Interpreting the results of a study on prognosis

The results in an article about prognosis can be presented in different ways. For example, you can simply state the probability of the outcome at a given point in time:

• 23% of patients with Grade A colon cancer have died at 5 years of follow-up
• 30% of patients with Alzheimer's dementia are institutionalized by 3 years following diagnosis

A somewhat richer way to present this information is in a survival curve. Before discussing survival curves, let's look at some sample data from a prognosis study:

Clearly, at any point in the study, patients have been followed for different periods of time, and some patients have died. By the end of the study, one patient has been lost to follow-up (D) and one is still alive (B). How do we make sense of these data?

These kinds of observations are called "censored observations"; when patients are not all enrolled at the same time (as in the graph above), they are called "progressively censored observations". The fundamental principle of analyzing these data is that for each point in time, we look at how many patients are eligible to be counted, and how many are still alive at that point.

The table below shows some censored data for a study of kidney transplant rejection:

Whew! Quite a table. Where do those numbers come from? Let's review:

• Column 1: The number of months since the start of the study. In this case, all 31 of the patients were enrolled at the same time.
• Column 2: How many were alive at the beginning of the interval? Obviously, this number gets smaller as the study goes on and patients die.
• Column 3: How many rejections occur during this interval? The number of rejections seems higher earlier in the study, which is biologically plausible.
• Column 4: How many patients withdrew from the study, or were lost to follow-up? If a patient is lost to follow-up, we would like to make use of the information gained during the time they were in the study.
• Column 5: Be careful!  Now it gets a little tricky. The probability of rejection is given by the formula q = d/[n-(w/2)]. The numerator (d) is the number of rejections during the interval - that's the easy part. In the denominator (n - (w/2)), we have to account for the patients lost to follow-up (w). We divide by 2 because we don't know when in the interval they were lost, and therefore assume that they were lost half-way through.
• Column 6: The probably of retaining a kidney during the interval is simply 1 minus the probability of losing one.  For example, if the probability of losing one is 0.1, the probability of retaining one is 1 - 0.1 = 0.9.
• Column 7: Finally, the cumulative probability of retaining a kidney is the product of each interval probability. Thus, for the 2^nd interval it is 0.9 x 0.88 = 0.79, and for the 3^rd interval is 0.9 x 0.88 x 0.95 = 0.75.

These data can be presented graphically in a survival curve. A survival curve for hypothetical data comparing men with women over a four year period of follow-up is shown below:

In this graph, the proportion of survivors is shown along the y-axis, and the years of follow-up along the x-axis. What proportion of men are still alive at 3 years of follow-up?

        0.2          0.4          0.6         0.8

Let's answer our original question. Recall, we wanted to know the prognosis for a 64 year old man with newly diagnosed congestive heart failure. Refer to the Framingham article, which we have already decided is valid. Sure enough, there is a group of four survival curves on the bottom right corner of page 111, in Figures 1 and 2. Since our patient is a man, we are interested in the two left-hand curves. In particular, Figure 1 gives us the survival rates for the most recent years of the study (1970 to 1988) stratified by age. What is the approximate 5 year survival rate for our patient?

            5%         20%         30%         70%

We also notice in Figure 2 that the cause of CHF is an important predictor of mortality, particularly for men. Patients with CHF caused by valvular heart disease do:

        Worse than average          Better than average

Since our patient does not have valvular heart disease, we find this somewhat reassuring.

That's it!  You've critically appraised the validity of this article about prognosis.  Please select "Quiz" from the menu at left, and if you successfully answer the questions, move on to the Overviews and Meta-analyses Module.