https://cpw.cvlcollections.org/files/original/b7a6158b14329e9f48a16eb45b676ed3.pdf a5e096aaa7056905ac88a8f9ed28c4f0 PDF Text Text Formalin Sensitivity in Rainbow Trout Adrian Gehr In collaboration with: Lindsay Rencoret Soo-Young Kim Charlie Vollmer Departments of Mathematics and Statistics Colorado State University Eric Fetherman Aquatic Research Section Colorado Parks and Wildlife Version: May 8, 2014 Abstract Formalin is a commonly used prophalyctic antifungal and antiparasitic treatment of fish and fish eggs, yet little is known about the differential sensitivity among strains after exposure as eggs. This study seeks to determine the sensitivities (measured by mortality) of four rainbow trout strains, after first exposure to formalin as eggs, and a later exposure as fingerlings. The data is analyzed using logistic regression and a Cox proportional hazard model. Both models yield consistent conclusions; the different strains do die at different rates as fingerlings, but the egg treatment does not contribute to these differences. 1 Introduction 1.1 Background Formalin is among the most effective and commonly used antifungal and antiparasitic treatments in fish and fish eggs (Bills et. al 1977). As such, a better understanding of the sensitivities of various strains to treatment conditions commonly used in hatcheries has commercial relevance. Past research has demonstrated different sensitivities among strains exposed to formalin post-hatch (Piper and Smith 1973), yet little to no research has explored the effects of exposure as eggs. Therefore, the purpose of this study is to determine whether different formalin exposure levels as eggs affects mortality later as fingerlings, after secondary exposure conditions. Four strains of rainbow trout are considered here: pure Hofer, pure Harrison Lake, 50:50 cross, and 75:25 Hofer:Harrison cross. 1.2 Questions of Interest 1. Does dosage as eggs affect mortality as fingerlings? 1 �2. Are there sensitivity differences among the different strains? 3. Does dosage as fingerlings affect mortality, among fish previously exposed as eggs? 4. Does duration of exposure as fingerlings affect mortality, among fish previously exposed as eggs? 5. How does fish size affect sensitivity to formalin? 1.3 Experimental Design The experiment is composed of two stages. In the first stage, eggs are treated with formalin for 15 minutes, at two different levels: 1667 or 5000 ppm. Subsequently, the surviving eggs are allowed to grow to the fingerling stage (approx. 3 inches in size), whereupon they are re-exposed to one of eight treatment conditions, according to a complete randomized design. The eight fingerling treatment conditions consist of the combinations of four exposure dosages (0, 167, 250, 500 ppm) at two possible durations (30 or 60 minutes). These levels are chosen to be in line with common hatchery treatment conditions, which, according to a survey of Colorado Parks and Wildlife hatchery managers, range from 130-250 ppm, with 167 ppm for 30 minutes being the most common. The 500 ppm condition is included to test for toxicity at extraordinarily high dosages. After treatment, the fish are observed over five days, and time of death is recorded. Following the observation period to test for delayed mortality effects, the the fish are sacrificed (i.e. the data are censored), and the weight, length, and strain of each fingerling is recorded. 2 Exploratory Data Analysis We begin by viewing the overall structure of the data, and then move on to visualizations that highlight the effects of different explanatory variables. We consider all possible explanatory variables that were measured, except length. Length was excluded due to its high colinearity with weight (r = .958). Weight serves as a general proxy for size. For ease of reference, the explanatory variables under consideration follow: X1 X2 X3 X4 X5 X6 X7 = = = = = = = Duration of exposure Exposure concentration as fingerlings Weight as fingerlings Indicator for pure Hofer strain Indicator for 50:50 cross Indicator for 75:25 Hofer:Harrison hybrid Exposure concentration as eggs The measured response variable is survival time. It will also be convenient to create a response vector of zeros and ones, where a one corresponds to a fish that survived and a zero corresponds to a fish that died. Figure 1 shows that fish tended to either die quickly or survive until censored, suggesting that we are not losing a much information if we replace time of death with this binary response vector. Doing so will allow us to analyze the data with a logistic regression model. 2 �While the majority of fish survived the full duration of the experiment, a significant fraction did not. To get an idea of which treatments were having an effect on the proportion of survivors, figure 2 shows a bar graph broken down by treatment. There are three main things to notice from figure 2: 1. The blueish blocks tend to show substantially higher mortality rates than the reddish blocks, suggesting that the 60 min group experienced higher rates of death than the 30 min group (i.e. longer duration of exposure as fingerlings appears to increase the probability of death.) 2. The mortality rate tends to increase within each block as fingerling dosage increases, suggesting that increased dosage as fingerlings is associated with higher mortality. 