Abstract Summary
The occurrence of significant second-order interactions for group characteristics was examined using real data in a randomized controlled trial (RCT). The interactions exist in all RCTs; they could be easily overlooked when using the simple randomization or stratification methods, but could become more obvious when minimization methods are used. Using real data from an RCT, the minimization method enabled balancing the distributions of the four selected stratified factors. Analyses for 3-way second-order interactions including 6 additional potential confounding variables (for a total of 10 variables) presented 8 significant second-order interactions with the treatment groups. Interaction effects need to be evaluated when treatment effects are examined to maximize the power of the treatment effects in any RCTs. A stepwise regression method with piecewise linear functions would be useful to select the significant variables with interaction effects affecting the treatment outcomes in RCTs. Additional ways to handle interaction effects in RCTs are presented in this paper.
Keywords: Second-Order Interactions, Minimization Random Allocation Method, RCTs
Introduction
The benefits and significance of evidence-based practice (EBP) have been widely acknowledged in the health care professions [1–3]. As research findings are used to advance the standards of care through EBP, reliable evidence from well-designed randomized clinical trials (RCTs) aimed at improved health outcomes is pivotal [2–3]. With the greater emphasis on the quality of RCTs, random allocation methods need to be examined more closely. In addition, as the scientific fields move forward, newly documented confounding variables identified for the population of interests on selected outcomes for the treatment effects need to be controlled by using more efficient random allocation methods. Thus, to advance the quality of RCT designs, the purpose of this paper is to present the real case examples with the confounding variables and their interactions with the treatment effects, using the computerized minimization method.
The random allocation of the research participants using the minimization method, and the occurrence of significant second-order interactions for group characteristics, were examined using real data in an RCT of high-risk mother-baby dyads. One hundred eighty eight dyads were randomly allocated into two groups using the minimization method, including four stratified variables selected based on prior studies in the population. Six additional variables (less significant, however could be additional confounders in the field) were used to examine the frequency of imbalance and magnitude of interactions in combinations. Three-way interactions (23 blocks) were computed by using multi-way contingency table analysis. The interactions exist in all RCTs; they could be easily overlooked when using the simple randomization or stratification methods, but could become more obvious when minimization methods are used. Interaction effects need to be evaluated when treatment effects are examined to maximize the power of the treatment effects in any RCTs.
Random Allocation
Random assignment of research participants into treatment conditions with blinding to the treatment is a significant quality indicator for the objectivity of the treatment effects in RCTs [4–7]. Random allocation is performed with the aim of balancing the distribution of confounding factors (variables) between two or more treatment groups. However, simple randomization cannot assure the balance of heterogeneous characteristics between and among groups, particularly when the sample size is fewer than 1,000 [8,9]. With the aid of computer programs, the minimization method not only enhances the objectivity of the random assignment; but also the feasibility of stratifying more than three binary confounding variables. This is the feasibility limit when using the stratified block randomization method [10]. The unbalanced covariates in an RCT would decrease the statistical power when comparing treatment effects. And, without balancing group confounders, erroneous conclusions could be derived [11,12]. Therefore, when additional confounding variables are identified for the outcomes, it is critical to balance and to control the newly documented confounding variables by using a more efficient random allocation method such as the minimization method.
Minimization Program
To enhance the quality and objectivity of the randomization, the computer-aided minimization method has been widely used to balance the confounding variables including subject characteristics between treatment groups in RCTs. Pocock and Simon’s minimization method and Zelen’s balancing method enable the balancing of each confounding factor (variable) between and among treatment subgroups over the entire duration of the trial [13–17]. The method was used increasingly in the 1990s due to the availability of computer programs [9]. The minimization method is more efficient than the simple random method and the stratified block randomization when measuring treatment effects, needing fewer subjects, by balancing confounding factors between and among treatment groups. Thus, a computer-aided minimization program can be used to not only balance the confounding variables, but to also enhance the objectivity, the efficiency, and the quality of randomization method for RCTs.
