Common Statistical Methods Used in Transgenic Fish Research

Session #6:

Common Statistical Methods Used In Transgenic Fish Research

M.Afifi

M.Sc., Biostatistics(Joint Supervision with ISSR, Cairo University) Ph.D., Candidate (AVC, UPEI, Canada)

E-mail: Afifi-stat6@hotmail.com

Tel: +201060658185

Before gene transfer After gene transfer

Statistics role

Before gene transfer

Experimental Design: CRD, CBD

Experimental unit: Single Fish or Fish tank, Replicates homogenous, same exper. condition

Sample Size: 3, 6, 8, 12????

Basic Experimental Design for Transgenic Fish Research:

1. Setting experimental questions >>>> statistical questions

2. Setting hypotheses and then statistical null hypotheses

4. Statistical consideration (treatment groups, sample size, true replication, confounding factors etc.)

5. Sampling design (independent, random, samples)

6. Data collection & measurement (Quality Control and Quality Assurance Procedures)

7. Data analysis–Too few data: cannot obtain reliable conclusions–Too many data: extra effort (time and money) in data collection

pseudoreplication

True replication

Fish

The transgenic fish used in this experiment were produced and raised in a biosecure facility at the DFO/UBC Centre for Aquaculture and Environmental Research (CAER) in West Vancouver, B.C., Canada.

Due to differences in growth rate, which produces fish of large size differences at each age, control fish used were 1 year older than transgenic fish in order to match fish to the same developmental stage and size.

Fish were cultured in filtered, aerated, flow-through well water at approximately 10 °C prior to and during the experiment. Since the two types of salmon reach smolt size at different times of the year (the normal time of May/June in their second year for non-transgenic fish, and in August/September of their first year for the growth accelerated fish).

After gene transfer

Qualitative QuantitativeCold-tolerance growth reproductive traits

Salinity-tolerance Massbiomass

food consumedspecific growth rate (SGR), Protein efficiency ratio (PE)

Food conversion efficiency (EC)Q-PCR

Comparative Biochemistry and Physiology journalImpact Factor: 1.551

Introduction to Two of Basic Statistical Techniques:

Group comparison methods for selection of appropriate tests

Correlation based methods

Flowcharts for selection of appropriate tests

Basic rules of any statistical test

Assumption Hypothesis testing

Basic rules of hypothesis testing Hypothesis:

• Null hypothesis, H0:

• Difference in (means, proportions, medians) is not actual (non-sig),

• Difference not due to treatment effect but due to any other reasons (Chance , Error)

• Alternative hypothesis HA : VS H0

Test statistic- value: value calculated from the data (an algebraic expression particular to the

hypothesis we are testing),

t-test >>>> t-value

F-test >>>> F-value

χ2-test >>>>>> χ2 value

P-value: probability value (0-1) (Sig): Attached to each value of the test statistic It

the probability of getting the observed effect (or one more extreme) if the null hypothesis is true

Comparison of Means

2-Independent sample Means

Two-sample t-test (unpaired t-test) Compare the means in two independent groups of observations using representative

samples.

Assumptions

Two samples must be independent unrelated

Normality A small departure from Normality is not crucial and leads to only a marginal loss in power

Homoscedastic (equal variances) >>>> Checked by Levene’s test

Aquaculture International Journal, IF:1.878

Figure 2. Growth performance in F1 transgenic and full sibling non-transgenic zebrafish. Fifty-four zebrafish of

F1 fry were randomly selected and grown individually under similar conditions. At the beginning of the

experiment, they were four week old. Zebrafish were weighed weekly during 6 weeks to monitor growth

performance. In the course of the experiment, fin DNA was extracted and assayed for transgene identification.

Weight of transgenic and non-transgenic full siblings was compared employing a Student t-Test (*, P < 0.05).

Welch's t-test

(Unequal variances t-test) widely used modification of the t-test,

adjusts the number of degrees of freedom when the variances are not equal to

each other.

If the sample sizes are not large,

equal variances not assumed

non-parametric method,

Mann–Whitney U test

Paired (dependent) t-test

FreezingRefrigeration

Methods of pairing: Self-pairing: each animal used as its own control (Before and After)

Natural pairing: each pair of animals is biologically related (e.g. litter mates).