3. The two reddish blocks look roughly the same, as do the two blueish blocks. This suggests that egg treatment may have no significant effect on mortality rate as fingerlings. Figure 3 attempts to illuminate the other two research questions (2 and 5). There are couple things to notice from figure 3. The points on the left side (representing fish that died) are somewhat more densely clumped near the low weight side of the spectrum, and get more sparse as weight increases, possibly suggesting that increased weight tends to reduce mortality. However, this requires that the points on the right side of the plot (those that survived) are not also more clumped on the low weight side of the spectrum, which is difficult to tell from this plot. Secondly, there appears to be relatively fewer green points, and relatively more purple and blue points toward the left side of the plot, suggesting that Harrison Lake strain may be less sensitive, and Hofer may be relatively more sensitive. We have now provided suggestive answers to our questions of interest. Next we turn to formal analysis to quantify our results. 3 Formal Analysis We built two models to analyze the data, both commonly used in survival analysis. First we will describe a logistic regression model, and follow up with a Cox proportional hazard (PH) model. The logistic regression model has advantage of simplicity and more intuitive interpretations, but at the cost of ignoring time of death, and instead treating survival as an indicator variable. The Cox PH model has the advantage of accounting for the time of death information, while still appropriately handling the censored nature of the data. Both models yield consistent results, providing additional confidence for our conclusions. 3.1 Logistic Regression Model The logistic regression model treats survival as an indicator variable, where any fingerling that survived for more than 70 hours was coded as ”success” (Y=1) and all others as ”failure” (Y=0). The choice of the 70 hour time cutoff is appropriate because all fish that survived past 70 hours, did in fact survive until censored (see Figure 1). In this model, each Yi is assumed to be a Bernouli random variable with probability of survival pi that depends on the values of the covariates for the ith fish. The value of pi depends on the covariates according to the following relation: 3 �logit(pi ) = ln( pi ) = β0 + β1 x1i + β2 x2i + β3 x3i + β4 x4i + β5 x5i + β6 x6i + β7 x7i 1 − pi where pi = probability of surviving, and the covariates are those outlined above. In other words, the ln(odds of survival) are assumed to follow a linear relationship with the covariates. Equivalently, the model can be stated as: E[Yi ] = pi = logit−1 (β0 + β1 X1 + ... + β7 X7 ) = 1 1+ e−(β0 +β1 X1 +...+β1 X7 ) This function has a sigmoidal shape and assymptotically approaches 0 and 1, making it an appropriate choice for modeling a probability measure. For model selection, we started with all the listed covariates and used successive loglikelihood ratio tests to check for significant effects (i.e Ha : βi 6= 0). By this procedure, exposure concentration as eggs did not have a statistically significant effect (p = .1297 in the model with all covariates), while all other covariates were significant at the .05-level (see Table 1). It is important to note that the likelihood ratio test works by comparing the goodnessof-fit of a full model to a reduced model that drops the covariate(s) of interest. As such, the results of likelihood-ratio test depend critically on which covariates are included in the full model. Nonetheless, these conclusions were robust to model selection effects, as long as interaction terms were not considered. Specifically, concentration of exposure as eggs was consistently not significant and all the other covariates consistently were, across many choices of full model. Interaction terms were ignored for three reasons: because there are so many possible interactions that could potentially be considered (almost 27 ), because they complicate the interpretation of the model and in many cases have no straightfoward interpretation at all, and most importantly, because they are not necessary to answer our questions of interest. The best model, according to our criteria of parsimony and significant covariates is given in table 1. (Intercept) fingerling concentration 50:50 Hofer:Harrison 75:25 Hofer:Harrison Hofer weight duration Estimate 7.53 -0.01 -1.63 -0.53 -1.74 0.03 -0.06 Std. Error 0.36 0.00 0.22 0.25 0.23 0.01 0.01 exp(coef) 1863.106 0.990 0.196 0.589 0.176 1.030 .942 p-value 0.00 0.00 0.00 0.03 0.00 0.00 0.00 Table 1: Here, the reported p-values are actually generated using the Wald test, which approximates the likelihood ratio test for one covariate. The results are very close to what is given by the likelihood ratio test where the full model has these six covariates, and the reduced model excludes just the covariate of interest. 