Three-Way or Second-Order Interactions in RCTs
The minimization method does not guarantee the balanced distribution of interactions of factors between the treatment groups, especially when additional significant confounding factors interacts with the treatment effects for the population of interests. However, the interaction effects can be more clearly presented when using the minimization method, to suggest the needed controls in the analyses and the stratifications for future RCTs. A binary variable such as “race status” includes two marginal cells of “White” and “Non-white”, or “multiple birth status” includes two marginal cells of “singleton” and “twins”. When these two binary variables are associated, there are 22 or 4 cells (blocks). In binary 3-factor interactions, a third binary variable “sex of newborns”, with two marginal cells of “boys” and “girls”, would yield 23 or 8 cells, including interactions between all 3 pairs of variables.
In RCTs, if the interaction of factors is overlooked, it could yield a serious bias in estimating the treatment effects. For example, two medications are examined in an RCT, the new drug (D1) and the standard drug (D2). D1 has a much greater effect on male gender with positive complications than the D2. As the simple random assignment could not achieve balanced groups in the RCT, if the male patients in the D1 group accidentally have more complications at considerable greater effects, the treatment effect of the D1 group would be overestimated with complications. In this case, the distributions of “gender” and “the status of complications” might be completely balanced between D1 and D2 using the minimization method, considering the significant interaction effects for the treatments within the RCTs. In addition, the interactions of treatment effects could be compared using multiple regression models such as a logistic regression model and Cox’s proportional hazards model [18]. Although the need to address these interaction effects has been mentioned, and it would become more obvious when using the minimization method [10,18]; to-date, however, limited reports have presented the interaction effects using the minimization method.
Methods
Random allocation was performed using a web-based minimization program [19] [Figure 1] in a study involving high-risk mother-baby dyads. The RCT lasted 5 years at three tertiary care centers located in two metropolitan areas where both high-risk pregnant mothers and newborns could be cared for [20]. A total of 353 mothers agreed and gave their consent to participate in the study, with 388 newborns that included 33 pairs of twins and 1 set of triplets. There were 239 premature births. Mean gestational age at birth was 31 weeks, and birth weight was 1672 grams. Mother’s mean ages were 25 years. To qualify for the study, high-risk infants without severe congenital defects had to be intubated with an endotracheal tube; needed ventilatory support with respiratory failures, and also umbilical central line catheters to assess oxygenation and supply nutrients. The treatment group had advanced central-line monitoring of body’s oxygenation status, and the control group had the routine peripheral only monitoring. The courses of oxygen support and oxygenation complications for the hospital stay were the outcome variables of the study. Some cases that were not included in the trial because of emergency admissions with uncertain prognosis for high-risk of death, or being cared for by the clinicians who were unable to coordinate with the computerized allocation due to their lack of familiarity with the treatment allocations.
Figure 1.
Web access to allocate subjects using minimization method, supported by Kyushu University Hospital, Japan, with login security.
Random Allocation
Using the computerized minimization programs, we randomly allocated 188 cases (see Table 1). Random allocation in this RCT was done using Pocock and Simon’s minimization method [13] and Zelen’s method [17]. Appropriate human subjects approvals were obtained from institutional review boards. High-risk newborn babies were enrolled immediately after birth, with informed consents obtained from parents and appropriate guardians prior to delivery or right after delivery when they were accessible. Both a web-based program [19] and a DOS program [9] were used for joint 24-hour accessibility. Subjects were enrolled using the web-based program most of time; the DOS minimization program was used as a supplemental access.
Table 1.
