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

After 2 days …

Reproduction test

After 21 days …

Range of Concentrations

Plot response vs. dose Response log concentration What pattern to expect?

Linear? Response log concentration

Threshold, linear? Response log concentration

Threshold, curve? Response log concentration

S-shape? Response log concentration

Hormesis? Response log concentration

Essential chemical? Response log concentration

Contr. Standard approaches NOEC Response log concentration LOEC * assumes threshold 1. Statistical testing 2. Curve fitting

Standard approaches EC50 Response log concentration usually no threshold 1. Statistical testing 2. Curve fitting

Standard summary statistics NOEC  highest tested concentration where effect is not significantly different from control EC50 or LC50  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  Number of live animals after fixed exposure period  Example: Daphnia exposed to nonylphenol mg/L0 h24 h48 h

Plot dose-response curve Procedure –plot fraction survival after 48 h –concentration on log scale Objective –derive LC50 –(seldom NOEC) concentration (mg/L) survival (%) first: parametric analysis

What model? Requirements –start at 100% and decrease to zero –inverse cumulative distribution? concentration (mg/L) survival (%)

Cumulative distributions E.g. the normal distribution … probability density cumulative 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” 1 cumulative density 1 20% mortality

What is the LC50? 1 cumulative density 1 50% mortality ?

Graphical method Probit transformation probits std. normal distribution + 5 Linear regression on probits versus log concentration concentration (mg/L) data mortality (%)

Fit model, least squares? concentration (mg/L) survival (%) Error is not normal: –discrete numbers of survivors –response must be between 0-100% Error is not normal: –discrete numbers of survivors –response must be between 0-100%

How to fit the model  Result at each concentration as binomial trial  Probability to survive is p, to die 1-p  Predicted p = f(c)  Estimate parameters of the model f –maximum likelihood estimation –weighted least-squares … –chi-square for goodness of fit … 11

Fit model, least squares? concentration (mg/L) survival (%)

Max. likelihood estimation concentration (mg/L) survival (%)

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 concentration fraction surviving data log-logistic log-normal Weibull gamma LC50-log lik. Log-logistic Log-normal Weibull Gamma

Non-parametric analysis Spearman-Kärber: wted. average of midpoints log concentration (mg/L) survival (%)  weights is number of deaths in interval  only for symmetrical distributions  weights is number of deaths in interval  only for symmetrical distributions

“Trimmed” Spearman-Kärber log concentration (mg/L) survival (%) Interpolate at 95%Interpolate at 5%

Summary: survival  Survival data are quantal data, reported as fraction responding individuals  Analysis types –parametric (tolerance distribution) –non-parametric (trimmed Spearman-Kärber)  Model hardly affects LC50  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 NOEC Response log concentration Contr.LOEC *

Derivation NOEC  ANOVA: 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  Trend tests –stepwise: remove highest dose until no sign. trend is left

What’s wrong?  Inefficient use of data (most data are ignored)  No statistically significant effect does not mean no effect –large effects (>50%) may occur at the NOEC –large variability leads to high NOECs  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 concentration (mg/L) reproduction (#eggs) Note: lsq is equivalent to max. likelihood, assuming normally- distributed errors

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 EC50

Example: Daphnia and Cd NOEC is (probably) zero concentration # juv./female

Example: Daphnia repro Put data on log-scale and fit sigmoid curve concentration # juv./female EC mM ( ) EC mM ( )

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 Protection goalAvailable data different exposure time different temperature different species time-variable conditions limiting food supplies interactions between species …

Extrapolation? single time point single endpoint Available dataAssessment factor Three LC50s1000 One NOEC100 Two NOECs50 Three NOECs10 ‘Safe’ level for field system LC50 ECx NOEC Response logconcentration

Where’s the science? No attempt to understand process of toxicity  Dose-response approaches are descriptive  Extrapolation through arbitrary ‘assessment factors’  Ignores that LC50/ECx/NOEC change in time

Effects change in time concentration fraction surviving 24 hours 48 hours LC50s.d. tolerance 24 hours hours

Toxicokinetics Why does LC50 decrease in time? Partly: –effects are related to internal concentrations –accumulation takes time time internal concentration time internal concentration chemical A chemical B chemical C small fish large fish Daphnia Change in time depends on 1.chemical 2.test species Change in time depends on 1.chemical 2.test species

Chronic tests With time, control response increases and all parameters may change … increasing time (t = 9-21d)

EC10 in time survival body length cumul. reproduction carbendazim Alda Álvarez et al. (2006) time (days) pentachlorobenzene time (days)

Toxicity is a process in time  Effects change in time, how depends on: –endpoint chosen –species tested –chemical tested  Ignored by standardising exposure time  No such thing as the ECx/LC50/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 toxico- kinetics toxico- dynamics internal concentration in time external concentration (in time) effects in time

Toxicokinetics  Simplest form: 1-compartment model  More detail in Module 2 … time internal concentration elimination rate

? Why do animals die? Instant death at certain threshold? Newman & McCloskey (2000) lethal exposure lethal exposure ?

Hazard modelling  Chemical increases probability to die internal concentration hazard rate internal concentration hazard rate survival in time  Effect depends on internal concentration 1 comp. kinetics blank value NEC

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

toxicant Sub-lethal effects

Dynamic Energy Budgets growth reproduction assimilation maintenance

growth and repro in time DEBtox basics DEB toxicokinetics  Effect depends on internal concentration  Chemical changes parameter in DEB model

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  Follow growth/repro/survival over large part of the life cycle Alda Álvarez et al. (2006)  Example: –nematode Acrobeloides nanus –exposed to cadmium in agar for 35 days –body size, eggs and survival determined regularly

Example: A. nanus and Cd Alda Álvarez et al. (2006) Mode of action: costs for growth Parameters: 7 for basic life history 7 for chemical behaviour Mode of action: costs for growth Parameters: 7 for basic life history 7 for chemical behaviour

Alternative approach  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  Usually acute Growth / repro  Usually (sub)chronic

Remember Survival  Usually acute  Quantal response (dead or alive) Growth / repro  Usually (sub)chronic  Graded response (#eggs, size)

Remember Survival  Usually acute  Quantal response (dead or alive)  Needs at least 10 animals per dose Growth / repro  Usually (sub)chronic  Graded response (#eggs, size)  Needs 1 animal per dose (more for NOEC)

Remember Survival  Usually acute  Quantal response (dead or alive)  Needs at least 10 animals per dose  Analyse by finding tolerance distribution or non-parametric Growth / repro  Usually (sub)chronic  Graded response (#eggs, size)  Needs 1 animal per dose (more for NOEC)  Analyse by standard regression techniques (curve fitting)

Remember Survival  Usually acute  Quantal response (dead or alive)  Needs at least 10 animals per dose  Analyse by finding tolerance distribution or non-parametric  LC50, EC50 … Growth / repro  Usually (sub)chronic  Graded response (#eggs, size)  Needs 1 animal per dose (more for NOEC)  Analyse by standard regression techniques (curve fitting)  NOEC, EC50, EC10 …

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 Cd concentration (mg/L) total juveniles after 15d high food low food EC50 Data Heugens et al. (2006) Does food limitation increase effect of cadmium?

Food limitation growth reproduction assimilation maintenance ad libitum 5%

Food limitation growth reproduction assimilation limiting maintenance 50%

Electronic DEB laboratory DEBtox –Windows version (2007) –data from standard tests Free downloads from DEBtool –open source (Octave, MatLab) –full range of DEB research –advanced DEBtox applications