The figures below show the influence of both dialysis fluid temperatures on blood pressure over time. Each check-up represents measurements taken after an additional hour of dialysis on a given day and the results in the figures are average values for patient blood pressure over certain periods and temperatures.
As we can see, both systolic and diastolic blood pressures drop no matter the temperature of dialysis fluid. Although warm diastolic blood pressure in period suggests otherwise, this appears to be due to missing data for later checkups. Initial observations imply that cool dialysis performs slightly better at retaining blood pressure, which is contrary to the thoughts of researchers. This was the case for period 2 blood pressures and interpretation of period 1 pressures was not possible using these graphs, due to the previously mentioned problem of missing data.
Similar results occur for hypotension rates. The proportion of hypotension rate amongst warm dialysis fluid experiments was \( \frac{86}{475}\approx 0.181 \), whilst with cool fluid the rate dropped to \( \frac{41}{455}\approx 0.090 \).
Analysis was next conducted using the change in blood pressure between the pre-dialysis reading and the reading after check-up 1, or in other words after 1 hour. This prevented baseline values from influencing the final results. By considering patients in group 1 to be the patients who first had cool dialysis and group 2 patients to have the warm dialysis first, we obtain the following table for blood pressure readings:
## |id | Avg change score diff (group1)| Avg change score diff (group2)| Avg change scores (group1)| Avg change scores (group2)|
## |:----------|-------------------------------:|-------------------------------:|---------------------------:|---------------------------:|
## |Diastolic | 3.828| -0.4414| -5.876| -4.598|
## |Systolic | 6.051| 1.6818| -12.790| -12.154|
This table can be interpreted as follows. Change scores are considered to be the blood pressure measurement pre-dialysis subtracted from the blood pressure at check-up 1. Then the difference in change scores is taken to be change score for the first temperature of dialysis minus the change score for the second temperature. In other words, for group 1 the difference in change scores is the change score for cool dialysis minus the change score for warm dialysis. Therefore this table shows change scores averaged approximately -5.9 for group 1 and -4.6 for group 2 which gave a difference of -1.3. We can conduct a two sample t-test on this data to analyse treatment-period interaction. Doing so gives a p-value of 0.4329 and \( 95\% \) confidence interval of \( ( -4.534419,1.978955) \) for which -1.3 lies inside, suggesting the treatment-period interaction is not significant.
Similarly, doing the same test for period effect gives a non-significant p-value of 0.1365. Here the average difference in blood pressure between periods was 3.386168 which lay comfortably inside the \( 95\% \) confidence region \( (-1.131657,7.903994) \). Since neither are significant we can test the treatment effect which has a p-value of 0.06316. This is not significant at the \( 95\% \) level, which means that there is not a significant difference in blood pressure when warm or cool dialysis is used, at least in the case of diastolic blood pressure.
In the case of systolic blood pressure, the period and treatment-period effect obtained p-values of 0.01303 and 0.8223 and \( 95\% \) confidence intervals \( (1.715485,13.750657) \), \( (-6.316481,5.044256) \) respectively. This suggests that there is a significant period effect, or in other words the order of warm or cool dialysis fluid influences systolic blood pressure change. This is not a good sign and consequently there is little point in conducting a hypothesis test on treatment effect since the experiment in this case has too large a flaw.
Looking further into these results we can again seperate the measurements into period and temperature. The figures below show the change scores for these respective groups.
These figures do not appear to suggest a period effect. Values seem faily consistent across periods, however this will be analysed in more depth by ANCOVA.
An alternative approach was also considered, namely analysis of covariance. In this case the full data set was used, compared to the cleaned and therefore smaller data set used in the previous approach. ANCOVA also takes into account the baseline imbalance due to regression to the mean. Here the response was take to be the first check-up blood pressures, with baseline measures included in the covariates along with temperture, period and a temperature-period interaction term. For both diastolic and systolic blood pressure all covarites apart from the period appeared to be significant. This is rather different to outcomes using the previous method. In particular the emphasis on temperature being significant in both blood pressure cases and period effects not being prevalent (p-values of 0.88 and 0.30 for diastolic and systolic respectively) were completely contrary to previous results. Moreover, in this example there appears to be a significant temperature-period interaction term with low p-values in both systolic (\( 8.2e^{-6} \)) and diastolic (\( 7.97e^{-5} \)) cases. This will need to be investigated further.