1. Dose-response analysis Tjalling Jager Dept. Theoretical Biology

2. Contents ‘Classic’ dose-response analysis  Background and general approach  Analysis of survival data  Analysis of growth and reproduction data Critique and alternatives  Limitations of the classic approach  Dynamic modelling as an alternative

3. Why dose-response analysis? How toxic is chemical X? –risks of production or use of X –ranking chemicals (compare X to Y) –environmental quality standards Need measure of toxicity that is: –good indicator for (no) effects in the field –comparable between chemicals Scientific interest: –how do chemicals affect organisms? –stress organism to reveal how they work …

4. Test organisms (aquatic)

5. Tests are highly standardised (OECD, ISO, ASTM etc.): –species –exposure time –endpoints –test medium, temperature etc.

6. Reproduction test 50-100 ml of well- defined test medium, 18-22°C

7. Reproduction test Daphnia magna Straus, <24 h old

8. Reproduction test Daphnia magna Straus, <24 h old

9. Reproduction test wait for 21 days, and count total offspring …

10. Reproduction test at least 5 test concentrations in geometric series …

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

12. Linear? Response log concentration

13. Threshold, linear? Response log concentration

14. Threshold, curve? Response log concentration

15. S-shape? Response log concentration

16. Hormesis? Response log concentration

17. Essential chemical? Response log concentration

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

19. Standard approaches EC50 Response log concentration 1. Statistical testing 2. Curve fitting

20. Standard summary statistics NOEC  highest tested concentration where effect is not significantly different from control EC50  the estimated concentration for 50% effect can be generalised to ECx

21. Difference graded-quantal Quantal: count fraction of animals responding –e.g., 8 out of 20 = 0.4 –always between 0 and 1 (or 0-100%) –usually mortality or immobility –LC50, LCx Graded: measure degree of response for each individual –e.g., 85 eggs or body weight of 23 mg –between 0 and infinite –usually body size or reproduction –NOEC, ECx

22. Contents ‘Classic’ dose-response analysis  Background and general approach  Analysis of survival data  Analysis of growth and reproduction data Critique and alternatives  Limitations of the classic approach  Dynamic modelling as an alternative

23. Survival analysis Typical data set –number of live animals at observation times –example: Daphnia exposed to nonylphenol mg/L0 h24 h48 h 0.00420 0.03220 0.05620 0.10020 0.18020 16 0.32020132 0.5602020

24. Plot dose-response curve Procedure –plot percentage survival after 48 h –concentration on log scale Objective –derive LC50

25. What model? Requirements curve –start at 100% and monotonically decreasing to zero –inverse cumulative distribution?

26. Cumulative distributions E.g. the normal distribution … probability density cumulative density 1

27. Distribution of what? Assumptions for ‘tolerance’ –animal dies instantly when exposure exceeds ‘threshold’ –threshold varies between individuals –spread of distribution indicates individual variation probability density cumulative density 1

28. Concept of ‘tolerance’ 1 cumulative density 1 20% mortality

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

30. Graphical method Probit transformation 2 3 4 5 6 7 8 9 probits std. normal distribution + 5 Linear regression on probits versus log concentration 0 20 40 60 80 100 0.0010.010.11 concentration (mg/L) 0 20 40 60 80 100 0.0010.010.11 data mortality (%)

31. Fit model, least squares? 0 20 40 60 80 100 0.0010.010.11 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%

32. How to fit the model Maximum likelihood  Result at each concentration is binomial trial, B(n,p) –probability to survive is p, to die 1-p –predicted p is function of concentration 11

33. How to fit the model Maximum likelihood  Result at each concentration is binomial trial, B(n,p) –probability to survive is p, to die 1-p –predicted p is function of concentration  Estimate parameters of model for p 11

34. Fit model, least squares? 0 20 40 60 80 100 0.0010.010.11 concentration (mg/L) survival (%)

35. Max. likelihood estimation 0 20 40 60 80 100 0.0010.010.11 concentration (mg/L) survival (%)

36. Which model curve? 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.

37. Which model curve? 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 concentration fraction surviving data log-logistic log-normal Weibull gamma LC50log lik. Log-logistic0.225-16.681 Log-normal0.226-16.541 Weibull0.242-16.876 Gamma0.230-16.582

38. Non-parametric analysis Spearman-Kärber: wted. average of midpoints 0 20 40 60 80 100 0.0010.010.11 log concentration (mg/L) survival (%)  weights: number of deaths in interval  symmetric distribution (on log scale)  weights: number of deaths in interval  symmetric distribution (on log scale)