Balance of cases per groups for four minimization variables with different sample sizes:
| A.n = 55 | |||||
|---|---|---|---|---|---|
| Variables | Groups | Control | Experimental | Subtotal | Imbalance |
| Race | |||||
| Other | 16 | 16 | 32 | 0 | |
| White | 12 | 11 | 23 | 1 | |
| C-section | |||||
| No | 9 | 7 | 16 | 2 | |
| Yes | 19 | 20 | 39 | 1 | |
| Gestation Age, weeks | |||||
| ≤ 28 | 6 | 5 | 11 | 1 | |
| > 28 | 22 | 22 | 44 | 0 | |
| Multiple Birth Status | |||||
| Single | 26 | 22 | 48 | 4 | |
| Twins | 2 | 5 | 7 | 3 | |
| Total (% Total) | 28 (51%) | 27 (49%) | 55 (100%) | 12 (22%) | |
| B. n = 188 | |||||
| Race | |||||
| Other | 68 | 67 | 135 | 1 | |
| White | 26 | 27 | 53 | 1 | |
| C-section | |||||
| No | 36 | 36 | 72 | 0 | |
| Yes | 58 | 58 | 116 | 0 | |
| Gestation Age, weeks | |||||
| ≤ 28 | 30 | 30 | 60 | 0 | |
| > 28 | 64 | 64 | 128 | 0 | |
| Multiple Birth Status | |||||
| Single | 80 | 79 | 159 | 1 | |
| Twins | 14 | 15 | 29 | 1 | |
| Total (% Total) | 94 (50%) | 94 (50%) | 188 (100%) | 4 (2%) | |
The web-based program for the RCT was developed on the web server (UNIX workstation, SUN Microsystems SPARK Station 20), and the CGI script was written with PERL version 5.004 (Figure 1). The program was accessible to multiple users from clinical sites, and could be available through some carriers of wireless phone access to the website. The web-based program was designed with security features such as user authentication, firewall, and checking web contents to assure the confidentiality of the study subjects.
Four significant confounding variables were identified for the study outcomes, by reviewing the literature and by the results of an observational study [20–22]. These variables included race (white or other), delivery by cesarean (C-) section (yes or no), gestational age in weeks (≤28 weeks or > 28 weeks), and multiple-birth status (singleton or twins). To evaluate the interaction effects from these four variables and the treatment, a sample size of 160 subjects should be needed for this trial, for 4 binary factors in addition to the treatment group variable (with 5 subjects in each cell: 2×2×2×2×2×5 = 160 total subjects). Additional six variables were less significantly associated to neonatal outcomes in the observational study or less feasible to assess during emergency admissions. Thus, they were not chosen in the trial because of the limited sample size, considering the interaction effects. These factors include gender (boy or girl) and birth weight (≤1.5 Kg or > 1.5 Kg) of newborns; and prenatal vaginal bleeding (yes or no), prematurely ruptured membrane (yes or no), prenatal antibiotic treatments (yes or no), and prenatal steroid treatments (yes or no) of mothers.
Statistical Analysis
Statistical software [Statistical Package for Social Sciences (SPSS) and the Statistical Analysis System (SAS)] was used for the analysis. Three-way interactions (23 blocks) were computed by using multi-way contingency table analysis in the SAS program. To present the interaction effects, all 10 variables were analyzed for their potential interactions. Additional bivariate chi-square or Fisher’s exact tests (22 blocks) were performed within each treatment group to examine the post-hoc analyses for the variables that showed significant three-way interactions.
Results
Table 1 presents the balance of the factors and cell distribution at two stages of trial with respective sample sizes (A = at an early stage of the trial, B = at the completion stage). The values represent the extent of imbalances for the factors (Table 1 A & B). Respective imbalances were 22% of total subject dyads (12 for n = 55) at the early stage and only 2% of total dyads (4 for n = 188) at the completion stage of the trial. Thus, the imbalances for these strata-factors got smaller as the sample size increased.
Table 2 includes six additional variables that were not selected in the trial because they were less significantly associated with the health outcomes than the variables selected. The imbalance from these six additional variables was 40% of the total subject dyads (76 for n = 188). Among these additional variables, only prenatal steroid use of the mothers was significantly different between the treatment groups (P < 0.05).