Artificial (matched) pairing: each animal is paired with an animal matched with

respect to one or more factors that affect response.

To avoid allocation bias in an experiment when there is self-pairing, each animal is

randomly allocated to receive one of the two treatments initially; it then receives

the other treatment later.

If there is natural or matched pairing, one member of the pair is randomly allocated

to one of the two treatments and the other member receives the second treatment.

Paired Vs. Independent Test

If the sample sizes are not large,

equal variances not assumed

non-parametric method,

Wilcoxon rank test

F-test

ANOVA

Comparing more than two means

Suppose, for example, we have four groups. >>>>> compare using a two-

sample t-test) for every combination of pairs of groups >>> six possible t-tests

Principle

Total variability in a data set is partitioned into a different source of variation.

The sources of variation comprise one or more factors, each explained by the

levels or categories of that factor (e.g. the two levels, ‘male’ and ‘female’, defining

the factor ‘sex’, or three dose levels for a given drug factor), and also unexplained

or residual variation which results from uncontrolled biological variation and

technical error.

We can assess the contribution of the different factors to the total variation by

making the appropriate comparisons of these variances.

The variation is expressed by its variance

The analysis of variance encompasses a broad spectrum of experimental

designs ranging from the simple to the complex.

One-way analysis of variance Single factor with several levels or categories where each level comprises a group

of observations.

For example, the levels may be:

Feed formula for dogs: dry feed formula, a tinned feed and a raw meat

Different treatment dose levels of a drug, one of which is a placebo representing

simply the drug vehicle, while the others are, say, 50%, 100% and 200% of the

presumed effective dose. Consider the simple case >>> only one factor , 2 sources of variation:

Between the group means

Within the groups

In the experimental situation, the animals should be randomly allocated to one of

the levels of the factor, i.e. to one of the groups, in order to avoid allocation bias

Assumptions:

results are reliable only if the assumptions on which it is based are satisfied

samples representing the levels are independent

Observations in each sample come from a Normally distributed population with

variance σ2; this implies that the group variances are the same. Approximate

Normality may be established by drawing a histogram; moderate departures

from Normality have little effect on the result.

Constant variance, the more important assumption, may be established by

Levene’s test

Post-hoc testMultiple Comparisons of Means

Which group means Differs?????

Post-hoc Test

Multiple Comparison

Multiple comparisons

Conducting a number of tests, but the more tests that we perform, the more

likely it is that we will obtain a significant P-value on the basis of chance alone.

We have to approach this problem of multiple comparisons in such a way that

we avoid spurious P-values.

Adjusted p-values are simply the unadjusted p-values multiplied by the number of possible comparisons (six in this case);

If multiplying a p-value by the number of comparisons produces a value greater than one, the probability is given as 1.00.

Most Common Multiple comparisons

Least significant difference (LSD)

Duncan’s multiple range test, (DMRT)

Tukey’s (HSD)

Newman–Keuls tests,

Bonferroni’s correction

Scheffe’s

. Be aware: they often produce slightly different results!

Example Fig. 1. Growth rates and hormone profiles of wild-type (W),

domesticated (D), and GH transgenic (T) salmon. (A)

Specific growth rates (SGR).

(B) Plasma IGF1 levels. n = 10 per genotype.

Letters above bars denote significant differences among

groups (1-way ANOVA, P < 0.05).

Error bars represent standard SEM.

Example 2 .

Example Fig. 1. Plasma concentrations of growth hormone (A) in non-

transgenic and transgenic salmon fed full rations and inration-

restricted transgenic coho salmon (pair fed with controls).

GH values (A) are pooled from samples (N = 23) taken on Sept.

11, 2002 and Oct. 11, 2002, which did not differ significantly.

Statistical relationships between groups are indicated by letters

where significant differences occur.

Bars are means ± SE, letters denote significant differences.

TABLE 2.—Sample size (n), mean body weight, mean fork length, and mean condition factor (CF) for

all fish sampled.

Different lowercase letters indicate statistically significant differences between populations (ANOVA).

The letters H, T, and N represent hatchery, transgenic, and cultured nontransgenic fish, respectively.

Detailed statistical analysis

by category of analyzed data

and sex of coho salmon.

Asterisks indicate statistically

significant values.

