The ability to evaluate effects of factors on outcomes is increasingly important for studies that control some but not all of the factors. Although important advances have been made in methods of analysis for such partially controlled studies, work on designs has been limited. To help understand why, we review the main designs that have been used for such partially controlled studies. Based on the review, we give two complementary reasons that explain the limited work on such designs, and suggest a new direction in this area.
Zelen M.A new design for randomized clinical trials . New England Journal of Medicine1979; 300: 1242-1245 .
3.
Sommer A , Zeger S.On estimating efficacy from clinical trials . Statistics in Medicine1991; 10: 45-52 .
4.
Connor R , Prorok PC , Weed DL.The case-control design and the assessment of the efficacy of cancer screening . Journal of Clinical Epidemiology1991; 44: 1215-1221 .
5.
Imbens GW , Rubin DB.Causal inference with instrumental variables. Discussion paper # 1676. Cambridge, MA: Harvard Institute of Economic Research , 1994.
6.
Robins JM , Greenland S.Adjusting for differential rates of prophylaxis therapy for PCP in high - versus low-dose AZT treatment arms in an AIDS randomized trial . Journal of the American Statistical Association1994; 89: 737-749 .
7.
Angrist J , Imbens GW , Rubin DB.Identification of causal effects using instrumental variables (with discussion) . Journal of the American Statistical Association1996; 91: 444-472 .
8.
Imbens GW , Rubin DB.Bayesian inference for causal effects in randomized experiments with noncompliance . Annals of Statistics1997; 25: 305-327 .
9.
Goetghebeur E , Molenberghs G.Causal inference in a placebo-controlled clinical trial with binary outcome and ordered compliance . Journal of the American Statistical Association1996; 91: 928-934 .
10.
Baker SG.Analysis of survival data from a randomized trial with all-or-none compliance: estimating the cost-effectiveness of a cancer screening program . Journal of the American Statistical Association1998; 93: 929-934 .
11.
Barnard J , Frangakis CE , Hill JL , Rubin DB.A Principal Stratification approach to broken randomized experiments: a case study of School Choice vouchers in New York City . Journal of the American Statistical Association2003; 98: 299-323 (with discussion).
12.
Joffe MM , Colditz GA.Restriction as a method for reducing bias in the estimation of direct effects . Statistics in Medicine1998; 17: 2233-2249 .
13.
Frangakis CE , Rubin DB.Principal stratification in causal inference . Biometrics2002; 58: 21-29 .
14.
Palmgren J.Models for direct and indirect effects of exposure on response . The 19th Nordic conference on mathematical statistics, 2002, Stochholm, Sweden. NORDSTAT 2002 (abstract).
15.
Gilbert PB , Bosch RJ , Hudgens MG.Sensitivity analysis for the assessment of causal vaccine effects on viral load in AIDS vaccine trials . Biometrics2003; 59: 531-541 .
16.
Rubin DB.Direct and indirect causal effects via potential outcomes . Scandinavian Journal of Statistics2004; 31: 161-170 (with discussion).
17.
Rubin DB.Bayesian inference for causal effects . Annals of Statistics1978; 6: 34-58 .
18.
Card D.Using geographic variation in college proximity to estimate the return to schooling. National Bureau of Economic Research 1993; Paper No. 4483.
19.
McClellan M , McNeil BJ , Newhouse JP.Does more intensive treatment of acute myocardial infarction in the elderly reduce mortality? Analysis using instrumental variables . Journal of the American Medical Association1994; 272: 859-866 .
20.
Frangakis CE , Rubin DB.Addressing complications of intention-to-treat analysis in the presence of all-or-none treatment-noncompliance and subsequent missing outcomes . Biometrika1999; 86: 365-379 .
21.
Zhang JN , Rubin DB.Estimation of causal effects via principal stratification when some outcomes are truncated by ‘Death’ . Journal of Educational and Behavioural Statistics2003; 28: 353-368 .
22.
Loeys T , Goetghebeur E.A causal proportional hazards estimator for the effect of treatment actually received in a randomized trial with all-or-nothing compliance . Biometrics2003; 59: 100-105 .
23.
O’Malley J , Normand S-LT.Likelihood methods for accounting for all-or-nothing treatment non-compliance and subsequent non-response in randomized clinical trials . Biometrics2005 (in press).
24.
Rubin DB.Estimating causal effects of treatments in randomized and nonrandomized studies . Journal of Educational Psychology1974; 66: 688-701 .
25.
Lee S-J , Zhang Y , Lee SDet al.Targeting prostate cancer with conditionally replicative adenovirus using PSMA enhancer . Molecular Therapy2004; 10: 1051-1058 .
26.
Baker SG , Lindeman KS.The paired availability design: a proposal for evaluating epidural analgesia during labor . Statistics in Medicine1994; 13: 2269-2278 .
27.
Cuzick J , Edwards R , Segnan N.Adjusting for non-compliance and contamination in randomized clinical trials . Statistics in Medicine1997; 16: 1017-1029 .
Card D , Krueger AB.Minimum wage and employment: a case study of the fast-food industry in New Jersey and Pennsylvania . American Economic Review1994; 84: 772-793 .
Rosenbaum PR , Rubin DB.The central role of the propensity score in observational studies for causal effects . Biometrika1983; 70(1): 41-55 .
33.
Hill JL , Rubin DB , Thomas N.The design of the New York School Choice Scholarship Program Evaluation. In: Bickman L ed. Donald Campbell’s Legacy. New York: Sage Publications , 2000.
34.
Rubin DB , Thomas N.Matching using estimated propensity scores: relating theory to practice . Biometrics1996; 52: 249-264 .
35.
Jo B.Power to detect intervention effects in randomized trials with noncompliance. Technical Report, Graduate School of Education and Information Studies, UCLA , 1999.
36.
Jo B.Statistical power in randomized intervention studies with noncompliance . Psycological Methods2002; 7: 178-193 .
37.
Frangakis CE , Baker SG.Compliance sub-sampling designs for comparative research: estimation and optimal planning . Biometrics2001; 57: 899-908 .
38.
West KP Jr , Katz J , Shrestha SRet al.Mortality of infants <6 mo of age supplemented with vitamin A: a randomized, double-masked trial in Nepal . American Journal of Clinical Nutrition1995; 62: 143-148 .
39.
Korhonen P , Loeys T , Goetghebeur E , Palmgren J.Vitamin A and infant mortality: beyond intention-to-treat in a randomized trial . Lifetime Data Analysis2000; 6: 107-121 .
40.
Loeys T , Vansteelandt S , Goetghebeur E.Accounting for correlation and compliance in cluster randomized trials . Statistics in Medicine2001; 20: 3753-3767 .
41.
Frangakis CE , Rubin DB , Zhou XH.Clustered encouragement design with individual noncompliance: Bayesian inference and application to Advance Directive Forms . Biostatistics2002; 3: 147-164 (with discussion).
42.
Rosenbaum PR , Rubin DB.Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome . Journal of the Royal Statistical Society B1983; 45: 212-218 .
43.
Scharfstein DO , Rotnitzky A , Robins JM.Adjusting for nonignorable drop-out using semiparametric nonresponse models . Journal of the American Statistical Association1999; 94: 1096-1146 (with discussion).
44.
Li F , Frangakis CE , Varadhan R.Polydesigns in causal inference: definition and motivation . In Proceedings of the Biopharmaceutical Section of the American Statistical Association2003; 2404-2408 .