Table 2.
Balance of cases per groups on additional five related variables as comparison (n = 188).
| Variables | Groups | Control | Experimental | Subtotal | Imbalance |
|---|---|---|---|---|---|
| Gender | |||||
| Boy | 54 | 49 | 103 | 5 | |
| Girl | 40 | 45 | 85 | 5 | |
| Birth Weight, Kg | |||||
| ≤ 1.5 | 46 | 54 | 100 | 8 | |
| > 1.5 | 48 | 40 | 88 | 8 | |
| Vaginal Bleeding | |||||
| No | 82 | 83 | 165 | 1 | |
| Yes | 12 | 11 | 23 | 1 | |
| Ruptured Membrane | |||||
| No | 66 | 63 | 129 | 3 | |
| Yes | 28 | 31 | 59 | 3 | |
| Prenatal Antibiotics | |||||
| No | 45 | 38 | 83 | 7 | |
| Yes | 49 | 56 | 105 | 7 | |
| Prenatal Steroid* | |||||
| No | 65 | 51 | 116* | 14 | |
| Yes | 29 | 43 | 72* | 14 | |
| Total (% Total) | 94 (50%) | 94 (50%) | 188 (100%) | 76 (40%) |
P < .05
Table 3 presents 42 P-values for three-way interactions using multi-way contingency table analysis, including the treatment groups and two other variables for the second-order interactions. Three-way interaction could not be computed in three situations where there were 0 frequencies (or lack of responses) in the following three combinations: multiple-birth and race (and the treatment groups), multiple-birth and prenatal vaginal bleeding (and the treatment groups), and gestational age and birth weight (and the treatment groups). Of the 42 possible combinations, 8 combinations denoted by asterisk (*) had significant interactions (P < 0.05, the distributions of the corresponding variables were significantly different between the treatment groups). Particularly, a significant interaction was detected in the combination of two stratified variables, multiple-birth and C-section (and the treatment groups).
Table 3.
Significant interactions (* P values listed) at 3 factorial levels (2×2×2 = 8 cells each) for listed paired variables and experimental groups.
| C-section | Race | Multiple | Weight | Age | Bleed | Rupture | Antib | Steroid | |
|---|---|---|---|---|---|---|---|---|---|
| Race | 0.964 | ||||||||
| Multiple | 0.008* | NA | |||||||
| Weight | 0.093 | 0.922 | 0.345 | ||||||
| Age | 0.940 | 0.455 | 0.365 | NA | |||||
| Bleed | 0.964 | 0.617 | NA | 0.001* | 0.082 | ||||
| Rupture | 0.746 | 0.988 | 0.002* | 0.194 | 0.691 | 0.022* | |||
| Antibiotics | 0.611 | 0.629 | 0.012* | 0.810 | 0.148 | 0.011* | 0.404 | ||
| Steroid | 0.869 | 0.902 | 0.591 | 0.849 | 0.286 | 0.518 | 0.372 | 0.772 | |
| Gender | 0.340 | 0.881 | 0.614 | 0.273 | 0.008* | 0.366 | 0.023* | 0.306 | 0.605 |
NA: 3-way interactions could not be calculated with lack of response in 1 of 8 cells
For the significant three-way interactions, additional bivariate Fisher’s exact tests were performed within each treatment subgroup for the post-hoc analyses of significance, to clarify the interaction effects. In Table 4, the variables that had significant interactions with multiple-birth status within the treatment groups were presented. In Table 5, variables that had significant interactions with prenatal vaginal bleeding status were presented. And, in Table 6, variables that had significant interactions with newborn gender were presented. To summarize the significant interactions presented in Table 4, more twins (as compared to singletons) in the treatment group (compared to the control group) had C-section; but more twins (rather than singletons) in the control group (compared to the treatment group) had prenatal premature rupture of membranes and antibiotics use.
Table 4.