Abbreviations are as follows:

GSI 5 gonadosomatic index,

H 5 hatchery fish, T

5transgenic fish, and N 5

cultured nontransgenic fish.

2-way ANOVA

Enzyme activities were measured before (pre-diet treatment, n=8) and after a 12-week feeding trial (post-

diet treatment, n=3 replicates, n=4 fish/replicate). Differences between C and T pre-diet treatment

(p<0.05) are indicated by on the larger value, and differences between fish (F) and diet (D) groups post-⁎diet treatment are indicated by differing letters (a, b, c).

Reporting results in table:

If the sample sizes are not large,

equal variances not assumed

non-parametric method,

Kruskal-wallis test

Correlation and regression

Correlation (r)

measure the degree of association by calculating Pearson’s product moment

correlation coefficient, usually just called the correlation coefficient or, sometimes, the

linear correlation coefficient.

take any value from −1 to +1.

Correlation (r)

(a) perfect positive association,r = +1;

(b) perfect negative association, r = −1;

(c) positive association, r = +0.86;

(d) negative association, r = −0.85;

(e) no association, r = 0;

(f) no linear association, r = 0.

Above hatched cells includes analysis with all groups combined (non-transgenic, full-ration

transgenic and ration-restricted transgenic fish). Below hatched cells displays correlations for non-transgenic and full-ration transgenic fish

only. Correlation coefficients are shown for significant correlations only. aLiver GH correlations do not include non-transgenic fish in which expression was

undetected.

Regression linear relationship between two numerical variables with a change in one variable

being associated with a change in the other, we may be interested in determining the

strength of that relationship.

Are the points in the scatter diagram close to this line or are they widely dispersed

around it? Provided a linear relationship exists between the two variables, the closer

the points are to the line, the stronger the linear association between the two variables.

Linear regression lines

Body composition and energy content in relation to wet body weight of growth enhanced transgenic

Linear regression lines

Atlantic salmon >>>open triangles

controls >>>solid circles. fed to satiation three timesrday on a commercial diet.

Each data point represents a subsample of five fish. Data is presented with fitted regression lines solid lines. surrounded by 95% confidence intervals (dashed lines).

Regression coefficients for the relation between body composition and energy content per fish wet weight of growth enhanced transgenic Atlantic salmon and controls fed to satiation three timesrday on a commercial diet: Y=b0+b1×BW where ‘Y ’ is absolute nutrient or energy content, ‘b0’ and ‘b1’ are regression coefficients, ‘BW’ is wet body weight

Nonlinear regression

Second degree polynomial

Nonlinear regression

second degree polynomial

Nonlinear regression

Chi-square test

χ2

International Journal of Molecular Sciences

The genotype frequencies in HWE

Statistical analysis

The genotype frequencies were calculated and HWE was tested using a chi-

square test of

The population genetic indexes including He, Ho, effective allele numbers (Ne)

and PIC were calculated by Nei’s method [25]. Generally, polymorphism

information content (PIC) is classified in to the following three types: low

polymorphism (PIC value < 0.25), median polymorphism (0.25 < PIC value <

0.5) and high polymorphism (PIC value > 0.5). The LD structure measured by

D’ and r2 was performed with the HAPLOVIEW software (Ver.3.32) [26].

Association analyses between genotypes or haplotypes of GH gene and four growth

traits were performed using general linear model (GLM) procedure with SPSS 17.0

software (IBM, Armonk, NY, USA). We used the following statistical model:

Y = u + G + e where Y is the phenotypic value of each trait;

u is population mean value of 4 growth traits,

G is the fixed genotype effect of each SNP, and

e is the random error effect.

Multiple comparisons between different genotypes were tested using the LSD

method with Bonferroni correction adjustment [27].

How would these results be reported in a scientific journal article?

Tabular Presentation.

Mean ± SD or SEM with Both t-value and P-value

Mean ± SD or SEM with only P-value

Representing P-values with astrikes

Representing P-values with superscripts

Graphical presentation

Simple Bar Box plots

Report your results in words

Your Formal sentence must includes:

Dependent , independent variable

Exact p-value (unless the p value is less than .001). < 0.000 Or < 0.0001

The direction of the effect as evidenced by the reported means, as well as a

statement about statistical significance,

Symbol of the test (t), the degrees of freedom (6), the statistical value (2.95)