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# Thorough QT (Interval) Studies in Biostatistics

In the mid-1900s it was recognized that certain drugs interfered with the ability of the heart to "recharge" its muscles between beats, which could lead to a particularly life-threatening form of cardiac arrhythmia called Torsades de Points (TdP). Fortunately, warning signs of this arrhythmia show up as a distinctive pattern on an electrocardiogram (ECG) well before it progresses to TdP.

You've seen the typical squiggly pattern of an ECG in movies (usually just before it becomes a flat line). ECGs graphically depict the propagation of electrical "triggering" signals racing around the heart from one beat to the next. Cardiologists have labeled the various peaks and dips on an ECG tracing with consecutive letters of the alphabet, from P through T, like you see here.

That last bump, called the T-wave, is the one to look at. It depicts the movement of potassium ions back into the heart muscle cell (called repolarization), getting it ready for the next beat. If repolarization is slowed down, the T-wave will be stretched out. If repolarization is slowed down too much, the heart muscle might not be fully recharged by the time the electrical triggering signal for the next beat reaches it, resulting in a cardiac arrhythmia, or (in the worst case) full-blown TdP.

For various reasons, cardiologists measure that stretching out time as the number of milliseconds between the start of the Q wave and the end of the T wave; this is called the QT interval.

The QT interval is usually adjusted to compensate for variability in heart rate by any of several formulas, resulting in a "heart-rate-corrected" QT interval (QTc), which is typically around 400 milliseconds (msec). If a drug prolongs QTc by 50 milliseconds or more, things start to get dicey. Ideally, a drug shouldn't prolong QTc by even 10 milliseconds.

Data from all preclinical and human drug trials are closely examined for the following so-called signals that the drug may tend to mess up QTc:

• Any in-silico or in-vitro studies indicate that the drug molecule might mess up ion channels in cell membranes.

• Any ECGs (in animals or humans) show signs of QTc prolongation.

• Any evidence from other studies that drugs that are chemically similar to the new drug have produced QT prolongation.

If any such signals are found, the FDA will probably require you to conduct a special thorough QT trial (called a TQT or QT/QTc trial) to determine whether your drug is likely to cause QT prolongation.

A typical TQT trial may enroll about 100 healthy volunteers and randomize them to receive either the new drug, a placebo, or a drug that's known to prolong QTc by a small, safe amount (this is called a comparator or a positive control, and it's included so that you can make a convincing argument that you'd recognize a QTc prolongation if you saw one).

ECGs are taken at frequent intervals after administering the product, clustered especially close together at the times near the expected maximum concentration of the drug and its known metabolites. Each ECG is examined; the QT and heart rate are measured; and the QTc is calculated.

The statistical analysis of a TQT is similar to that of an equivalence trial. You're trying to show that your drug is equivalent to a placebo with respect to QTc prolongation, within some allowable tolerance, which the FDA has decreed to be 10 milliseconds. Follow these steps:

1. For each subject, subtract the QTc of the placebo from the QTc of the drug and from the QTc of the positive control at the same time point, to get the average amount of QTc prolongation (for the drug, and for the positive control, relative to placebo) at each time point.

2. Calculate the 90 percent confidence intervals around the QTc prolongation values.

3. Plot the average prolongations, along with vertical bars representing the confidence intervals.

To pass the test, the drug's QTc mean prolongation values and their confidence limits must all stay below the 10-millisecond limit. But for the positive control (comparator) drug, the means and their confidence limits should go up; in fact, the confidence limits should lie completely above 0 (that is, there must be a significant increase) at those time points where the control drug is near its peak concentration.

In the chart above, the average QTc prolongation for the drug (the curve with the circles) and its confidence interval always stayed below 10 milliseconds, even for the time point with the highest prolongation (at 45 minutes). In contrast, the average QTc prolongation for the active comparator (the curve with the triangles) was much higher, as it should be (because the active comparator, by definition, is known to prolong QTc). So this drug passes the TQT test.