Revival: CRC Handbook of Sample Size Guidelines for Clinical Trials (1990)

Jonathan J. Shuster

• Publisher: CRC Press
• Year: 2019
• eBook ISBN: 9781351366250
• Edition: 1
• Topic: Medicine
• Subtopic: Pharmacology

The aim of this unique volume is to help medical researchers design clinical trials to improve survival, remission duration, or time to recurrence of disease. Written in a user-friendly step-by-step format, this work enables the researcher-with no background in statistics-to determine sample size and write statistical considerations for their protocols. It provides critical language which can help with FDA submissions and/or research grants. It also provides the mathematical justification of the material at a level consistent with one year of undergraduate mathematical statistics. It presents survival analysis methods at a more elementary level than any known text. Filled with tables, figures, plus an extensive appendix, this one-of-a-kind reference is an absolute must for all clinical researchers and biostatisticians.

Chapter 1

HOW TO USE THE SAMPLE SIZE TABLES

Introduction

It is vital that a clinical trial has a reasonable chance of achieving its objectives. Small negative studies could be harmful, as they might not have had adequate power to find important differences. Researchers might falsely conclude from the completed trial that a new therapy lacks efficacy. Freiman et al (1978) reviewed a large number of published negative studies and concluded that the vast majority were not adequately sensitive to clinically meaningful differences. To avoid this problem, clinical trials must be well designed, and must have sufficient numbers of patients to answer the study question.

In order to use the sample size tables, the user must supply several values called parameters. The worksheet, Figure 2, will be helpful. Before getting too formal, let us have a glance at a “Statistical Consideration” of a research protocol. At first, it probably will look quite technical, but we shall unravel the details.

STATISTICAL CONSIDERATION

“Historically, the Institute has been able to accrue 125 patients per year with newly diagnosed X-disease. Based on our prior studies, the three year survival rate is expected to be about 60% on the standard therapy (or control therapy). In order to detect a 15% improvement under the experimental therapy (three year survival of 75%), at “alpha”=.05 (one-sided) and 80% “power”, a sample size of 204, half randomly assigned to each treatment, will be needed. This calculation assumes exponential survival with all patients followed to death or termination point of the study. Allowing for a 10% loss to follow-up, a figure consistent with past history, a revised sample size of 227 (1.8 years of accrual) is needed. Patients will be followed until death, loss to follow-up, or the completion of the study (up to 4.8 years). The logrank test will be used to make the treatment comparison.”

1.1 Identification of Parameters

(1) Minimum Planned Follow-up: At how many years will the key survival
comparison be made?

3 years

(2) Annual Accrual

125 Patients per year

(3) Expected Accrual thru Minimum Follow-up

125 × 3=375 (This parameter is used in tables)

(4) PCONT=Planning value for survival thru the minimum follow-up period (In this case 3 years) under the CONTROL treatment.

.6 (ie 60%) (This parameter is used in tables)

(5) DEL=Planning value of improvement under the experimental treatment at the endpoint (ie at three years in this case.)

.15 (ie 15%) (This parameter is used in tables)

(6) ALPHA=Chance of falsely concluding experimental therapy is superior to the control, when in fact it is equivalent to the control. In most studies, a value of .05 (ie 5%) is used. There is no special reason to pick this value other than standardization. For further discussion, see Chapter 2, especially as to one-sided versus two-sided tests. See also the footnote at the conclusion of the chapter.

.05 (ie 5%) (This value is used in the tables)

(7) POWER=Chance of correctly concluding that the experimental therapy is superior to the control, when in fact the planning values (4) and (5) are correct. The most common values for power are 80% and 90% depending on the field. This is discussed further in Chapter 2 and in the footnote at the end of this chapter.

.80 (ie 80%) (This value is used in the tables)

(8) FACT (for factor). This asks the following question. Consider a typical day before and after the endpoint. A value of FACT is the ratio of the instantaneous death rate after the endpoint to that before the endpoint. The exponential distribution implies a value of 1.0. If you consider patients cured after three years, you would use a value of 0. However, the tables can be used for intermediate situations. For example, you might consider that the typical day more than three years out carries half the risk of the typical day less than three years out. In that case, you would use a value of FACT=.5 (or 50%). A value of FACT=BIN is for comparison only. This gives the sample size required if you only looked the “Binary” event of surviving three years or not surviving three years. The comparison would ignore time of death and all data collected after the patient had made it to the three year point. This comparison is distinct from the logrank test and carries a different sample size. This alternate and less powerful test is discussed in Chapter 2 under the name “Kaplan-Meier.” If you browse through the tables, you will note that for many situations, the FACT=.00 and FACT=BIN sample size requirements are very close. When FACT=.00, no deaths are expected after the endpoint.

FACT=1.0 (Exponential) (This value is used in the tables)

SUMMARY

(3) EXPECTED ACCRUAL THRU MINIMUM FOLLOW-UP=375

(4) PCONT=.60

(5) DEL=.15

(6) ALPHA=.05 (One-sided)

(7) POWER=.80

(8) FACT=1.0

To look up the sample size, we start from ALPHA and POWER. These are coded as follows:

To look up the sample size, on the basis of (6) and (7), we shall employ the TABLE 7. This is arranged in order of increasing expected accrual (3). Once the chart for ALPHA=.05, POWER=.80, and EXPECTED ACCRUAL=375 is located, locate the PCONT=.60 row and the DEL=.15 column.

The following six sample sizes:204,211,220,231,245, and 235 correspond respectively to FACT=1.0,.75,.50,.25,.00, and BIN. Since our FACT=1.0, we use

$\text{Sample}\text{Size}=204$

The statistical section inflated the sample size to adjust for 10% losses to follow-up, for a total of 227 patients. By dividing by the accrual rate of 125 patients per year, this means that the accrual is expected to take 1.8 years, (22 months) and the study will require 4.8 years to complete.

*** Footnote on one-sided vs two-sided tests. In situations where you wish to compare two treatments, neither of which can be viewed as a control, you should run a two-sided test. Basically, you proceed exactly as above but replace the value of ALPHA by ALPHA/2. If the above study consisted of two experimental therapies, we would use ALPHA=.025. (TABLE 5) For the 45% vs 60% comparison, we would use PCONT=.45 and DEL=.15, with FACT=1.0. This would require 282 patients. For the 60% vs 75% comparison, we would use PCONT=.60 and DEL=.15 with FACT=1.0. This would require 250 patients. To be safe, we take the larger of these two numbers, 282. Allowing for 10% loss to follow-up, the final sample size would be 313 (2.5 years of accrual).

*** Further Reading. The sample size results of this handbook are similar to those of Schoenfeld (1981), Rubinstein et al. (1981), and especially Lachin (1981, where his equations (25) and (26) are employed). Another interesting method is due to Halpern and Brown (1987), who offer a computer program which can simulate the properties of the logrank statistic under any survival distributions provided by the user.

Finally, a method of Sposto and Sather(1985) is usefu...

Table of contents

• Cover
• Title Page
• Copyright Page
• Table of Contents
• Chapter 1 HOW TO USE THE SAMPLE SIZE TABLES
• Chapter 2 DESIGN AND ANALYSIS OF RANDOMIZED CLINICAL TRIALS
• Chapter 3 DERIVATION OF THE STATISTICAL RESULTS
• FIGURES
• Notation Chart
• APPENDIX I A REVIEW OF MATHEMATICAL STATISTICS
• APPENDIX II TABLES
• INDEX