4 �The estimated βi s indicate the estimated change in ln(odds of survival) associated with an increase of one unit in Xi , while holding all other covariates constant. For ease of interpretation, it is convenient to take eβi which gives the estimated change in odds of survival associated with an increase of one unit in Xi . Thus, if βi is significantly less than zero, then increasing Xi tends to harm the odds of survival, while if βi is significantly greater than zero, then increasing Xi tends to improve odds of survival. Note, though, that we did not standardize the covariates. Therefore, the magnitude of the βi s can only be compared directly across the three indicator variables. Other direct comparisons do not make sense, because the meaning of a one unit increase differs across the variables. This model allows us to make predictions of the probability of survival for a fingerling at any level of the covariates. For example, a roughly average weight (10g) Hofer strain fingerling, treated at 167 ppm for 30 min, has an estimated probability of survival given by: pi = logit−1 (7.53 + (−.01 ∗ 167) + (−1.74) + (.03 ∗ 10) + (−.06 ∗ 30)) = .932 3.2 Cox Proportional Hazard Model The Cox proportional hazard (PH) model is concerned with modeling the time to some event (in our case, the time to death). The model utilitizes the concept of a hazard function, which intuitively, can be thought of as the instantaneous risk of death at time t. If we define a random variable T to be the time to death, with a probability density function f(t), and cumulative density function F(t) = P(T<t), then the hazard function is given by: h(t) = limδt→0 P (t<T ≤t+δt|T >t) δt = f (t) 1−F (t) = f (t) S(t) where S(t) = 1 - F(t) = P(T ≥ t) is the survivor function. The Cox PH model makes the assumption that the hazard function at each level of the covariates is proportional to some baseline hazard h0 (t). Specifically, the Cox PH model is: h(t|X1 , ..., X7 ) = h0 (t)e(β0 +β1 X1 +···+β7 X7 ) assuming we consider the same covariates as before. Equivalently, we can say that the natural log of the hazard ratio is a linear combination of the covariates. That is, � � 7) ln h(t|Xh10,...,X = β0 + β1 X1 + β2 X2 + · · · + β7 X7 (t) The Cox PH model is known as a semiparametric model because it does not require specification of the baseline hazard; it only assumes that the baseline hazard is nowhere negative (because a negative hazard would imply immortality). This is acceptable as long as we only care about the hazard ratio between to levels of the covariates, because in calculating the ratio, the baseline hazard cancels out, as shown: h0 (t)e(β0 +β1 x1 +···+β7 x7 ) h(t|x1 , ..., x7 ) = h(t|z1 , ..., z7 ) h0 (t)e(β0 +β1 z1 +···+β7 z7 ) where x and z represent two different levels of the covariates. Since no underlying distribution for the hazard function is assumed, the βs must be estimated using non-parametric methods (specifically, the estimates can be calculated by using Newton’s method to maximize the partial log-likelihood function.) 5 �Like before, we can use likelihood ratio tests for significance of the covariates. Doing so tends to yeild p-values very close to that given by the logistic regression model. Again we find that egg dosage is not significant (p=.1493 in the model with all other covariates.) By the same criteria as before, we get the same six covariates in the best model. The model is given in table 2. dur treat ppm factor(color)O factor(color)P factor(color)R weight coef 0.05 0.00 1.47 0.48 1.55 -0.03 exp(coef) 1.05 1.00 4.37 1.62 4.72 0.97 se(coef) 0.00 0.00 0.20 0.23 0.20 0.01 z 10.73 14.14 7.44 2.11 7.62 -3.09 Pr(>|z|) 0.00 0.00 0.00 0.04 0.00 0.00 Table 2: Here again the p-values are actually given by the Wald test, but are very close to that given by the likelihood ratio test where the full model has all six covariates and the reduced model has all but the covariate of interest. Here, the interpretation of the estimated βs is slightly different than before. In this case, βi corresponds to the change in the ln(hazard ratio) (instead of ln(odds of survival)) that is associated with an increase in one unit of Xi , while holding all other covariates constant. Therefore, unlike before, in the Cox PH model, positive βs correspond to an increase in sensitivity, and negative βs correspond to a decrease in sensitivity. Note that this would have been the case in the logistic regression model too if we had instead considered death as ”success” and survive as ”failure”. In any case, the magnitude of the βs should not be compared directly across the models, because they mean different things. Again, it is convenient for interpretation to take eβi , which corresponds to the change in the hazard ratio for every increase of one unit in Xi , while holding other covariates constant. An advantage of the Cox PH model is that it allows us to generate survival curves with associated confidence intervals. In all cases, we see a steep drop in survival early and then a leveling off. Non-overlaping confidence intervals indicates a significant difference between the groups. Figure 4 emphasizes the decreased survival among fish in the 60 minute condition versus the 30 minute condition. It also shows that the Harrison Lake strain is less sensitive than the Hofer strain. Figure 5 emphasizes the effect of increased dosage as fingerlings. 