9 th International Workshop on Plant Disease Epidemiology. Laederneau, France, April 10-15,2005

1. Introduction 9th International Workshop on Plant Disease Epidemiology.Laederneau, France, April 10-15,2005

2. International Workshop on Plant Disease Epidemiology • Pau, France, 1963 • The Netherlands, 1971 • Penn State Univ. 1979 • North Carolina State Univ., 1983 9. Landerneau, France, 2005 • Jerusalem, Israel, 1986 • Giessen, Germany, 1990 • Papendal, The Netherlands, 1994 • Ouro Preto, Brazil, 2001 Beijing, China 2009 L. V. Madden

3. IEW9 • Time: April 10-15,2005 • Address: Landerneau, France • Subject: Facing challenges of the 21th century • Country Number: • Research scientist: 100 • Keynote Number: 13 • Chair: Laurence V.Madden(OSU)

4. Botanical epidemiology:Some key advances, and its continuing role in disease management

5. Historical Background • 1963—a most important year: • Plant Disease: Epidemics and Control by J. E. Vanderplank (“van der Plank”) • NATO Advanced Study Institute international meeting on plant disease epidemiology • Now ‘known’ as the “1st International Workshop on Plant Disease Epidemiology” • Vanderplank made the compelling argument that: • “Chemical industry and plant breeders have forged fine tactical weapons; but only epidemiology sets the strategy.” • Although this audience would certainly accept this statement, unfortunately not all plant pathologists consider epidemiology, especially some of the ‘sophisticated’ aspects, in developing and testing controls

6. Historical background • Tremendous growth in the discipline in the 1960s, 1970s, and 1980s. • Eclipsed by the even larger growth in molecular biology across all of the biological sciences • Nevertheless, epidemiology has been, and will continue to be, of critical importance until • Broad-acting durable resistance to all major diseases is achieved, or • Until there are highly effective and inexpensive fungicides, with no environmental concerns, and no pathogen resistance • The new concerns about invasive pathogen (and pest) species around the world, as well as emerging (re-emerging) diseases, and biosecurity and risk assessment, only serve to increase the importance of epidemiology

7. Botanical epidemiology • Numerous advances have been made over the last 40+ years, and many of the speakers at this workshop will highlight some of them • Multiple pathogen and host taxa, multiple pathosystems, crop loss, genetics (including molecular), spatial analysis, evolution, and many more topics…. • I will outline two major areas of research, both of which have implications for control strategies and tactics • Temporal and spatio-temporal disease dynamics • Importance of models, mathematics, and statistics – general • Prediction of epidemics (or the need for a control intervention) on a real-time basis, using concepts of decision theory • Importance of prior knowledge of the prevalence of epidemics, accuracy of predictors, and costs of decisions – specific example

8. Temporal disease dynamics The fundamental importance of disease progress curves for characterizing, comparing, understanding, and predicting epidemics has been understood for 40+ years. For polycyclic diseases, the logistic model has been the first choice for quantifying epidemics, for practical and theoretical reasons. From Vanderplank (1963, page 29)

9. Temporal disease dynamics All models are simplifications of reality, and as one would expect, all polycyclic epidemics are not adequately described by the logistic model. Many alternatives are possible, some of which have some theoretical justification, and some of which are very flexible. As easily shown (but not here), a good fit to a particular model is not proof of a particular mechanism. However, a consistent fit of a given model could lead one to hypothesize about a mechanism (that could be further tested). Using an appropriate model is important for comparing epidemics, forecasting magnitude of disease increase, and developing controls. Nevertheless, the logistic (or mononmolecular) is remarkably useful for summarizing epidemics.

