Most clinical trials with repeated measures use a traditional complete design: every subject is scheduled to be evaluated at each time point (“visit” or “evaluation occasion”). Recent advances in mixed model statistical methods make it practical to create more efficient, intentionally incomplete longitudinal designs (IILDs). An IILD schedules some subjects to skip some evaluation occasions. A group of subjects with the same schedule is a cohort; an IILD has multiple cohorts. For example, an IILD for a clinical trial with five postbaseline visits might have three cohorts: Cohort 1 subjects would be scheduled for all five visits, Cohort 2 subjects for visits one, three, and five, and Cohort 3 subjects for visits one and five. An IILD is determined by the number of subjects assigned to each of the three cohorts. A traditional design would place all subjects in Cohort 1. Under reasonable conditions, more than 400 IILDs have greater power and less cost than the traditional design for comparing three treatments.
HelmsRW. Definitions of Linear Model Parameters and Hypotheses as Functions of E[Y]. Comm Stat. 1988;A17 (No. 8):2715–2723.
2.
HelmsRW. Comparisons of Parameter and Hypothesis Definitions in a General Linear Model. Comm Stat. 1988;A17 (No. 8):2725–2753.
3.
HelmsRW. Manipulating Statistical Hypotheses and Tests as Boolean Functions. Am Statis. 1988;42: 253–256.
4.
HelmsRonald W. Comparisons of Parameters and Hypotheses between Related Experimental Designs. Manuscript in draft form, available from the author. 1991.
5.
HelmsRonald W. Intentionally Incomplete Longitudinal Designs: I. Methodology and Comparison of Some Full Span Designs. Stat Med.1992;11: 1889–1913.
6.
HelmsRonald W. The Joy of Modeling: General Linear Models for the Analysis of Continuous Data. Copyrighted unpublished manuscript. Chapel Hill, NC: The University of North Carolina; 1991.
7.
GoldfarbN. An Introduction to Longitudinal Statistical Analysis. Glencoe, Illinois: Free Press; 1960.
8.
GoldsteinH. The Design and Analysis of Longitudinal Studies. New York: Academic Press; 1979.
9.
KowalskiCJGuireKE. Longitudinal Data Analysis. Growth. 1974;38: 131–169.
10.
LairdNMWareJH. Random Effects Model for Longitudinal Data. Biometrics. 1982;38: 963–974.
11.
CookNRWareJH. Design and Analysis Methods for Longitudinal Research. Ann Rev Pub Health. 1983;4: 1–23.
12.
WareJH. Linear Models for the Analysis of Longitudinal Studies. Am Statis. 1985;39: 95–101.
13.
BaltesPB. Longitudinal and Cross-Sectional Sequences in the Study of Age and Generation Effects. Hum Develop. 1968;11: 145–171.
14.
VollmerWMJohnsonLRMcCamantLEBuistAS. Longitudinal Versus Cross-Sectional Estimation of Lung Function Decline—Further Insights. Stat Med.1988;7: 686–696.
15.
Prahl-AndersonBKowalskiCJ. Mixed Longitudinal Interdisciplinary Study of the Growth and Development of Dutch Children. Growth. 1973;37: 281–295.
16.
van't HofMARoaedMJKowalskiCJ. A Mixed Longitudinal Data Analysis Model. Hum Biology. 1977;49: 165–179.
17.
RaoMNRaoCR. Linked Cross-Sectional Study for Determining Norms and Growth Rates. Sankyha. 1966;28: 237–258.
18.
MachinD. On a Design Problem in Growth Studies. Biometrics. 1975;31: 749–753.
19.
WoolsonRFLeeperJDClarkeWR. Analysis of Incomplete Data from Longitudinal and Mixed Longitudinal Studies. J Roy Statis Soc A. 1978;141: 242–252.
20.
WoolsonRFLeeperJD. Growth Curve Analysis of Complete and Incomplete Longitudinal Data. Comm Stat. 1980;A9:1491–1513.
21.
BergerMPF. A Comparison of Efficiencies of Longitudinal, Mixed Longitudinal, and Cross-Sectional Designs. J Educ Stat. 1986;11: 171–181.
22.
ClarkeWRWoolsonRF. Methodologic Issues in Linked Cross-Sectional Studies: Experiences from the Muscatine Study. American Statistical Association: Proceedings of the Section on Survey Research Methods; 1987.
23.
HelmsRW. Longitudinal Designs and Their Statistical Analysis in Pediatric Pulmonary Research. Pediatr Pulmonol. 1990;8: 72–73.
24.
DuncanGJKaltonG. Issues of Design and Analysis of Surveys Across Time. Int Statis Rev. 1987;55: 97–117.
25.
BennettCAFranklinNL. Statistical Analysis in Chemistry and the Chemical Industry. New York: John Wiley & Sons; 1954.
26.
CochranWGCoxOM. Experimental Designs. New York: John Wiley & Sons; 1950.
27.
SearleSR. Linear Models. New York: John Wiley & Sons; 1971.
28.
HockingRR. The Analysis of Linear Models. Monterey, CA: Brooks/Cole Publishing Company; 1985.
29.
AndradeDalton FHelmsRonald W. ML Estimation and LR Tests for the Multivariate Normal Distribution with General Linear Model Mean and Linear-Structure Covariance Matrix: K-Population, Complete-Data Case. Comm Stat Theory Meth. 1986;15(1):89–107.
30.
AndradeDalton FHelmsRonald W. ML Estimation for the Multivariate Normal Distribution with General Linear Mean and Linear-Structure Covariance Matrix: One Population, Complete Data Case. Comm Stat Theory Meth. 1986;15(6):1927–1955.
31.
FaircloughDLHelmsRW. A Mixed Linear Model with Linear Covariance Structure: A Sensitivity Analysis of the Maximum Likelihood Estimators. J Stat Comput Simula. 1986;25: 205–236.
32.
HarvilleDA. Maximum likelihood approaches to variance component estimation and to related problems. J Am Statis Assoc. 1977;72: 320–340.
33.
LairdNMLangeNStramD. Maximum Likelihood Computations with Repeated Measures: Application of the EM Algorithm. J Am Statis Assoc. 1987;82: 97–105.
34.
CallananTPHarvilleDA. Some New Algorithms for Computing Restricted Maximum Likelihood Estimates of Variance Components. J Statis Comput Simula. 1991;38: 239–259.
35.
McCarrollKHelmsRW. An Evaluation of Some Approximate F statistics and Their Small Sample Distributions for the Mixed Model with Linear Covariance Structure. Chapel Hill, NC: The Institute of Statistics Mimeo Series, Department of Biostatistics, University of North Carolina; 1987.
36.
HelmsRonald WKathleenMcCarrollComparisons of Approximate F Statistics and Their Small Sample Distributions for Fixed Effect Hypotheses in Mixed Models. Manuscript submitted for publication. 1991.
