Dose-response and Non-linear Regression Analysis User Guide

InVivoStat User Guides – Dose-response and Non-linear Regression Analysis Version 4.3 November 2021

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Dose-response and

Non-linear Regression

Analysis

User Guide


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Contents

1 Introduction ......................................................................................... 3

2 Dataset format ..................................................................................... 4

3 Analysis procedure .............................................................................. 5 3.1 Analysis initialisation ............................................................................................................... 5 3.2 Four parameter logistic dose-response analysis ........................................................................ 6 3.3 User defined equation analysis ................................................................................................. 9

4 Output results .................................................................................... 10 4.1 Four parameter logistic dose-response analysis ...................................................................... 10 4.2 User defined equation ............................................................................................................. 10

5 Controlling the output ...................................................................... 11

6 Test dataset example output (Four parameter dose-response) .... 13 6.1 InVivoStat options .................................................................................................................. 13 6.2 Sample output ......................................................................................................................... 14


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1 Introduction

The Dose-response and Non-linear Regression Analysis module in InVivoStat is

available from the Statistics drop-down menu entitled ‘Dose-response and Non-linear

Regression Analysis’. The user interface is:

Users have the option of:

Modelling the response using a four-parameter logistic curve.

Testing multiple quality control (QC) samples.

Back calculating unknown samples onto the fitted curve.

Defining an alternative equation and calculating the best-fit line.


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2 Dataset format

The Dose-response and Non-linear Regression Analysis module accepts data in the

single measures format, for example:

Response Standards

Dose Quality Control

Response Quality Control

Dose Unknown Sample

0.02038835 0 0.75 0.079432823 0.2

0.031067961 0 0.72 0.079432823 0.6

0.031067961 0 0.77 0.079432823 0.4

0.033009709 0.001 0.05 0.031622777 0.2

0.031067961 0.001 0.47 0.031622777 0.5435

0.051456311 0.001 0.42 0.031622777 0.675543

0.274757282 0.01 0.38 0.007943282 0.8765

0.246601942 0.01 0.37 0.007943282 0.232

0.302912621 0.01 0.35 0.007943282 0.99

0.778640777 0.1

0.02

0.810679612 0.1

0.01

0.85631068 0.1 0.963106796 1 0.95631068 1 0.97184466 1 0.980582524 10 0.990291262 10 0.995145631 10


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3 Analysis procedure

The steps required to perform an analysis are described in this section.

3.1 Analysis initialisation

3.1.1 Select the analysis module

The analysis begins by selecting the

Dose-response and Non-linear

Regression Analysis module from the

drop-down list of available modules:

Parametric Analysis →

Dose-response and Non-linear

Regression Analysis

3.1.2 Select the dataset to be

analysed

Once the module is selected, the dataset

is chosen from the drop-down list of

available datasets.

Click ‘Submit’.

3.1.3 Select the analysis approach

To begin with the user should select

either the ‘Four parameter logistic dose-

response’ analysis or the more general

‘User defined equation’ (i.e. a non-

linear regression model).


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3.2 Four parameter logistic dose-response analysis

3.2.1 Select the variables to

analyse

Once the dataset and method have been

selected, the user selects the response

variable to analyse by clicking on the

Responses box and selecting the

response variable to analyse.

The user should also select the dose

variable.

The user should also define whether the

dose variable is equally (or near

equally) spaced on the log10 or loge

scale.

3.2.2 Select quality controls

When using this module to analyse

assay data, the user can select a quality

control response and dose variable

(used in assay validation) and a variable

containing some unknown samples

requiring back-calculation.

Any transformation applied to the

response variable will also be applied to

the samples response variable.

3.2.3 Defining the offset

If there is a vehicle or zero dose group

included in the dataset, then an offset of

10% of the lowest non-zero dose is

added to the dose variable (to allow a

vehicle group to be included on the log

scale). The user can override this choice

by adding a different value in the Offset

box.


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3.2.4 Selecting quality controls

The user can select quality controls

(QCs) to test against the standard curve.

QC responses and the QC doses are

selected by clicking on the relevant

boxes. Both a QC response and QC

dose are required for the QC analysis to

proceed.

Any user-defined transformation

applied to the response variable will

also be applied to the QC response

variable; similarly any user defined

offset will be applied to the QC dose

variable.

3.2.5 Selecting unknown samples

Similarly a list of unknown samples can

be selected by clicking on the Samples

box and selecting the variable. Any

transformation applied to the response

variable will also be applied to the

samples response variable.

3.2.6 Select a transformation for

the response

Once selected, the user has the option of

applying a transformation to the

response variable, either log10, loge,

square root, arcsine or rank.


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3.2.7 Fixing the parameters

Although InVivoStat models the four

parameter logistic curve to the data by

default, the user has the option to fix

some of the parameters when required.

This is achieved by entering values in

the ‘Fix coefficient at:’ boxes. This

allows the user to fit 1, 2 or 3 parameter

logistic curves.

3.2.8 Choosing the start values

While the default start values for the

unknown parameters should be

sufficient for the analysis to proceed, to

aid in convergence of the algorithm, the

user may need to enter specific start

values for the unknown parameters.

This is achieved by populating the ‘Start

value’ boxes.

3.2.9 Run the analysis

Click ‘Submit’ to run the analysis.


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3.3 User defined equation analysis

3.3.1 Defining the equation

When using this option, the user needs

to define the equation to fit.

The equation should be of the form:

y=f(x)

i.e. for a quadratic curve

a*x*x+b*x+c

3.3.2 Defining the start values

Every unknown parameter in the

equation has to have a start parameter.

This is entered in the ‘Start values for

parameters’ box and should be entered

in a comma separated list.

For example:

a=1,b=1,c=1

3.3.1 Defining the variables to

analyse

The user must then define the response

(Y-axis) variable and the X-axis

variable by drag and dropping variables

into the relevant boxes.

Click ‘Submit’ to run the analysis.


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4 Output results

4.1 Four parameter logistic dose-response analysis

The output from the four parameter dose-response analysis includes:

Analysis description and references

A description of the analysis performed.

Scatterplot with fitted curve

A scatterplot of the response variable vs. the dose variable, including the fitted curve

and any QCs.

Tables of analysis results

A table of curve parameter estimates.

A table of the back transformed IC50 estimate along with 95% confidence intervals.

A table of the back calculated QC samples and acceptance criteria (%CV and %RE).

A table of the predicted back calculated unknown samples.

Analysis description


References

A list of references for the methods applied in the analysis.

4.2 User defined equation

The output from the user defined equation analysis includes:

Analysis description and references


Scatterplot with fitted curve

A scatterplot of the response variable vs. the dose variable, including the fitted curve.

Tables of analysis results

A table of fitted curve parameter estimates.

References

A list of references for the methods applied in the analysis.


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5 Controlling the output

The user has the ability to control various aspects of the output. These are available in

the ‘Output Options’ dialogue:

Users can manipulate various plot

characteristics including line size, fonts

and marker size/type.


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The user has control over all text

included on the plots, for example text

position, size and font.

The user has control over the colour

scheme employed by InVivoStat,

including an option to produce all plots

in black & white.

Further information on these options can be found in the Getting Started User Guide.


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6 Test dataset example output (Four parameter dose-

response)

6.1 InVivoStat options


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6.2 Sample output


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Dose-response and Non-linear Regression Analysis User Guide

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