## Sampling and inferential statistics

Consider the comparison of a new treatment A to an existing treatment B for lowering blood pressure in mild to moderate hypertension in the context of a clinical trial conducted across Europe. The characteristics of the population of mild to moderate hypertensive patients to be studied will be defined by the inclusion (and exclusion) criteria and may well contain several millions of individuals. In another sense this population will be infinite if we also include those patients satisfying the...

## Nonconstant hazard ratio

However, it is not always the case, by any means, that we see a constant or approximately constant hazard ratio. There will be situations, as seen in Figure 13.4, when the hazard rate for one group starts off lower than the hazard rate for a second group and then as we move through time they initially move closer together, but then a switch occurs. The hazard rate for the first group then overtakes that for the second group and they continue to move further apart from that point on. In this...

## Basic ideas in clinical trial design

As many of us who are involved in clinical trials will know, the randomised, controlled trial is a relatively new invention. As pointed out by Pocock (1983) and others, very few clinical trials of the kind we now regularly see were conducted prior to 1950. It took a number of high profile successes plus the failure of alternative methodologies to convince researchers of their value. Example 1.1 The Salk Polio Vaccine trial One of the largest trials ever conducted took place in the US in 1954...

## Confidence intervals for noninferiority

For non-inferiority, the first step involves defining a non-inferiority margin. Suppose that we are developing a new treatment for hypertension and potentially the reason why the new treatment is better is that it has fewer side effects, although we are not anticipating any improvement in terms of efficacy. Indeed, suppose that we are prepared to pay a small price for a reduction in the side effects profile say up to 2 mmHg in the mean reduction in diastolic blood pressure. In Figure 12.2, and...

## Intentiontotreat and timetoevent data

In order to illustrate the kinds of arguments and considerations which are needed in relation to intention-to-treat, the discussion in this section will consider a set of applications where problems frequently arise. In Chapter 13 we will cover methods for the analysis of time-to-event or so-called survival data, but for the moment I would like to focus on endpoints within these areas that do not use the time-point at which randomisation occurs as the start point for the time-to-event measure....

## The chisquare test for binary data 441 Pearson chisquare

The previous sections have dealt with the t-tests, methods applicable to continuous data. We will now consider tests for binary data, where the outcome at the subject level is a simple dichotomy success failure. In a between-patient, parallel group trial our goal here is to compare two proportions or rates. In Section 3.2.2 we presented data from a clinical trial comparing trastuzumab to observation only after adjuvant chemotherapy in HER2-positive breast cancer. The incidence rates in the test...

## Example 153 Metaanalysis of adjuvant chemotherapy for resected colon cancer in elderly patients

Sargent et al. (2001) provide a meta-analysis of seven phase III randomised trials, involving a total of 3351 patients, that compares the effects of fluorouracil plus leucovorin (five trials) or fluorouracil plus levamisole (two trials) with surgery alone in patients with stage II or stage III colon cancer. NCCTG NCCTG Intergroup INT 0035 FFCD NCIC-CTG Siena GIVIO Overall Adjuvant therapy better Surgery alone better NCCTG NCCTG Intergroup INT 0035 FFCD NCIC-CTG Siena GIVIO Overall Adjuvant...

## Confidence intervals for proportions

The previous sections in this chapter are applicable when we are dealing with means. As noted earlier these parameters are relevant when we have continuous, count or score data. With binary data we will be looking to construct confidence intervals for rates or proportions plus differences between those rates. Example 3.3 Trastuzumab in HER2-positive breast cancer The following data (Table 3.4) are taken from Piccart-Gebhart et al. (2005) who compared trastuzumab after adjuvant chemotherapy in...

## Timetoevent data and censoring

In many cases an endpoint directly measures time from the point of randomisation to some well-defined event, for example time to death (survival time) in oncology or time to rash healing in Herpes Zoster. The data from such an endpoint invariably has a special feature, known as censoring. For example, suppose the times to death for a group of patients on a particular treatment in a 24 month oncology study are as follows Here the first patient died after 14 months from the time of randomisation,...

## Example 91 A series of trials in hypertension hypothetical

In a collection of four placebo-controlled trials in hypertension a difference of 4 mmHg in terms of mean fall in diastolic bp is to be considered of clinical importance anything less is unimportant. The results, are given in Table 9.2, where and are the mean reductions in diastolic bp in the active and placebo groups respectively. Table 9.2 p-values and confidence intervals for 4 trials Table 9.2 p-values and confidence intervals for 4 trials

## Biocreep and constancy

One valid concern that regulators have is the issue of so-called biocreep. Demonstrating that a second generation active treatment is non-inferior to the active control may well mean that the new treatment is slightly less efficacious that the active control. Evaluating a third generation active to the now established second generation active may lead to a further erosion of efficacy and so on, until at some stage a new active, whilst satisfying the 'local' conditions for non-inferiority, is,...