10. Temporal disease dynamics Vanderplank understood that to increase understanding of polycyclic epidemics, more complex models were required. Differential-delay equation to relate rate of disease increase toinfectiousdisease intensity A cumbersome approach for developing principles of epidemics (and control), expansions for additional epidemic features, and model fitting

11. The “Contemporary” Approach Coupled differential equations(SEIR model) Susceptible-Exposed-Infectious-Removed (Recovered) or Healthy-Latent-Infectious-Removed Four host states in the population 1/ω: mean latent period 1/μ: mean infectious period

12. Coupled differential equations Y = L+I+R One basis for defining the basic reproduction number (ratio), R0

13. Coupled differential equationsExpansion for: host dynamics, simple-interest component, vector transmission,spatial heterogeneity, etc.) Primary infections Host ‘growth’ and mortality Inoculum mortality

14. R0Number of new infected individuals (e.g., diseased plants, sites on leaves, etc.) resulting from a single infected individual placed in a disease-free host population • Threshold for an epidemic of a polycyclic disease • R0= 1 • Final intensity of disease (“epidemic size”) • Or steady-state intensity of disease • Prediction of exponential rate of increase early in epidemic (rE) – the link to more descriptive approaches • Other threshold formulae when there is a simple-interest component

15. Coupled differential equations: Control strategies (vector-virus example)

16. Temporal dynamics:SelectedReferences • C. A. Gilligan (2002). Advances in Botanical Research 38: 1-64. • Excellent review and synthesis of many modeling approaches for understanding epidemics and developing control strategies (with a special emphasis on root diseases) • Lots of references to important work (great place to start) • M. J. Jeger, J. Holt, F. van den Bosch, and L. V. Madden (2004). Physiological Entomology 29: 291-304. • Synthesis of approaches for modeling plant viruses and phytoplasma (i.e., pathogens with arthropod vectors), with an emphasis on control strategies • Lots of references to other work with plant viruses • J. Segarra, M. J. Jeger, and F. van den Bosch (2001). Phytopathology 91: 1001-1010. • Linkages (and commonality) of various modeling approaches

17. Temporal disease dynamics:Contemporary statistical models for repeated measures • Disease progress curves are comprised of longitudinal data (repeated measures) • Considerable advances have been made in statistics over the last 20 years for analyzing longitudinal data that have not been adequately incorporated into botanical epidemiology (or plant pathology), including: • Linear Mixed Models • Simultaneous modeling of disease progress and treatment effects • Complex covariances (correlations) • Fixed or heterogeneous variances • Generalized linear mixed models (non-normal) • Nonlinear Mixed Models • Wider class of models (and, thus, biological realism) • Narrower class of experimental designs (but growing) • Not for the timid (!) • Nonparametric models (“relative marginal effects”) • Ideal for common ordinal disease ratings • Considerable advances in statistical computation It could be argued that we are not retrieving the maximum amount of information from the experiments and surveys we conduct (or are using results with excessive type I and II error rates)

18. Temporal disease dynamics:Contemporary models for repeated measures Instead of a regression line through the replicated data at each time, think of the profiles of Y over time for each experimental unit. There is variation within each unit and between units. F(y) = f(t; parameters) + between-plot error + within-plot error Nonzero correlations and unequal variances

19. Temporal disease dynamics:References • Schabenberger & Pierce (2002). Contemporary Statistical Models for the Plant and Soil Sciences. CRC Press. • Outstanding new general textbook. • Diggle, Liang, & Zeger. (1994). Analysis of Longitudinal Data. Clarendon Press. • Brunner, Domhof, and Langer. (2002). Nonparametric Analysis of Longitudinal Data in Factorial Experiments. Wiley. • Great for ordinal rating data. • Garrett, Madden, Hughes, and Pfender. (2004). Phytopathology 94: 999-1003. • Discussion of several of the developments in statistics that are relevant in plant pathology. • Gives the reader key references for learning methods.

