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- Table 1 shows the mean, standard deviation, and percentages of various baseline variables stratified by treatment. Means and SDs are poor descriptive statistics for asymetrically distributed variables. Quartiles are far better. And there is no need to stratify by treatment in a randomized trial. Apparent baseline imbalances would have been misleading and would have been counterbalanced by baseline characteristics omitted from Table 1. Table 1 should have thus included only one column. Much more valuable would have been a table or graphic containing patient responses stratified by levels of baseline variables. Who is having contrast-agent-induced reductions in renal function?
- The authors use improper nomenclature. On the bottom right of P. 181 the authors use the term "relative risk". It is not clear whether this is actually "odds ratio". Odds ratios are preferred (and should be labeled correctly) as they can apply to high- as well as low-risk patients. Odds ratios arise from logistic regression modeling.
- In a parallel-group randomized trial design, comparisons of major interest are always between treatment arms. In a few places the authors have slightly overemphasized changes over time within patients. Regression to the mean and natural history can make such changes difficult to interpret.

- The authors analyzed the effect of acetylcysteine on restoration of renal function after use of radiographic contrast agents for patients with renal dysfunction (serum creatinine > 1.2 mg/dl) undergoing CT. The authors made a common mistake in trying to categorize a continuous variable, which requires an arbitrary cutpoint to be used, results in a major loss in power, and is prone to problems with measurement errors. An artificial construct "acute contrast agent-induced reduction in renal function" was defined as an increase in creatinine (cr) of at least 0.5 mg/dl 48h after administration of the contrast agent. Besides the serious statistical problems listed above, this procedure suffers from the fact that cr does not "work" on a simple difference scale (see below).
- To make matters worse, the authors used Fisher's exact test after dichotomizing cr change. This test is conservative (loses power) as compared to the ordinary Pearson chi-square test.

- The authors used multiple logistic regression to analyze the binary response of acute reduction. Besides the general and particular problems of dichotomizing cr indicated above, the authors adjusted for the wrong variables. They adjusted for baseline blood pressure while also having treatment in the model. It is mandatory to adjust for baseline renal function, which we expect to be a strong predictor in general but especially when the inappropriate change score was chosen. The model needs to compensate for the fact that those with larger baseline cr are easier to change by a fixed absolute amount (0.5 mg/dl). Adjustment for the baseline version of response variables will always increase power. Adjustment for cause of renal insufficiency may also be warranted.

- Find the transformation so that a difference between transformed values has no relationship between the average of the two transformed values (Bland-Altman plot). This is a way to demonstrate that the change measure is independent of baseline.
- Find the transformation so that transformed crs have equal variability across levels of other important variables (e.g., etiology, baseline cr, age). This makes the transformed values satisfy usual multiple regression assumptions.
- Find the transformation that makes serum cr linearly related to log odds of short-term death or, when follow-up is long, of log hazard of death. In the case of cr and other lab parameters (the most common situation of interest is a parameter such as white blood count that has a two-sided normal range), the transformation of the parameter that makes it optimally predict death is not monotonic (e.g., very low and very high values can achieve the same mortality risk). There may be a need to analyze changes in the parameter after making such a complex transformation to a "risk score" scale.

To try method 2 on the same dataset, we first stratify patients by intervals of day 1 cr (

`crea1`

) having 100 patients per interval. Within each interval the quartiles (25th and 75th percentiles and the median) of cr at day 14 (`crea14`

) are plotted against the mean `crea1`

in the interval. Results are shown below.It is easy to see that variability of

`crea14`

increases with `crea1`

. It is easy to "move" cr when it is already large. The authors confirm this in their nice figure 1 but do not act accordingly. Next, a nonparametric regression model called AVAS (additivity and variance stabilization) was used. This methods solves for optimum transformations in `crea1`

and `crea14`

that maximizes their linear correlation coefficient while making the variance in `crea14`

as stable as possible across levels of `crea1`

. The estimated transformations and their confidence intervals follow.These transformations are almost logarithms. The bottom left panel shows how close the optimum transformation is to a log. A straight line would indicate that log was perfect. Stratified quartiles of

`crea14`

against intervals of `crea1`

are shown below but using the optimum transformed transformation for `crea14`

.Variability is much more constant across the whole range of

`crea1`

.
I | Attachment | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|

s | creatinine.s | manage | 1.8 K | 08 Nov 2004 - 22:08 | FrankHarrell | S code used to analyze SUPPORT data and graph data |

png | creatinine1.png | manage | 4.4 K | 08 Nov 2004 - 22:07 | FrankHarrell | |

png | creatinine2.png | manage | 5.2 K | 08 Nov 2004 - 22:07 | FrankHarrell | |

png | creatinine3.png | manage | 8.7 K | 07 Nov 2004 - 05:59 | FrankHarrell | Altman-Bland plots |

png | creatinineOptimum.png | manage | 4.6 K | 06 Nov 2004 - 08:25 | FrankHarrell |

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