When using data to measure progress, it is useful to have a clear picture of what the baseline is. This can help to ensure that any changes are being made in the right direction.

One way to do this is to simply look at change scores, either absolute differences (“CHANGE”) or percentage shifts (“FRACTION”) from the baseline. But this can be misleading.

Percentage Changes

Percentage change is a common measure of an increase or decrease in something. To calculate a percentage change, start with the original number, then change from the baseline and multiply by 100%. Percentage changes are commonly used in finance and business, such as comparing the performance of stocks and other investments over time. They can also be used to compare the performance of different cities and nations’ economies, such as the GDP of the United States versus the GDP of France.

When analyzing results from a clinical trial, it is important to determine how much the treatment has changed an individual’s baseline score. This information can help identify the most effective treatments. However, it is not always possible to compare differences in baseline scores because the number of individuals who are at a given level may differ greatly. To eliminate this problem, some researchers use a statistic called percent change from baseline. This statistic is calculated by subtracting an earlier value from a later one and dividing the difference by the original number.

The percentage change from baseline is a statistical measure of the amount of improvement an individual has made. In some cases, an analysis based on this statistic is more efficient and powerful than comparison of final measurements. In addition, it can be more appropriate for outcomes that are unstable or difficult to accurately measure, because it removes a component of between-person baseline variability.

Despite these advantages, there are problems with the use of percent change from baseline for analyzing treatment effects. A key issue is that the method of calculating a percentage change from baseline involves correlating two mathematically coupled variables. This practice is questionable, as it has been shown that such a correlation can lead to biased conclusions12.

The results of a statistical analysis based on a change from baseline are often reported in terms of an average change score. This is a convenient way to present the results of a clinical trial in terms that are easily understood by patients and clinicians. However, if an analysis is based on this statistic it is important to use the corresponding standard error or SE for the baseline measurement. This will ensure that the average change score is not misleadingly low.

ANCOVA

ANCOVA is an extension of ANOVA that helps to control for differences between groups in the baseline measurement. It can also be used to correct for changes in the way an outcome is measured, such as when changing from using a questionnaire to a different scale or method of scoring (e.g., converting scores to percentages). In addition, it can be used to adjust for the effects of any covariate variable in an experiment.

Often, when an RCT compares two groups on a single posttreatment measure, the treatment and control group will have differences in their pre-treatment measures that can affect the change score. This is why ANCOVA is often preferred to simple analysis of differences (SACS). Its advantages are especially evident when there is a significant correlation between the two measures, or when there is a large amount of baseline imbalance.

The advantage of ANCOVA is that it reduces the amount of variance in the change score due to changes in the covariate and regression to the mean. This can help to make more valid conclusions about the effect of the treatment. It can also reduce the uncertainty in the change score estimate and increase its statistical power.

Some researchers have claimed that ANCOVA is biased if the groups are not equal at the baseline, but this would require that the equality be only in expectation and not actually observed (known as Lord’s paradox). However, it has been shown that, even when there is a small amount of bias from baseline imbalance, ANCOVA yields estimates that are closer to the true treatment effect than ANOVA. This is not because of a difference in the precision of the results, but because of a change in the way that the size of the change score is calculated. This has implications for the reporting of results from clinical trials. In fact, it is recommended that ANCOVA be reported for all RCTs where there is baseline imbalance, regardless of the magnitude of the imbalance. In this case, it should be reported along with the adjusted treatment effect estimate and the standard error of the treatment effect.

Graphing

A baseline is a point from which you measure changes in a process. It can be used to document the project’s initial plan or it can be compared with data collected throughout the course of a project to determine whether an intervention is working. It’s important to save a project’s original baseline so that you can return to it later for comparisons.

A graph is a useful tool for visualizing a baseline. The y-axis represents time, and the x-axis is the range of values. A line that represents the average of these values is drawn on the graph to show the trend. A slant upwards means the behavior has increased, while a downward slant indicates that it’s decreasing. The steepness of the slant can also help you decide whether an intervention is working.

You can also use a graph to make an estimate of the amount of change that has occurred. To calculate the change, divide the difference between the data points by the value of one of the data points. The result is the relative change, which can be converted to a percent change by multiplying it by 100. For example, if the difference between data points is 20 and the value of the control group is 10, the relative change is 22%.

When creating a graph, it’s important to start with a zero baseline when possible. It will make it easier to understand the trends in the data. If you’re using a simple line graph, you can do this by omitting the baseline from the y-axis. However, this method is not always effective, and you may lose a lot of valuable information about the data.

Keep in mind that it can take a while for a method or an intervention to produce the desired effect. If your results don’t seem to be improving after a certain period of time, it might not be because the method isn’t working; it could just be that the problem is too large for the solution you’ve chosen. In this case, you might need to try a different approach.

Regression

Changing project scope, cost and timelines can make it difficult to track and document the performance of a project. While these changes aren’t always bad, it is important to be clear about the impact on the baseline and the new forecasts. This will help avoid confusion about the project’s current state and prevent inaccurate estimating.

When analyzing longitudinal data, a number of statistical methods have received general acceptance to assess the association between change and the initial value, or baseline (1, 28, 29). Linear random effects models and Blomqvist’s method can be used if sufficient measures are available, but these require multiple measurements of the variable of interest to be reliable. Other methods use correlation or analysis of the pattern of changes in the spread of data to reveal an association between the initial value and subsequent change (e.g., Bland-Altman plots) (1, 29, 30).

In general, there will be some correlation between the change score and the initial value, i.e., corr(Y1 – Y0) will be positive if the change score and Y0 have similar variances, and vice versa. ANCOVA is one of the most commonly used analysis techniques for addressing this question. It adjusts each patient’s follow up score for his or her baseline score. Thus, if a treatment is better than the control, the difference will be underestimated by a comparison of the change scores and overestimated by comparing only the mean change score (regression to the mean).

The main concern with this approach is that the baseline will be contaminated with the same variance that will affect the follow up data. To counter this issue, several methods have been proposed to determine whether the correlation between initial and subsequent changes is actually due to the variation in measurement error and not the baseline variation (1, 33). The most commonly used method is the linear random effects model, which requires repeated measurements to be reliable (33). However, it cannot be applied if only two waves of data are available because it is based on the assumption that the individual growth curves are linear (34). Another option is the analysis of covariance, which does not depend on the amount of variation in the baseline, but does require a large sample size.