Change scores

Blume, A. W., Marlatt, G. A. (2000). Recent important losses predict readi-ness-to-change scores in people with co-occurring psychiatric disorders. Addictive Behaviors, 25, 461—464. 

Raw numbers provide the clinician with a feel for what actually happened, whereas the mean change scores on some abstract scale may have little intuitive meaning to the clinician. It is best to have the data speak directly to the reader in an uncomplicated fashion, and such information should always be included. 

Janicak et al. (87) studied the relative efficacy and safety of risperidone versus haloperidol in the treatment of schizoaffective disorder. Sixty-two patients (29 depressed type, 33 bipolar type) entered a randomized, double-blind, 6-week trial of risperidone (up to 10 mg/day) or haloperidol (up to 20 mg/day). They found no difference between risperidone and haloperidol in the amelioration of psychotic and manic symptoms nor any significant worsening of mania with either agent. For the total PANSS, risperidone produced a mean decrease of 16 points from baseline, compared with a 14-point decrease with haloperidol. For the total CARS-M scale, risperidone and haloperidol produced mean change scores of 5 and 8 points, respectively and for the CARS-M mania factor, 3 and 7 points, respectively. 

Using meta-analytic techniques based on the means and the standard errors presented graphically in the poster, we estimated pooled data of the four effective dosages of quetiapine both for the BPRS and the CGI severity of illness change scores from baseline to endpoint. Quetiapine produced an improvement of 0.43 effect-size units in comparison with placebo, a difference that was highly statistically significant and about the same improvement as haloperidol. Thus, based on the BPRS or PANSS, quetiapine was similar to neuroleptics in efficacy (i.e., differences were nonsignificant). Based on our meta-analysis, quetiapine is clearly superior to... 

FIG. 5-11. Brief Psychiatric Rating Scale (BPRS) change scores in relationship to trifluoperazine plasma levels. (From Janicak PG, Javaid Jl, Sharma RP, et al. Trifluoperazine plasma levels and clinical response. J Clin Psychopharmacol 1989 9 340-346, with permission.)... 

Calculate the mean change score for each treatment group. 

Calculate the difference between the mean change score for the drug treatment group and the mean change score for the placebo group, i.e., the effect size. 

As an example, consider two groups of 10 subjects and 11 subjects, respectively. These group totals are clearly unrealistically small in terms of a randomized clinical trial, but they allow the methodology of the /-test to be demonstrated. Imagine that these hypothetical data represent SBP change scores ... 

In the present example, an effect size of 3.00 mmHg was observed. That is, the difference between the drug treatment group mean change score and the placebo treatment group mean change score was 3.00 mmHg. This effect size has been precisely calculated on the basis of the data obtained in the clinical trial. Recall, however, that in a randomized clinical trial the subjects used are a random sample of all the people in the disease population of interest. Our interest actually lies with the effect size in that population. The population effect size is not known, and a question of interest is How well does the effect size calculated in our sample reflect the unknown effect size in the population This question is at the heart of inferential statistics. 

As antihypertensive drugs are intended to lower blood pressure, their evaluation in clinical trials requires at least two measurements. One of these is an initial measurement, typically called a baseline measurement, and the other is a measurement some time later, such as at the end of the treatment phase (the end-of-treatment measurement). These two measurements allow us to calculate a change score that represents the change in blood pressure from the start to the end of the treatment phase. Change scores can be calculated in several ways. One of these, and the method that is used in all of the examples in this book, is simply to calculate the arithmetic difference between each individual s baseline measurement and his or her end-of-treatment measurement. 

The one-sample t test will be used to test the null hypothesis. As there are 10 observations and assuming the change scores (the random variable of interest) are normally distributed, the test statistic will follow a t distribution with 9 df. A table of critical values for the t distribution (Appendix 2) will inform us that the two-sided critical region is defined as t < -2.26 and t > 2.26 - that is, under the null hypothesis, the probability of observing a t value < -2.26 is 0.025 and the probability of observing a t value > 2.26 is 0.025. 

Baseline and end-of-study values of SBP are presented for the 10 participants in Table 6.5, along with their respective change scores. 

The mean change score is -7 and the standard deviation is 7.1. (We leave it to you to verify this.) The test statistic is therefore calculated as ... 

Table 6.5 Systolic blood pressure (SBP) values and change scores ...

There is evidence at the a = 0.05 level that the levels of the factor "dose of drug" differ. Therefore, there is a statistically significant difference in SBP change scores between the groups. (The p value of 0.002 indicates that the null hypothesis would also have been rejected at smaller a levels, for example, at the a = 0.01 level.)... 

The above statement by itself does not, however, tell us anything about which group showed the greatest change score, or indeed how any specific group compared with any of the other groups. Consideration of the group means is necessary to do this. These means, with the associated units of measurement reinserted, are ... 

Statistical analyses were performed using the change scores from the NBAS evaluation (Time 2-Time 1). Multivariate analysis of covariance (MANCOVA) was performed for each of the NBAS clusters with group membership (high, low, and no fish consumption) as the independent variable and the 24 components representing potential confounders as covariates. Approximately 75% of each fish consumption group was included in the analysis (n=416). The loss of subjects occurred because only subjects with data for all variables were included. Multiple regression was also performed for each of the NBAS clusters with inclusion of component covariates for confounder control. 

D-S decrease in mean total score from 28.9 to 16.5 (ref 28.5 to 13.6), not significant for equivalence CGI change score showed a trend in favour of imipramine (p=0.079, equivalence test by Anderson and Hauck), for therapeutic effect score hypothesis of non-equivalence could not be rejected Patient s global assessment 61.2% of patients with "very good" or good" improvement under Hypericum and 70.1% on imipramine, ik0.032 for equivalence (descriptive)... 

Will simple analysis of change scores deal with imbalance ... 

The analysis of covariance estimator also has the advantage that its variance is generally lower than that using raw outcomes or simple analysis of change scores. Figure 7.2 takes the case where the variances of baselines and outcomes are equal and plots the variance of the three estimators as a function of the correlation between baseline and outcome. It will be seen that the analysis of covariance estimator is everywhere superior to the other two and that the change-score estimator is actually inferior to raw outcomes (which is a constant whatever the correlation coefficient) unless the correlation is greater than 0.5. 

Is clinical relevance a relevant consideration when choosing whether to use change scores or raw outcomes as the effit at y measure ... 

The answer is analysis of covariance . If we employ analysis of covariance using the baseline as a covariate, it makes absolutely no difference whether our measure is raw outcomes or change scores. Formally, as regards the estimate of the treatment effect and its standard error, exactly the same result is produced (Laird, 1983). Hence, provided analysis of covariance is employed, the whole debate is rendered irrelevant. 

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