"Determining sample sizes for cancer trials involving Quality of Life instruments

Professor Michael Campbell 1
Sarah Walker (Research Assistant) 1
Steve George 2                                                                                        

David Machin 3                                                                                                   Steven Julious 1

1 Dept of Medical Statistics & Computing, Southampton General Hospital
2 Institute of Medical Health Medicine, University of Southampton
3 MRC Cancer Trials Office, Cambridge

Executive Summary

BACKGROUND

Quality of Life (QoL) is an important endpoint in cancer clinical trials, particularly in trials of new treatments where the survival advantage relative to the standard treatment is likely to be modest. When planning a clinical trial comparing the outcomes of interventions on groups of patients, the sample size calculation is critical. The sample size must allow a reasonable chance (power) of detecting a predetermined difference (effect size) in the outcome variable, at a given level of statistical significance. As there are in general no accepted, or even in many cases, known, values for the effect sizes measured by QoL instruments they must, at present, be determined from experience, published data or pilot studies. The sample size required in a cancer clinical trial is critically dependent on the significance level (alpha), power (1 - beta) and the proposed   effect size, and as such these variables are all interlinked. The term outcome, is merely the measurable change in some outcome variable, which is attributed to some preceding intervention. For a QoL to be able to measure outcome, it must be able to detect a change in the outcome reliably, or at least be able to detect differences between two populations. Much statistical work is required in the design, use and analysis of QoL instruments. The aim of this research was to produce guidelines for establishing sample sizes of clinical trials having QoL as an integral outcome measure.

METHODS

An MRC lung cancer trial was analysed with respect to the data generated from two QoL measures: the Hospital Anxiety and Depression Scale (HADS), and the Rotterdam Symptom Checklist (RSC). Recently published techniques were used to calculate the required sample sizes for future trials enabling a sample size table to be generated.

RESULTS

QoL scores were not normally distributed, and transformations would not make them normal. A formula for the effect size was developed. Parametric and non-parametric methods were used to calculate sample sizes. The non-parametric method is based on the odds ratio and proportional odds. A sample size table was produced to compare the two methods. Non-parametric techniques were found to determine sample size estimates more reliably than parametric methods. Although these techniques are widely available they are not often used because of the lack of normative data sets and the complexity of the calculations required. One solution to the problem has been to dichotomise the data at pre-defined cut-offs. However, care must be taken when subsequently analysing the outcomes to work with the dichotomised data and not with the raw data as this can lead to substantial overestimates of the sample size required. The non-parametric method uses a technique for ordered categorical data.

INTERPRETATION

Many researchers quote means and standard deviations and hence assume a Normal distribution to calculate their required sample size for QoL outcomes. It is evident that the methodology which assumes a symmetric Normal distribution for the QoL dimensions gives symmetric sample sizes, as the parametric techniques for Normal data depend only on the absolute value of the difference regardless of the sign of the expected effect size. However, the non-parametric techniques used for the QoL dimensions give markedly different sample sizes according to the direction of the expected effect size. This project demonstrates that the assumption of Normality can lead to unrealistically sized studies. The sample size tables produced highlight the discrepancies between parametric and non-parametric techniques. We recommend that researchers use the non-parametric formulas described for both the effect sizes and for the sample size estimations. This will allow health professionals involved in the care of cancer patients to develop interventions that maximise outcome in terms of both a patient's overall survival and their QoL. 

Publications

Walker SJ, Campbell MJ, George S, Machin D & Julious SA. - A literature review of three quality of life questionnaires used in cancer trials. 

Walker SJ, Campbell MJ, George S, Machin D & Julious SA. - Determining sample sizes for cancer trials involving quality of life instruments.

The views presented here are those of the authors and not necessarily those of the Department of Health

This research was carried out at the University of Southampton

Further information may be obtained from:

Professor Michael Campbell     
School of Health and Related Research (ScHARR)
Community Sciences Centre
Northern General Hospital
University of Sheffield
Herries Road
Sheffield       S5 7AU

UK