20. Disease Dynamics—some considerations • “As a matter of fact all epidemiology, concerned as it is with variation of disease from time to time or from place to place, must be considered mathematically…if it is to be considered scientifically at all.” • Sir Ronald Ross (1911) • However, Anderson & May (1991) and Jeger (2004) lament that insights gained from advanced theoretical (i.e., mathematical) work have had inadequate impact on empirical studies and on practical disease management • In plant pathology, most characterizations of epidemics, and evaluations of controls, rely on the simpler (one-variable) population growth models (e.g., logistic), and the related AUDPC • It is our challenge to continually ‘bridge the gap’ between mathematical/statistical and empirical disciplines • One area where the gap is bridged involves disease prediction, because it involves many empirical observations of disease intensity, and (often) descriptive and/or more mechanistic models

21. Disease prediction • “Of the potential benefits of mathematical modeling to improving the efficiency of control of crop disease, prediction stands foremost.” • C. A. Gilligan (1985) • Concept: • Prediction of an outbreak of disease, or an increase in disease intensity, based on weather, crop, pathogen, and/or vector variables, or prediction of the need for a control intervention • Also called disease forecasting or disease warning • Generally based on completed infection events • Long history in botanical epidemiology: • Early predictors of late blight, apple scab, etc. • 1960 book chapter by Paul Waggoner • Many reviews

22. Prediction or forecasting • A humbling experience… • “Forecasting is difficult, especially forecasting the future” • Victor Borge (also attributed to Niels Bohr) • “The trouble with … forecasting is that it's right too often for us to ignore it and wrong too often for us to rely on it” • Patrick Young (regarding the weather) • As stated by R. D. Shrum (1978): • “…forecasting means ‘to foresee or to calculate beforehand’. Thus, the calculation of probabilities is implicit in the meaning of the word” • With probabilities (and right and wrong decisions) there are statistics, so one must keep in mind: • "An unsophisticated forecaster uses statistics as a drunken man uses lamp-posts -- for support rather than for illumination” • Andrew Lang • But, hopefully, in botanical epidemiology, we use statistics (correctly) for illumination (i.e., understanding)

23. Prediction • Although epidemiologists have been developing predictive (warning, forecasting) systems for decades, major conceptual advances have been made in the last 5-10 years • The advances center on the use of formal decision theory, with explicit application of Bayesian principles, to develop and assess disease predictors • Many of the concepts have been explored in medical diagnosis research • Jonathan Yuen and Gareth Hughes have pioneered these methods • Gives a quantitative basis for why real-time predictions are accepted and utilized (or not) • Some key references include: • J. Yuen & G. Hughes (2002). Plant Pathol. 51: 407-412. • J. Yuen et al. (1996). European J. Plant Pathol. 102: 847-854. • G. Hughes, N. McRoberts, & F. J. Burnett (1999). Plant Pathol. 48: 147-153. • G. Hughes & L. Madden (2003). Agric. Sys. 76: 755-774. • W. Turechek & W. Wilcox (2005). Phytopathology (in press). • Best explained with a (thorough) example…

24. Example: Fusarium head blight of wheat (scab) • Also known as ear blight • Economically important in U.S., Europe, and elsewhere • Disease intensity (severity and incidence) and mycotoxin (e.g., DON) varies considerably from location to location and from year to year • In particular, the disease is not rare, and is not so common that a major epidemic (or the need to apply fungicide) occurs virtually every year • There is considerable evidence from controlled experiments and empirical observations that epidemics depend on the environment • Thus, the disease is a good candidate for real-time forecasting or prediction for the risk of an epidemic • Note that risk is a term for the probability of an unfavorable event (e.g., epidemic). So, risk prediction can be another synonym for disease forecasting

25. Prediction • The success of a forecasting system depends, among other things, on • The commonness of epidemics (or need to intervene) • The accuracy of predictions of epidemic risk (based on weather in this example) • The ability to deliver predictions in a timely fashion • The ability to implement a control tactic (fungicide application, for example) • The economic impact of using a predictive system • I address some of these issues • Note: • Although there is more than one risk model for FHB, I emphasize the model developed at Ohio State and Penn State (with many collaborators), that is currently being used in 23 U.S. states