Significant interactions for 3 factors and 2 factors within each group for multiple birth Status.
| Control | Experimental | P (2×2×2) | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Multiple status | P (2×2) | Multiple status | P (2×2) | |||||||
| Variables | Groups | Single | Twin | Subtotal | Single | Twin | Subtotal | |||
| C-Section | 0.829 | 0.03* | 0.008** | |||||||
| No | 31 | 5 | 36 | 34 | 2 | 36 | ||||
| Yes | 49 | 9 | 58 | 45 | 13 | 58 | ||||
| Race | 0.063 | 0.007** | NA | |||||||
| Other | 55 | 13 | 68 | 52 | 15 | 67 | ||||
| White | 25 | 1 | 26 | 27 | 0 | 27 | ||||
| Bleeding | 0.121 | 0.124 | NA | |||||||
| No | 68 | 14 | 82 | 68 | 15 | 83 | ||||
| Yes | 12 | 0 | 12 | 11 | 0 | 11 | ||||
| Rupture | 0.002** | 0.078 | 0.002** | |||||||
| No | 61 | 5 | 66 | 50 | 13 | 63 | ||||
| Yes | 19 | 9 | 28 | 29 | 2 | 31 | ||||
| Antibiotics | 0.117 | 0.092 | 0.012* | |||||||
| No | 41 | 4 | 45 | 29 | 9 | 38 | ||||
| Yes | 39 | 10 | 49 | 50 | 6 | 56 | ||||
| N Total | 80 | 14 | 94 | 79 | 15 | 94 | 188 | |||
p < .05,
P < .01;
NA: Not computable for lack of (or 0) responses in one of the cells.
The following pairs presented no responses in the factor cells: multiple-birth with race and multiple-birth with prenatal vaginal bleeding. These lack of responses were implicit from the uneven distributions (< 20% and > 80% responses) presented in Table 1 and Table 2. To summarize further the findings from Table 5, more newborns whose mothers had prenatal vaginal bleeding (as compared to those who did not) in the control group (compared to the treatment group) were bigger babies (> 1.5 Kg). In addition, more babies whose mothers had prenatal vaginal bleeding (as compared to those who did not) in the treatment group (compared to the control group) had mothers with prenatal premature rupture of membrane and antibiotics use. Furthermore, as presented in Table 6, more boys (than girls) in the treatment group (compared to the control group) were younger babies (≤28 weeks gestation) and had mothers with prenatal premature rupture of membrane. The differences of the distributions between groups had occurred by chance in this trial. These interactions could not have been avoided in any RCTs, but became clearer using the minimization method.
Table 5.
Significant interactions for 3 factors and 2 factors within groups for vaginal bleeding status.
| Control | Experimental | P (2×2×2) | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bleeding | P (2×2) | Bleeding | P (2×2) | |||||||
| Variables | Groups | No | Yes | Subtotal | No | Yes | Subtotal | |||
| Baby weight, Kg | 0.076 | 0.082 | 0.001*** | |||||||
| ≤1.5 | 43 | 3 | 46 | 45 | 9 | 54 | ||||
| > 1.5 | 39 | 9 | 48 | 38 | 2 | 40 | ||||
| Rupture | 0.287 | 0.105 | 0.022* | |||||||
| No | 56 | 10 | 66 | 58 | 5 | 63 | ||||
| Yes | 26 | 2 | 28 | 25 | 6 | 31 | ||||
| Antibiotics | 0.874 | 0.024* | 0.011* | |||||||
| No | 39 | 6 | 45 | 37 | 1 | 38 | ||||
| Yes | 43 | 6 | 49 | 46 | 10 | 56 | ||||
| N Total | 82 | 12 | 94 | 83 | 11 | 94 | 188 | |||
P < .05,
p < .001.
Table 6.
