Having identified that the time profiles for the two drugs are different - as indicated by the significant interaction - you are now trying to work out whether the difference is due to the drugs or whether it is due to the observation that one of the groups had high baseline values.  It's hard to be sure without inspecting the plots for individual patients but adjusting for baseline makes the difference between the two drugs at later time points clearer.  Using a derived statistic - such as change from baseline - would probably give you the same results. 

You still have a problem though. 

The difference could be a genuine effect of the drug.  Or it could be attributable to regression to the mean: the biggest change from baseline is observed in that group that has the highest starting values.  Right now I'd say the results are suggestive of a treatment effect but not conclusive.  This may not be what you were hoping for, but I hope this helps.

It means that you can not reject the null hypothesis that different individuals react similarily on the treatments.

While on average there is no overall difference between the two drugs, the time course for the two drugs is significantly different.  This could be genuinely interesting.  Or it may just arise because your two groups are different at time zero?  Hope this helps.

Consider that when you add an interaction in a regression analysis, the interpretation for each coefficient is a function of the interaction ; this is the effect of each variable is the effect  in the reference population of the other involved in the interaction. In this  specified case , the coefficient for the "group variable" indicates differences in Y( outcome) between groups  IN time zero ; something like the effect of allocation ( which for example in a clinical trial should not be statistically significant since the beginning, Y  would be the same in both groups if randomization worked) . The coefficient for time ( if it is incorporated as a categorical variable) indicates the change in time with respect to time zero but only IN those untreated (or the reference) group ( as would many times coefficients minus one).  Finally the interaction time X group , I think here 's your problem. Given It is better to incorporate time as a qualitative variable and then you have three times and the basal time is the reference , you have two interaction coefficients. One for each time except the reference time. So that the interaction is interpreted as the effect of treatment at echar times. ( except possibly at zero time as this as I mentioned is the coefficient group). Also if you want to calculate the mean of Y for each subgroup would be the effect of time + effect + group at time zero treatment effect. Many programs can be estimated. Consider that you incorporate time as quantitative, you would suggest than the effect of the grupo on time increasing lineally and It is unlike. So, I suggest to incorporate time as a categorical variable, and it makes easy the interpretation as I tried to clear up. Regards

Dear All,

There is a non-statistically significant difference (P = 0.178) between the two groups at baseline. When we control the baseline value of the outcome variable C, the test of between-subject contrasts became significant for the group (figure).

So, should we control the baseline value of the outcome variable in the repeated measure analysis?

Having identified that the time profiles for the two drugs are different - as indicated by the significant interaction - you are now trying to work out whether the difference is due to the drugs or whether it is due to the observation that one of the groups had high baseline values.  It's hard to be sure without inspecting the plots for individual patients but adjusting for baseline makes the difference between the two drugs at later time points clearer.  Using a derived statistic - such as change from baseline - would probably give you the same results. 

You still have a problem though. 

The difference could be a genuine effect of the drug.  Or it could be attributable to regression to the mean: the biggest change from baseline is observed in that group that has the highest starting values.  Right now I'd say the results are suggestive of a treatment effect but not conclusive.  This may not be what you were hoping for, but I hope this helps.

Dennis,

The % of change (T1-T2/T1) was calculated for the outcome variable and it was 5% more with the drug compared with placebo which was significant. Also, treatment response was defined as a change of at least 30% in the outcome variable and again, treatment response was significantly higher in the drug group (77% vs 37%). These results are suggestive of an effect for the drug. However, the regression to the mean is also possible.

Thanks

Dear Martin,

In Figure 2 both the time x treatment and treatment effects are significant.

Thanks

Hi Ali - here's what the three contrasts in the repeated measures anova mean to me:

1) for the between group comparison, scores are laid out from, say, time1 to time 2 along the x-axis while the magnitude of the variable is represented by the y axis. This contrast takes a mean value between time1 and 2 for each group and does a simple significance test (akin to an independent t-test) to see if these plots are significantly far apart. So in studying subjects with high blood pressure against normal control subjects, those with HBP would likely have higher values both at time1 & 2 than the controls. To me, this is the least helpful of the contrasts, but it is worth noting - there are times when it will lead you to investigate whether or not there was a lack of effect 'cause one group had extreme scores which made change impossible.

2) The between time comparison is a within subjects comparison that measures whether subjects change significantly from time1 to time1 - here each subject is their own control. It is akin to a dependent t-test and measures across groups. This test is least helpful when the comparison is between an experimental effect and standard practice in which you'd expect change in both groups.

3) The interaction effect measures whether or not there is a significant difference in the way the groups behave from time1 to time2. In the example above, if the treatment was a HBP medication, you'd hope that the interaction would show that there was a differential effect of time on those who took the medication and those who didn't. Hopefully, those who took the medication would see their BP lowered between time1 & time2 while the control values would be fairly flat over time.

Two other points - a plot of a significant interaction should either show the horizontal lines representing each groups values crossing - or pointing towards a crossing point outside the frame of the current plot. Also, it is very difficult to interpret a significant interaction effect without requesting the marginal means from your stat package - this will breakdown mean values by group X time.

Hope this is helpful

Dear Ali,

You analyzed your data with GLM (a mixed anova with both within and between-subjects factors). Your findings might have happened because GLM doesn't account for the correlations between repeated measures of the same subjects across time. In fact, one of the assumptions of GLM procedures is the independency of observations - which, in your study design, was violated. This could explain your unexpected results.

I suggest you run a linear mixed model considering group, time and group * time as fixed factors and including time as a random factor. Linear mixed models are within the scope of "multilevel models" and have been preferred over GLM in recent RCTs.  This procedure accounts for the depedency within repeated measures and may provide a more realistic interpretation of your data. For more details of how to conduct such analysis you may read this guide (http://www.spss.ch/upload/1126184451_Linear%20Mixed%20Effects%20Modeling%20in%20SPSS.pdf)

Hope it helps

Thank you, these explanations are very helpful.

We submitted a paper recently that used a linear mixed model with a time*group interaction to analyze whether there was a significant difference in change (baseline-follow up) between the two groups. However, our paper was rejected because a reviewer said that our results were biased due to the fact that one group had a higher baseline value than the other group. We would like to resubmit, and I'm trying to decide between keeping the linear mixed model or changing to ANCOVA. We initially used linear mixed models due to some missing pre-post observations, however, I'm thinking about reanalyzing using ANCOVA, although that'd mean we'd lose some patients or have to impute due to missing values. Does anyone have advice on this? Dennis William Lendrem, should we just say as you put it that "results are suggestive of a treatment effect but not conclusive" due to a difference in baseline values?

You don't need to change your analysis, as this won't change the fact that the baseline values are different. You should not try to mask or hide this, because this can be important.

A difference in baseline values can be a problem but is not neccesarily a problem. Are there some resonable possible explanations for the differences? How large is the difference? Is it of any practical relevance? How large is it compared to the treatment effect? Could you have ceiling effects (that is: if the value has some upper limit and the baseline is already high, the treatment cannot increase the value so much - so even if the treatment effect would have to be identical, you will get a lower apparent treatment effect in the group with the higher baseline; the same is true if a lower limit exists and the treatment effect is negative)?

You need to discuss all these things.