26. Fusarium head blight predictor Flowering date is key

27. How common are scab epidemics? • There is no simple answer. • Depends on definition of “epidemic” (or the need to use a fungicide, i.e., intervene) • High disease severity or high toxin, or both • We considered an epidemic to be >10% final severity • In our efforts to develop a prediction system, we considered N = 124 location-years (for 7 U.S. states) • 40% were classified as epidemics • Prob(E+) = 0.40 (estimated probability of an epidemic) • This is a “working concept” for the so-called prior probability of a scab epidemic. • It is very reasonable to use other information to estimate this prior probability.

28. Probability and Odds • Prior probability of epidemic: • Prob(E+) = 0.4 • Prior odds of an epidemic • Odds(E+) = Prob(E+) / [1 – Prob(E+)] = 0.67 • Note: with Prob(E+) = 1/2, Odds(E+) = 1 • Prior probability of no epidemic: • Prob(E-) = 0.6 • Prior odds of no epidemic: • Odds(E-) = Prob(E-)/[1 – Prob(E-)] = 1.5

29. Prediction Model • Initial model described in: • De Wolf, Madden, and Lipps (2003) Phytopathology 93:428-435. • Based on 50 location-years (compared with current 124). • Slightly different Prob(E+) • My Proceedings article uses results reported in 2003 article • Current prediction system on the web uses different variables and risk model, and is based on N = 124 location-years • Numbers in this talk reflect the more recent results • Current system exists because of the collaboration of many individuals, for either data collection, analysis, of prediction delivery, especially: • Pat Lipps (OSU) • Erick De Wolf (Penn State)

30. Prediction Model • Prediction model: Z = f(environment, crop factors) • Derived with logistic regression • Increasing favorability for an epidemic is associated with increasing Z (which is on a logit scale) • Predict an epidemic when Z > threshold(label this P+) • Predict a nonepidemic when Z < threshold (label this P-) • Note: predictor could be derived with • many different statistical modeling approaches • Logistic regression (including Bayesian logistic (or other) analysis) • Discriminant analysis • Neural networks, etc. • or with ad hoc “pencil and paper” methods • Late blight warning systems (severity values) • Mills’ tables for apple scab, etc., … • or formally using parameters from (mechanistic) population dynamic models (exponential or logistic rate parameter)

31. Fusarium head blight risk model (124 location-years) Possible thresholds for epidemic prediction Epidemics Predicted probability of an epidemic (Z) Non-epidemics Increasing favorableness of environment  

32. Four possible decisions

33. Fusarium head blight risk model:Different thresholds Epidemics Non-epidemics

34. Predictor Accuracy Proportion of epidemics correctly predicted Proportion of non-epidemics correctly predicted True positive proportion (TPP) 0.820 True negative proportion (TNP) 0.824 Overall accuracy 0.820 Positive prediction Likelihood Ratio LR(+) = TPP/(1-TNP) 4.70 Negative prediction Likelihood Ratio LR(-) = (1-TPP)/TNP 0.22 LR(+) and LR(-) are measures of the effectiveness of a predictor Large LR(+) and small LR(-) are ideal.

35. Receiver Operating Characteristic (ROC) curve: An overall measure of predictor accuracy

36. Receiver Operating Characteristic (ROC) curve Very accurate predictor Increasing accuracy Worthless predictor

37. Statistics such as TPP and TNP indicate how well one can predict known epidemics and non-epidemics. In application, one wants to know how well the model predicts unknown cases (location-years) based on calculated risk values. This can be estimated easily by invoking Bayes Theorem, using the so-called posterior odds. Predictors in practice Odds(E+|P+) = Odds(E+)LR(+) Odds(E-|P-) = Odds(E-)/LR(-) Odds(E+|P+): Posterior odds, post-prediction odds that there is an epidemic, given that one is predicted (or posterior odds that this not an epidemic when one is not predicted) Likelihood ratio Prior odds

38. Fusarium Model Accuracy Likelihood ratio of a positive prediction Posterior odds– Post-prediction odds that there is an epidemic, given that one is predicted Prior odds Odds(E+|P+) = Odds(E+)LR(+) Fusarium prediction model: 3.1 = 0.674.7 A little algebra shows that the posterior probability of an epidemic, given that one is predicted, Prob(E+|P+), is: 0.76 (compared with prior probability of 0.40).