Significant interactions for 3 factors and 2 factors within groups for gender.
| Control | Experimental | p (2×2×2) | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Gender | p (2×2) | Gender | p (2×2) | |||||||
| Variables | Groups | Girl | Boy | Subtotal | Girl | Boy | Subtotal | |||
| Age, weeks | 0.148 | 0.296 | 0.008** | |||||||
| ≤ 28 | 16 | 14 | 30 | 12 | 18 | 30 | ||||
| > 28 | 24 | 40 | 64 | 33 | 31 | 64 | ||||
| Rupture | 0.159 | 0.212 | 0.023* | |||||||
| No | 25 | 41 | 66 | 33 | 30 | 63 | ||||
| Yes | 15 | 13 | 28 | 12 | 19 | 31 | ||||
| N Total | 40 | 54 | 94 | 45 | 49 | 94 | 188 | |||
P < .05,
P < .01.
Discussion
Efficient allocation programs for the treatment groups are needed for future RCTs to ensure the quality of RCTs and efficient designs. The minimization method is an efficient computerized random allocation method. It can be used to better control and balance potential confounding variables for the assessment of treatment effects. The occurrence of interactions among variables became clearer using the minimization method. Examination of interaction effects among variables could be useful in RCTs as interactions among variables could yield significant differences of the subject characteristics for the treatment effects.
When comparing treatment effects using univariate analysis (using logrank test for survival times and Fisher’s exact test for binary response for example), different distributions may not affect the comparisons of treatment effects. However, galloping alpha and multiple Bonferroni corrections would decrease the power of the treatment effects. In addition, when multivariate analysis such as Cox’s proportional hazards model and multiple logistic regression analysis is used to evaluate the treatment effects, the negligence of second-order interaction terms can lead to a serious bias in the evaluation of treatment effects [18]. Therefore, it is important to investigate the frequency and the magnitude of interactions of confounding variables in RCTs. Thus, the findings in this paper could provide valuable information to construct multivariate model for selecting significant strata to evaluate the treatment effects.
Second-order interaction terms have not always been taken into consideration when constructing multivariate models. Our study suggests that the second-order interactions could have significantly different distributions, and thus need to be considered for the models of analyses. For a practical statistical analysis, if there are ten confounding variables to be considered, the number of interaction terms generated by the combinations of three variables, is 45. This is a significant number of combinations to consider for any RCTs, but needs attention for potential interaction terms. As the scientific fields move forward with more reliable results from RCTs, there is a greater need for networking within similar fields to be familiar with related confounding variables and second-order interactions for the population of interests when examining the treatment effects.
In a regression analysis to evaluate treatment effects in clinical trials, researchers often use a forward or backward stepwise regression method to select the significant confounding variables in an RCT. Concrete examples for constructing a regression model including second-order interaction terms have been referred to in some references [18]. When the variables x1 and x2 are continuous or binary, the second-order interaction term can simply be created by the multiplication of x1 and x2. However, in clinical trials, some variables are often ordered, which have more than three categories. For example, a lymph node metastasis in cancer clinical trials has four categories, they are, 0:none, 1:slight, 2:intermediate, 3:severe. With the variables having four categories, the second-order interaction terms can be created by the products of piecewise linear functions < x1 – i > and < x2– j >, where < x1 – i >= {(x1 – i)+| x1 – i |}/2; the suffix i and j indicate the i-th category of x1 and the j-th category of x2, respectively [24].
Future Plans
A minimization method has demonstrated its efficiency for quality random allocation method in RCTs, as the best method to balance the distribution of confounding factors between and among the treatment groups. The occurrence of significant interactions cannot be avoided in any RCTs, but will become clearer when using a minimization method. Therefore, interactive effects of the confounding factors for the population of interest must be considered when evaluating the treatment effects in RCTs. Once the interaction effects of the confounding variables have been identified within the treatment groups, future RCTs using the minimization method could design the trials to include the interactive cells between the two strata as additional factors for outcome evaluations. A stepwise regression method with piecewise linear functions would be useful to select the significant interactions affecting the outcomes in RCTs [18,24]. In this era of international collaboration, a web-based minimization program enables the balancing of the significant confounding variables, for a more efficient design and better quality RCTs. As wireless telephone technology has become conveniently available in recent years to access websites, a web-based program will be an excellent resource for multi-site studies to balance cases more efficiently in experiments.