39. ‘Trimmed’ Spearman-Kärber 0 20 40 60 80 100 0.0010.010.11 log concentration (mg/L) survival (%) Interpolate at 95%Interpolate at 5%

40. Summary: survival data Survival data are ‘quantal’ responses –data are fraction of individuals responding –underlying mechanism can be tolerance distribution but see GUTS (Jager et al., 2011) Analysis types –regression (e.g., log-logistic or log-normal)  LCx –non-parametric (e.g., Spearman-Kärber)  LC50

41. Contents ‘Classic’ dose-response analysis  Background and general approach  Analysis of survival data  Analysis of growth and reproduction data Critique and alternatives  Limitations of the classic approach  Dynamic modelling as an alternative

42. Difference graded-quantal Quantal: count fraction of animals responding –e.g. 8 out of 20 = 0.4 –always between 0% and 100% –usually mortality or immobility –LC50, LCx Graded: measure degree of response for each individual –e.g. 85 eggs or body weight of 23 mg –usually between 0 and infinite –usually growth or reproduction –NOEC, ECx

43. Analysis of continuous data Endpoints for individual –in ecotox, usually growth (fish) or reproduction (Daphnia) Two approaches –NOEC and LOEC (statistical testing) –ECx (regression modelling)

44. Derivation NOEC NOEC Response log concentration Contr. LOEC *

45. Derivation NOEC  ANOVA-type: 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 –Mann-Whitney test with correction  Step-down trend tests –remove highest dose until no sign. trend is left

46. What’s wrong?  Inefficient use of data –most data points are ignored –NOEC has to be a test concentration  Awkward use of statistics –no statistically significant effect ≠ no effect –large range of effects at NOEC ( 50%) –large variability in test leads to high NOECs  NOEC is still widely used … –see Jager (2012) See e.g., Laskowski (1995), Crane & Newman (2000)

47. Regression modelling Select model –log-logistic (ecotoxicology) –anything that fits (mainly toxicology) straight line exponential curve polynomial

48. Least-squares estimation concentration (mg/L) 0 20 40 60 80 100 0.0010.010.11 reproduction (#eggs) Note: equivalent to MLE, assuming independent normally- distributed errors, with constant variance

49. Example: Daphnia repro Plot concentration on log-scale  NOEC might be zero …. 10 -2 10 10 0 1 0 20 30 40 50 60 70 80 90 100 concentration (mM) # juv./female

50. Example: Daphnia repro Fit sigmoid curve  Estimate ECx from the curve 10 -2 10 10 0 1 0 20 30 40 50 60 70 80 90 100 concentration (mM) # juv./female EC10 0.13 mM (0.077-0.19) EC50 0.41 mM (0.33-0.49)

51. Regression modelling Advantage –use more of the data –ECx with confidence interval –poor data lead to large confidence intervals But, model is purely empirical –no understanding of the process –extrapolation beyond test is dangerous –interval is valid given that model is true …

52. Summary: continuous data Repro/growth data are ‘graded’ responses –look at average response of individual animals –not fraction of animals responding –thus, we cannot talk about tolerance distributions Analysis types –statistical testing (e.g., ANOVA)  NOEC –regression (e.g., log-logistic)  ECx

53. Critique and alternatives Tjalling Jager Dept. Theoretical Biology

54. Contents ‘Classic’ dose-response analysis  Background and general approach  Analysis of survival data  Analysis of growth and reproduction data Critique and alternatives  Limitations of the classic approach  Dynamic modelling as an alternative

55. Challenges of ecotox  Some 100,000 man-made chemicals  For animals, >1 million species described  Complex dynamic exposure situations  Combinations of chemicals and other stresses Test all these situations?

56. Extrapolation “Protection goal” Laboratory tests

57. 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

58. If EC50 is the answer … … what was the question? “What is the concentration of chemical X that leads to 50% effect on the total number of offspring of Daphnia magna (Straus) after 21-day constant exposure under standardised laboratory conditions?”

59. Time is of the essence Toxicity is a process in time  statistics like LC50/ECx/NOEC change in time  hidden by standardisation –Daphnia acute:2 days –fish acute:4 days –Daphnia repro21 days –fish growth28 days –…–…

60. 24 hours Effects change in time 00.10.20.30.40.50.60.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 concentration fraction surviving 48 hours LC50s.d. tolerance 24 hours0.3700.306 48 hours0.2260.267 Note: LC50 will (almost) always decrease in time, often reaching a stable (incipient) value

61. Chronic tests With time, control response increases and all parameters may change … increasing time (t = 9-21d) Note: ECx will not always decrease in time!