39. Fusarium Prediction Model(Prior and posterior odds, and LR) • Prob(E+|P+) = 0.76 Prob(E+) = 0.4 • Prob(E+|P-) = 0.13 • Prob(E-|P+) = 0.24 • Prob(E-|P-) = 0.87 Prob(E-) = 0.6 Probability before using predictor Probability after using the predictor Algebraic steps not shown

40. Fusarium Prediction Model(Value of predictor depends on LR and prior probability) • Prob(E+|P+) = 0.76 Prob(E+) = 0.4 • Prob(E+|P-) = 0.13 • Prob(E-|P+) = 0.24 • Prob(E-|P-) = 0.87 Prob(E-) = 0.6 New calculations can be done with any new information on prior odds.

41. Prior probability versus model accuracyTPP = 0.820, TNP = 0.824, LR(+) = 4.7, LR(-)=0.22 Nominal results Rare epidemics Very common epidemics Forecasters need to be EXTREMELY accurate to be of value for very rare or very common diseases!

42. Prior probability versus model accuracyTPP = 0.9, TNP = 0.91, LR(+) = 10.0, LR(-)=0.11 Example results, moreaccurate model (overall) Rare epidemics Very common epidemics

43. Other thresholds of predictor:

44. Prior probability versus model accuracy [use higher threshold for lower Prob(E+)] TPP, TNP, and hence LR(+) and LR(-) are changed Prob(E+|P+):

45. Prior probability versus model accuracy [use lower threshold for higher Prob(E+)] TPP, TNP, and hence LR(+) and LR(-) are changed Prob(E-|P-):

46. Optimum threshold Previous result: Odds(E+|P+) = Odds(E+)LR(+) Cost ratio (for a predictor): CR = (CFP – CTN)/(CFN-CTP) ≈CFP/CFN It can be shown that the optimum threshold to minimize costs (on average) is found from: CR = Odds(E+)f′(FPP) Where f′(FPP) is the first derivative of the ROC curve, the instantaneous likelihood ratio at point (FPP,TPP). ROC f (FPP) f ′(FPP)

47. Optimum threshold CFP/CFN≈CR = Odds(E+)f′ (FPP) In practice, for a given prevalence and CR, get: f′ (FPP) = CR/Odds(E+) Solve for corresponding FPP and TPP (from a ROC model) Find the corresponding threshold of Z for operating the predictor. Determine predictor results from Odds(E+|P+) ROC For high CR, move down the ROC curve, resulting in higher threshold For low CR, move up the ROC curve, resulting in lower threshold

48. Optimum threshold example Resulting threshold for predictor Three examples for CR

49. Predictor(Conclusions) • Although the terminology and methodology of Bayesian decision theory, etc., are foreign to most plant pathologists, the concepts are intuitive (once an initial hurdle is overcome) • Work to date in plant pathology has dealt with relatively simple scenarios • Binary reality (epidemic or not; need to spray or not) • Binary decisions (epidemic or not; spray or not) • The next phase of work will deal with more complex scenarios • (quantitative reality, decisions, results) • More work is also needed on predictor validation and costs of using a predictor

50. Overall conclusions • “Epidemiological analysis has come to stay” • Vanderplank (1963) • The prophetic words of Vanderplank certainly have come true • The discipline of botanical epidemiology has evolved in many ways, and will continue to evolve • There is a continuing need for epidemiology (in the broad sense), since many of the easy problems have been solved. • The hard problems may require novel research, which will likely involve complex research and analysis