Acknowledgments
This study is supported in part, by a grant from the National Institutes of Health, R01-NR04447. The authors would also like to acknowledge 1). Dr. Gene C. Anderson, a consultant on the study, making the DOS Minimization software program available; 2). Technical support from Ms. Yuko Kenjo and Mr. Yasuaki Antoku at Medical Information Center, Kyushu University, and Grant-in-aid from Niigata University Research Foundation, Japan, establishing a website access for random allocation of subjects using the minimization method; 3). Systems support from Mr. Bryan Hillier at the University of Texas-Houston Health Science Center; and 4) Editorial read from Dr. Sajiv Behl at the University of Houston Victoria.
Footnotes
Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Contributor Information
Shyang-Yun Pamela K. Shiao, M. G. & Lillie A. Johnson Professor of Nursing University of Houston Victoria University of Houston System at Sugar Land.
Chul W. Ahn, Professor, Department of Medicine, School of Medicine University of Texas Health Science Center at Houston.
Kouhei Akazawa, Professor, Department of Medical Informatics, Niigata University Medical Hospital, Japan.
References
- 1.Fliedner MC. Research within the field of blood and marrow transplantation nursing: how can it contribute to high quality of care? Int J Hematol. 2002;76 (Suppl 2):289–291. doi: 10.1007/BF03165135. [DOI] [PubMed] [Google Scholar]
- 2.Levitt SH, Aeppli D, Nierengarten MB. Evidence-based medicine: Its effect on treatment recommendation as illustrated by the changing role of postmastectomy irradiation to treat breast cancer. Int J Radiation Oncology Biol Phys. 2003;55:645–650. doi: 10.1016/s0360-3016(02)04076-2. [DOI] [PubMed] [Google Scholar]
- 3.Moher D, Cook DJ, Eastwood S, Olkin I, Rennie D, Stroup DF. Improving the quality of reports of meta-analyses of randomized controlled trials: the QUOROM statement. Lancet. 1999;354:1896–1900. doi: 10.1016/s0140-6736(99)04149-5. [DOI] [PubMed] [Google Scholar]
- 4.Allmark P, Mason S, Gill AB, Megone C. Is it in a neonate’s best interest to enter a randomized controlled trial? J Med Ethics. 2001;27:110–113. doi: 10.1136/jme.27.2.110. [DOI] [PMC free article] [PubMed] [Google Scholar]
- 5.Coalition for Critical Care Excellence. Consensus Conference on Physiologic Monitoring Devices: Standards of evidence for the safety and effectiveness of critical care monitoring devices and related interventions. Crit Care Med. 1995;23:1756–1763. doi: 10.1097/00003246-199510000-00022. [DOI] [PubMed] [Google Scholar]
- 6.Koski G. Research ethics and the intensive care unit: Getting behind the wheel. Crit Care Med. 2003;31 (Suppl 3):S119–120. doi: 10.1097/00003246-200303001-00001. [DOI] [PubMed] [Google Scholar]
- 7.Randolph AG, Lacroix J. Randomized clinical trials in pediatric critical care: Rarely done but desperately needed. Pediatr Crit Care Med. 2002;3(2):102–106. doi: 10.1097/00130478-200204000-00002. [DOI] [PubMed] [Google Scholar]
- 8.Therneau TM. How many stratification factors are “too many” to use in a randomization plan? Control Clin Trials. 1993;14:98–108. doi: 10.1016/0197-2456(93)90013-4. [DOI] [PubMed] [Google Scholar]