4 Conclusions Based on these results, we can return to our questions of interest, and conclude the following: 1. There is not sufficient evidence to suggest that the exposure dosage as eggs has any effect on mortality as fingerlings, within the range tested (p=.1296). This suggests that hatchery managers do not need to be particularly concerned about the dosage at which they treat eggs, assuming that they are only concerned with risk of death later on. Note, though, that this does not imply that dosage as eggs had no effect on mortality as eggs. That question was not tested in this experiment. 2. The different strains do express differential sensitivities to formalin treatment conditions. Specifically, pure Hofer is the most sensitive (i.e least likely to survive), 6 �followed by the 50:50 cross, then the 75:25 Hofer:Harrison cross, and finally the pure Harrison Lake strain is the least sensitive. This result is surprising in that the 75:25 Hofer:Harrison cross reacts more like the Harrison Lake strain, despite being genetically more similar to the Hofer strain. 3. Duration of exposure affects mortality, among fingerlings previously exposed to formalin as eggs (p<2e-16). Specifically, longer durations of exposure increase the probability of death. 4. Formalin dosage as fingerlings affects mortality in fingerlings previously exposed as eggs. Specifically, increased dosage increases the mortality rate. 5. Increased size (as measured by weight) increases probability of survival (p=.0004). That is, larger fingerlings tend to be less sensitive. 5 Bibliography Bills, T. D., L. L. Marking, and J. H. Chandler Jr. 1977. Formalin: its toxicity to nontarget aquatic organisms, persistence, and counteraction. Investigations in Fish Control Number 73, U. S. Department of the Interior, Washington, D. C. Piper, R. G., and C. E. Smith. 1973. Factors influencing formalin toxicity in trout. The Progressive Fish-Culturist 35:78-81. 7 �Survival Time across all Treatment Groups Frequency 1000 1500 2000 2238 500 607 308 300 221 15 0 10 0 20 81 1 1 40 0 59 0 60 80 100 120 Survival Time (hours) Figure 1: Note that all fingerlings in the >70 buckets survived the duration of the experiment. Therefore, all those on the right hand side of the histogram can be treated equally as survivors without great loss of fidelity. The discrepancy is due to a physical constraint of recording one fish tank at a time at the end of the observational period. 8 �Egg Treatment, Duration as Fingerlings 1667ppm, 30min 5000ppm, 30min 1667ppm, 60min 5000ppm, 60min 0.15 0.10 0.00 0.05 Proportion Died 0.20 0.25 Proportion of Death by Treatment 0 167 500 0 167 500 0 167 500 0 167 500 Fingerling Treatment (ppm) Figure 2: Mortality rates broken down by treatment group: there is one bar for each of the sixteen possible treatment combinations. To generate this plot, any fingerling surviving to >70 hours was coded as having survived, and all others as having died. 9 �Colored by Strain of Fish 0 10 Weight (g) 20 30 40 HL 50:50 GRxHL 75:25 GRxHL GR 0 20 40 60 80 100 Survival Time (hours) Figure 3: HL: Harrison Lake, GR: Hofer 10 120 �Figure 4: Note that the data for the two hybrid strains and the data for two of the fingerling dosage groups is not shown in this figure. 11 �Comparing treatment effect for Hofer and Harrison Lake 0.8 0.4 20 40 60 80 100 120 0 20 40 60 80 100 120 Time Hofer (duration 60min) Harrison Lake (duration 60min) 0.8 0.6 formalin = 0 ppm formalin = 167ppm formalin = 250ppm formalin = 500ppm 0.4 0.4 0.6 0.8 Proprotion survive 1.0 Time 1.0 0 Proprotion survive 0.6 Proprotion survive 0.8 0.6 0.4 Proprotion survive 1.0 Harrison Lake (duration 30min) 1.0 Hofer (duration 30min) 0 20 40 60 80 100 120 0 Time 20 40 60 80 100 120 Time Figure 5: Note that the data for the two hybrid strains is not shown in this figure. 12 � Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Documents Text A resource consisting primarily of words for reading. Examples include books, letters, dissertations, poems, newspapers, articles, archives of mailing lists. Note that facsimiles or images of texts are still of the genre Text. Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Formalin sensitivity in rainbow trout Description An account of the resource Formalin is a commonly used prophalyctic antifungal and antiparasitic treatment of fish and fish eggs, yet little is known about the differential sensitivity among strains after exposure as eggs. This study seeks to determine the sensitivities (measured by mortality) of four rainbow trout strains, after first exposure to formalin as eggs, and a later exposure as fingerlings. The data is analyzed using logistic regression and a Cox proportional hazard model. Both models yield consistent conclusions; the different strains do die at different rates as fingerlings, but the egg treatment does not contribute to these differences. Creator An entity primarily responsible for making the resource Gehr, Adrian Rencoret, Lindsay Kim, Soo-Young Vollmer, Charlie Fetherman, Eric Subject The topic of the resource Rainbow trout Formalin Extent The size or duration of the resource. 12 pages Date Created Date of creation of the resource. 2014-05-08 Rights Information about rights held in and over the resource <a href="http://rightsstatements.org/vocab/InC-NC/1.0/" target="_blank" rel="noreferrer noopener">In Copyright - Non-Commercial Use Permitted</a> Type The nature or genre of the resource Text Format The file format, physical medium, or dimensions of the resource application/pdf Language A language of the resource English