Analysis recommendation
Based on the diagram, this analysis should make a comparison between two or more groups. The analysis includes a single continuous outcome measure and a single, categorical factor of interest with two or more categories. It also includes at least one blocking factor and at least one covariate. All groups are independent and if animals are repeatedly measured, a summary measure is used in this analysis.
If this description is not accurate, please check your diagram and verify that all nodes are connected properly, all variables and variable categories are indicated and tagged to the relevant interventions or measurements and the information provided in the properties of each node is accurate; then critique it again.
Statistical analysis methods compatible with this design include the one-way ANCOVA with blocking factor(s).
The ANCOVA approach assumes that the data satisfies these assumptions: residuals are normally distributed, homogeneity of variance, independence of the errors, and the outcome is measured on a continuous scale (read more about parametric and non-parametric tests), as well as assuming the covariate(s) should be used in the analysis.
A covariate should be used if:
- The covariate is independent of the treatment.
- There is a strong relationship between the covariate and the outcome measure (i.e. either they both increase together or one increases while the other decreases).
- The relationship between the outcome measure and the covariate is similar for all treatments (i.e. there is no significant treatment by covariate interaction).
The above assumptions can be tested by plotting your data, details of what to look for and example graphs can be found on the independent variables page of the EDA website. If there are multiple covariates you are considering including in your analysis, ensure that the assumptions hold for each of them.
In many cases you will not know if including a particular covariate in your analysis is appropriate when planning your experiment. You should measure the covariate during your study, but only include it in your statistical analysis if the assumptions for covariate inclusion are met.
If you have reasons to think the data are not normally distributed, and/or the variability of the responses is related to their numeric size, you should first consider transforming the data to normalise it (read more about data transformation) and assess if the transformed data fits the parametric assumptions. Most data can be normalised using transformations such as log or square root and using parametric tests is preferable as they have more statistical power than non-parametric tests, as long as the parametric assumptions are met.
When parametric assumptions do not hold, even after a mathematical data transformation, a rank transformation can be applied to the data and parametric tests (in this case a one-way ANCOVA with blocking factors) can be performed on the ranked data. Note that there are assumptions associated with non-parametric tests also. For example, to perform a rank transformation the data must be able to be ranked, with only a few ties (e.g. identical values that will end up with the same rank), the observations must be independent and the covariate must have a linear relationship with the rank. If data cannot be rank transformed (e.g. it is mainly zeros with only a few non-zero measures), the data can be recoded into binary responses and then analysed using logistic regression. Another analysis option is ordinal logistic regression. Your local statistician can help advise on this. These approaches will lead to a loss in power due to the categorisation of continuous data.
Note that a one-way ANCOVA can answer the question: is there an overall difference between the groups; they do not provide information on which individual groups differ. To identify where any differences lie, it may be necessary to carry out a post-hoc test. Note that in this case the sample size might have to increase and the experiment should be powered to detect differences in the pairwise comparisons. Note the variability estimate used in the power calculation should be adjusted to account for the effect of any covariates if you have an idea of what this could be based on previous experiments. If you do not have an estimate of the effect that the covariates will have on unexplained variability to use in your power calculation, be aware that your experiment may end up with higher power once your analysis has taken account of the variability contributed by the covariate(s).
Please note that an experiment with a single variable of interest a covariate and a blocking factor might not make the most efficient use of the data. Consider using a factorial design.
Analysis software
Software such as InVivoStat can be used to run a one-way ANCOVA with blocking factors and apply data transformations. The test can be found in the following menu:
- Statistics>Single Measure Parametric Analysis
Dose-response experiments
In dose-response experiments, drug dose is often treated as a categorical factor of interest and different doses compared to one another. There is however an alternative approach which consists in treating drug dose as a continuous factor of interest and analysing the data using for example a non-linear regression. This is arguably more relevant as the statistical analysis strategy reflects the underlying biology better. For example, just because a drug has a statistically significant effect at 10 mg/kg, does not mean that it has no effect at 9 mg/kg. A non-linear regression analysis estimates the dose-response relationship and can provide, for example, an estimate of the dose which causes 50% of the maximal effect (ED50). Treating drug dose as a continuous factor of interest generally needs an increased number of different doses (generally at least five or six doses), but it allows the number of animals per dose group to be reduced, as you no longer need sufficient sample size to compare each dose back to the control group. As little as three animals per dose might be sufficient. For more information see Bate and Clark (2014).
Should you want to modify your design and treat your categorical factor of interest as a continuous factor, update the node properties of your independent variable of interest and update your diagram, and critique it again.
Analysis recommendation
Based on the diagram, this analysis should make a comparison between two or more groups. The analysis includes a single continuous outcome measure a single, categorical factor of interest, with at least two categories and at least one covariate. All groups are independent and if experimental units are repeatedly measured, a summary measure is used in this analysis.
