Ø Quantal response (dead or alive) Ø Needs at least 10 animals per dose Growth / repro Ø Usually (sub)chronic Ø Graded response (#eggs, size) Ø Needs 1 animal per dose (more for NOEC)
Remember Survival Ø Usually acute Ø Quantal response (dead or alive) Ø Needs at least 10 animals per dose Ø Analyse by finding tolerance distribution or non-parametric Growth / repro Ø Usually (sub)chronic Ø Graded response (#eggs, size) Ø Needs 1 animal per dose (more for NOEC) Ø Analyse by standard regression techniques (curve fitting)
Remember Survival Ø Usually acute Ø Quantal response (dead or alive) Ø Needs at least 10 animals per dose Ø Analyse by finding tolerance distribution or non-parametric Ø LC 50, EC 50 … Growth / repro Ø Usually (sub)chronic Ø Graded response (#eggs, size) Ø Needs 1 animal per dose (more for NOEC) Ø Analyse by standard regression techniques (curve fitting) Ø NOEC, EC 50, EC 10 …
Watch out! Problems with standard analyses – descriptive, no understanding of process – statistics depend on exposure time Alternative: biology-based – make assumptions on mechanisms – analyse effects data in time Standard analysis may have role in risk assessment but …
Science needs BB methods Does food limitation increase effect of cadmium? total juveniles after 15 d 100 high food 80 low food EC 50 60 40 20 0 0 0. 05 0. 15 0. 2 Cd concentration (mg/L) 0. 25 Data Heugens et al. (2006)
Food limitation assimilation ad libitum 5% reproduction maintenance growth
Food limitation assimilation limiting 50% reproduction maintenance growth
Electronic DEB laboratory Free downloads from http: //www. bio. vu. nl/thb/deblab/ DEBtox – Windows version 2. 0. 2. (2007) – data from standard tests DEBtool – open source (Octave, Mat. Lab) – full range of DEB research – advanced DEBtox applications
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