22. Confounding (40 Patients)

If in a parallel-group trial the patient characteristics are equally distributed between the two treatment groups, then any difference in outcome can be attributed to the different effects of the treatments. However, if not, we have a problem. The difference between the treatment groups may be due, not only to the treatments given, but also to differences in characteristics between the two treatment groups. The latter differences are called confounders or confounding variables. Assessment for confounding is explained.

Is one treatment better than the other in spite of confounding in the study.

A 40 patient parallel group study assesses the efficacy of a sleeping pill versus placebo. We suspect that confounding may be in the data: the females may have received the placebo more often than the males.

The first 10 patients of the 40 patient study are given above. The entire data file is in extras.springer.com, and is entitled “chapter22confounding”. Start by opening the data file in SPSS.

We will then draw the mean results of the treatment modalities with their error bars.

The above graph shows that the treatment 1 tended to perform a bit better than treatment 0, but, given the confidence intervals (95 % CIs), the difference is not significantly different. Females tend to sleep better than males, and we suspect that confounding may be in the data: the females may have received the placebo more often than the males. We, therefore, draw a graph with mean treatment results in the genders.

The graph shows that the females tend to perform better than the males. However, again the confidence intervals are wider than compatible with a statistically significant difference. We will, subsequently, perform simple linear regressions with respectively treatment modality and gender as predictors.

For analysis the statistical model Linear in the module Regression is required.

The above table shows that treatment modality is not a significant predictor of the outcome at p < 0,050.

We will also use linear regression with gender as predictor and the same outcome variable.

Also gender is not a significant predictor of the outcome, hours of sleep at p < 0,050. Confounding between treatment modality and gender is suspected. We will perform a multiple linear regression with both treatment modality and gender as independent variables.

The above table shows, that, indeed, both gender and treatment are very significant predictors of the outcome after adjustment for one another.

The above figure tries to explain what is going on. If one gender receives few treatments 0 and the other gender receives few treatments 1, then an overall regression line will be close to horizontal, giving rise to the erroneous conclusion that no difference in the treatment efficacy exists between the treatment modalities.

This phenomenon is called confounding, and can be dealt with in several ways: (1) subclassification (Statistics on a Pocket Calculator, Part 1, Chapter 17, Springer New York, 2011, from the same authors), (2) propensity scores and propensity score matching (Statistics on a Pocket Calculator, Part 2, Chapter 5, Springer New York, 2012, from the same authors), and (3) multiple linear regression as performed in this chapter. If there are multiple confounders like the traditional risk factors for cardiovascular disease, then multiple linear regression is impossible, because with many confounders this method loses power. Instead, propensity scores of the confounders can be constructed, one propensity score per patient, and the individual propensity scores can be used as covariate in a multiple regression model (Statistics on a Pocket Calculator, Part 2, Chapter 5, Springer New York, 2012, from the same authors).

If in a parallel-group trial the patient characteristics are equally distributed between the two treatment groups, then any difference in outcome can be attributed to the different effects of the treatments. However, if not, we have a problem. The difference between the treatment groups may be due, not only to the treatments given but, also to differences in characteristics between the two treatment groups. The latter differences are called confounders or confounding variables. Assessment for confounding is explained.

More background, theoretical, and mathematical information is available in Statistics applied to clinical studies 5th edition, Chap. 28, Springer Heidelberg Germany, 2012, from the same authors.