If this description is not accurate, please check your diagram and verify that all nodes are connected properly, all variables and variable categories are indicated and tagged to the relevant interventions or measurements and the information provided in the properties of each node is accurate; then critique it again.
Statistical analysis methods compatible with this design include a one-way ANCOVA and an ANCOVA on the rank transformed outcome measure.
The ANCOVA approach assumes that the data satisfies these assumptions: residuals are normally distributed, homogeneity of variance, independence of the errors, and the outcome is measured on a continuous scale (read more about parametric and non-parametric tests), as well as assuming the covariate(s) should be used in the analysis.
A covariate should be used if:
- The covariate is independent of the treatment.
- There is a strong relationship between the covariate and the outcome measure (i.e. either they both increase together or one increases while the other decreases).
- The relationship between the outcome measure and the covariate is similar for all treatments (i.e. there is no significant treatment by covariate interaction).
The above assumptions can be tested by plotting your data, details of what to look for and example graphs can be found on the independent variables page of the EDA website. If there are multiple covariates you are considering including in your analysis, ensure that the assumptions hold for each of them.
In many cases you will not know if including a particular covariate in your analysis is appropriate when planning your experiment. You should measure the covariate during your study, but only include it in your statistical analysis if the assumptions for covariate inclusion are met.
If you have reasons to think the data are not normally distributed, and/or the variability of the responses is related to their numeric size, you should first consider transforming the data to normalise it (read more about data transformation) and assess if the transformed data fits the normality assumptions. Most data can be normalised using transformations such as log or square root, and using parametric tests is preferable as they have more statistical power than non-parametric tests, as long as the required assumptions are met.
When normality assumptions do not hold, even after a mathematical data transformation, a rank transformation can be applied to the data and parametric tests (in this case a one-way ANCOVA) can be performed on the ranked data. Note that there are assumptions associated with non-parametric tests also. For example, to perform a rank transformation the data must be able to be ranked, with only a few ties (e.g. identical values that will end up with the same rank), the observations must be independent and the covariate must have a linear relationship with the rank. If data cannot be rank transformed (e.g. it is mainly zeros with only a few non-zero measures), the data can be recoded into binary responses and then analysed using logistic regression. Another analysis option is ordinal logistic regression. Your local statistician can help advise on this. These approaches will lead to a loss in power due to the categorisation of continuous data.
Note that a one-way ANCOVA or an ANCOVA on the rank transformed response can answer the question: is there an overall difference between the groups; they do not provide information on which individual groups differ. To identify where any differences lie, it may be necessary to carry out a post-hoc test. Note that in this case the sample size might have to increase and the experiment should be powered to detect differences in the pairwise comparisons. Note the variability estimate used in the power calculation should be adjusted to account for the effect of any covariates if you have an idea of what this could be based on previous experiments. If you do not have an estimate of the effect that the covariates will have on unexplained variability to use in your power calculation, be aware that your experiment may end up with higher power once your analysis has taken account of the variability contributed by the covariate(s).
Please note that an experiment with a single variable of interest and a covariate might not make the most efficient use of the data. Consider using a factorial design or taking other sources of variability into account by including blocking factors in the design.
Analysis software
Software such as InVivoStat can be used to run a one-way ANCOVA, and apply data transformations (including a rank transformation). The test can be found in the following menu:
-
Statistics>Single Measure Parametric Analysis
Dose-response experiments
In dose-response experiments, drug dose is often treated as a categorical factor of interest and different doses compared to one another. There is however an alternative approach which consists in treating drug dose as a continuous factor of interest and analysing the data using for example a non-linear regression. This is arguably more relevant as the statistical analysis strategy reflects the underlying biology better. For example, just because a drug has a statistically significant effect at 10 mg/kg, does not mean that it has no effect at 9 mg/kg. A non-linear regression analysis estimates the dose-response relationship and can provide, for example, an estimate of the dose which causes 50% of the maximal effect (ED50). Treating drug dose as a continuous factor of interest generally needs an increased number of different doses (generally at least five or six doses), but it allows the number of animals per dose group to be reduced, as you no longer need sufficient sample size to compare each dose back to the control group. As little as three animals per dose might be sufficient. For more information see Bate and Clark (2014).
Should you want to modify your design and treat your categorical factor of interest as a continuous factor, update the node properties of your independent variable of interest and update your diagram, and critique it again.
Expand the canvas
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Independent variables
How to identify independent variables of interest and nuisance variables and account for them in the design and the analysis of an in vivo experiment
Understanding your experiment
How to define hypotheses and set a biologically relevant effect size