- 9.Conlon M, Anderson GC. Three methods of random assignment: Comparison of balance achieved on potentially confounding variables. Nurs Res. 1990;39:376–379. [PubMed] [Google Scholar]
- 10.Pocock SJ. Clinical trials; A practical approach. Wiley; Chickchester: 1983. Methods of randomization in clinical trials; pp. 66–89. [Google Scholar]
- 11.Kinukawa N, Nakamura T, Akazawa K, Nose Y. The impact of covariate imbalance on the size of the logrank test in randomized clinical trials. Stat Med. 2000;19:1955–1967. doi: 10.1002/1097-0258(20000815)19:15<1955::aid-sim507>3.0.co;2-5. [DOI] [PubMed] [Google Scholar]; Pocock SJ. Clinical trials; A practical approach. Wiley; Chichester: 1983. Methods of randomization in clinical trials; pp. 66–89. [Google Scholar]
- 12.Weir JC, Lees KR. Comparison of stratification and adaptive methods for treatment allocation in an acute stroke trial. Stat Med. 2003;22:705–726. doi: 10.1002/sim.1366. [DOI] [PubMed] [Google Scholar]
- 13.Pocock SJ, Simon RM. Sequential treatment assignment with balancing prognostic factors in the controlled clinical trials. Biometrics. 1975;31:103–115. [PubMed] [Google Scholar]
- 14.Pocock SJ. Allocation of patients to treatment in clinical trials. Biometrics. 1979;35:183–197. [PubMed] [Google Scholar]
- 15.Scott NW, McPherson GC, Ramsay CR, Campbell MK. The method of minimization for allocation to clinical trials: A review. Control Clin Trials. 2002;23:662–674. doi: 10.1016/s0197-2456(02)00242-8. [DOI] [PubMed] [Google Scholar]
- 16.Taves DR. Minimization: A new method of assigning patients to treatment and control groups. Clin Pharmacol The. 1974;15:443–453. doi: 10.1002/cpt1974155443. [DOI] [PubMed] [Google Scholar]
- 17.Zelen M. The randomization and stratification of patients to clinical trials. J Chron Dis. 1974;27:365–375. doi: 10.1016/0021-9681(74)90015-0. [DOI] [PubMed] [Google Scholar]
- 18.Akazawa K, Nakamura T, Palesch Y. Power of logrank test and Cox regression model in clinical trials with heterogeneous samples. Stat Med. 1997;16:583–97. doi: 10.1002/(sici)1097-0258(19970315)16:5<583::aid-sim433>3.0.co;2-z. [DOI] [PubMed] [Google Scholar]
- 19.Kenjo Y, Antoku Y, Akazawa K, Hanada E, Kinukawa N, Nose Y. An easily customized, random allocation system using minimization method for multi-institutional clinical trials. Comput Meth Prog Biomed. 2000;62:45–49. doi: 10.1016/s0169-2607(99)00047-4. [DOI] [PubMed] [Google Scholar]
- 20.Shiao S-YPK, Andrews CM, Helmreich BH. Maternal race/ethnicity and predictors of pregnancy and infant outcomes. Bio Res Nur. 2005;7:55–66. doi: 10.1177/1099800405278265. [DOI] [PubMed] [Google Scholar]
- 21.Shiao S-YPK, Andrews CM, Ahn CW. Predictors of intubation and oxygenation complications in neonates. Newborn Infant Nurs Rev. 2002;2(2):128–137. [Google Scholar]
- 22.Shiao S-YPK, Andrews CM, Ahn CW. Ventilatory support and predictors of hospital stay in neonates. Newborn Infant Nurs Rev. 2003;3(4):166–172. [Google Scholar]
- 23.Hosmer DW, Lemeshow S. Applied survival analysis. John Wiley & Sons; New York: 1999. pp. 134–136. [Google Scholar]
- 24.Nakamura T, Akazawa K, Kinukawa N, Nose Y. Statistics for the Environment 4. Wiley; New York: 1999. Piecewise linear Cox model for estimating relative risks adjusting for the heterogeneity of the sample; pp. 281–289. [Google Scholar]