62. EC10 in time 0.5 1 1.5 2 2.5 05101520 0 survival body length cumul. reproduction carbendazim Alda Álvarez et al. (2006) time (days) 0246810121416 0 20 40 60 80 100 120 140 pentachlorobenzene time (days)

63. Toxicity is a process in time  Effects change in time, how depends on: –endpoint, species, chemical, conditions  No such thing as the ECx/LC50/NOEC –hampers comparing chemicals, species, endpoints –hampers extrapolation to the field  In summary, these statistics … –form a poor basis for RA –are of little use for science Baas et al. (2010), Jager (2011)

64. Contents ‘Classic’ dose-response analysis  Background and general approach  Analysis of survival data  Analysis of growth and reproduction data Critique and alternatives  Limitations of the classic approach  Dynamic modelling as an alternative

65. concentrations over time and space environmental characteristics and emission pattern Fate modelling mechanistic fate model physico-chemical properties under laboratory conditions

66. Fate modelling oil-spill modelling pesticide fate modelling

67. Learn from fate modelling effects data for one set of conditions predict effects in dynamic environment mechanistic model for species

68. model parameters for species test conditions Data analysis mechanistic model for species effects data for one set of conditions model parameters for toxicant

69. predict life- history traits over time model parameters for species model parameters for toxicant Educated predictions mechanistic model for species dynamic environment: exposure and conditions

70. external concentration (in time) toxico-kinetic model toxico-kinetic model TKTD modelling internal concentration in time process model for the organism process model for the organism effects on endpoints in time toxicokinetics toxicodynamics

71. external concentration (in time) toxico-kinetic model toxico-kinetic model TKTD modelling internal concentration in time toxicokinetics

72. TKTD modelling internal concentration in time process model for the organism process model for the organism effects on endpoints in time toxicodynamics

73. Organisms are complex … process model for the organism process model for the organism

74. Learn from fate modellers Make an idealisation of the system  how much biological detail do we minimally need … –to explain how organisms grow, develop, reproduce and die –to explain effects of stressors on life-history traits over time –to predict effects for untested (dynamic) situations –without being species- or stressor-specific

75. Learn from fate modellers A process model can be extremely simple!  Acute survival –death can be represented as a chance process in time –see ‘GUTS’ Jager et al. (2011)

76. Example nonylphenol 01020304050 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time (hr) fraction surviving 0.004 mg/L 0.032 mg/L 0.056 mg/L 0.1 mg/L 0.18 mg/L 0.32 mg/L 0.56 mg/L

77. Learn from fate modellers How do we deal with growth and reproduction?  These are not outcome of chance processes …  Organisms obey mass and energy conservation

78. Mass & energy conservation

83. Dynamic Energy Budget Organisms obey mass and energy conservation –find the simplest set of rules... –over the entire life cycle... –related species follow related rules Kooijman (2010)

84. Dynamic Energy Budget Organisms obey mass and energy conservation –find the simplest set of rules... –over the entire life cycle... –related species follow related rules www.debtox.info

85. Ex.1: maintenance costs time cumulative offspring time body length TPT Jager et al. (2004)

86. Ex.2: growth costs time body length time cumulative offspring Pentachlorobenzene Alda Álvarez et al. (2006)

87. Ex.3: egg costs time cumulative offspring time body length Chlorpyrifos Jager et al. (2007)

88. ‘Standard’ tests... mechanistic model for species A constant exposure, ad libitum food DEBtox examples, see: www.debtox.info/papers_debtox.php model parameters for species model parameters for toxicant

89. Non-standard tests... mechanistic model for species A time-varying exposure, limiting food,... DEBtox examples, see: www.debtox.info/papers_debtox.php model parameters for species model parameters for toxicant

90. Extrapolations... mechanistic model for species A time-varying exposure, limiting food,... DEBtox examples, see: www.debtox.info/papers_debtox.php model parameters for species model parameters for toxicant population consequences

91. Wrapping up Time is of the essence –an organism is a dynamic system … –in a dynamic environment … –with dynamic exposure to chemicals NOEC, EC50 etc. are limited … –for predicting effects in the field –for comparing toxicity –for helping understand toxic effects

92. Wrapping up Mechanistic models are essential –to elucidate underlying mechanisms –to extrapolate to untested conditions –to interpret non-standard test data To do that... –learn from fate and TK modellers … –but... more research is needed –and … more education …

93. More information on DEB: www.bio.vu.nl/thb course/symposium in 2015 (Marseille, FR) on DEBtox: www.debtox.info summercourse 2015 or 2016 (DK) free e-book on (toxicants in) DEB