European Journal of Clinical Nutrition (2015), 1–7 © 2015 Macmillan Publishers Limited All rights reserved 0954-3007/15 www.nature.com/ejcn

ORIGINAL ARTICLE

Estimating the causal effect of milk powder supplementation on bone mineral density: a randomized controlled trial with both non-compliance and loss to follow-up Y Chen, Q Zhang, Y Wang, Y Xiao, R Fu, H Bao and M Liu BACKGROUND/OBJECTIVES: Although previous studies reported that calcium supplementation can effectively improve bone mineral density in postmenopausal women, some studies showed the reverse conclusion. One of the reasons was that most of the studies did not take into full consideration the information of noncompliers, which seriously influenced the precision of conclusion. The aim of this paper was to investigate the effect of calcium supplementation on bone mineral density with correcting impact of noncompliance using the complier average causal effect (CACE). SUBJECTS/METHODS: A randomized controlled trial was designed to investigate the effect of high-calcium milk powder on bone mineral density. One hundred and forty-one postmenopausal women were randomly assigned to either a control group (n = 72) or a milk powder supplementation group (n = 69). The participants in the intervention group took 50 g of high-calcium milk powder containing 450 mg of elemental calcium and 400 IU vitamin D every morning and evening, respectively. The effects of the intervention on the primary outcome, bone mineral density, were assessed using the CACE model and intention-to-treat (ITT) and per-protocol (PP) analyses. RESULTS: Using the CACE model, the calcium supplementation was found to significantly reduce the bone loss at the lumbar spine compared with the control group at 24 months when adjusting the covariates (effect size 1.170, 95% confidence interval (CI) 0.376 ~ 1.964, P = 0.0040). At the hip site, there was no significant difference between the calcium group and the control group. Compared with the control group, no significant weight gain was found in the calcium group over 24 months. However, the calcium group had less height loss at 24 months (effect size 1.040, 95% CI 0.012 ~ 2.066, P = 0.0470) than the control group. High-density lipoprotein was significantly increased in the calcium group at 12 months (effect size 0.120, 95% CI 0.009 ~ 0.232, P = 0.0340). Serum total cholesterol, triglyceride and low-density lipoprotein were not affected over 24 months. The estimates of complier average causal effect of latent ignorability model with missing data assumption of latent ignorability were consistent with the CACE estimates. CONCLUSION: Consumption of high-calcium milk powder is effective in reducing the bone loss at the lumbar spine among healthy postmenopausal women. Supplementing with high-calcium milk powder had additional benefits of reducing height loss. European Journal of Clinical Nutrition advance online publication, 28 January 2015; doi:10.1038/ejcn.2015.3

INTRODUCTION Osteoporosis has been a major public health problem in the world. Rapidly aging population of the world suggests that the prevalence of osteoporosis and incidence of fracture will increase considerably.1 Therefore, it is imperative to take indispensable intervention to retard bone loss. Although many literatures have reported that calcium supplementation is effective in improving bone mineral density in postmenopausal women, reverse conclusion has more or less been made.2 It limits clear public health strategy to be made. Treatment effect of calcium supplementation is relative to the dose of calcium supplementation, dietary calcium intake, vitamin D and vitamin K supplementation, lifestyle changes and years since menopause.3–5 More importantly, nonadherence to treatment protocol affected severely real treatment effect to be estimated. However, most of the studies having been reported did not take into full consideration the information of noncompliers, which seriously influenced the precision of conclusion. In practice, many randomized trials with human subjects often suffer from two major complications, namely noncompliance

to treatment assignment and loss to follow-up.6–10 For the randomized trials with noncompliance, the gold-standard approach is intention-to-treat analysis (ITT).6,7,11 ITT analysis includes all randomized subjects in the assigned groups, regardless of their adherence with the treatment or deviation from the protocol. Although ITT analysis preserves the benefits of randomization, it focuses on the causal effect of assignment of treatment rather than the causal effect of receipt of treatment, which is the interest of researchers.11–13 Another commonly used analytic method, per-protocol analysis (PP), typically excludes the participants who do not comply with the treatment protocol.14 However, exclusion of participants from the analysis in this way can lead to selection bias and a reduced sample size. Therefore, neither standard ITT analysis nor PP analysis would provide unbiased estimates of treatment effects in the presence of noncompliance.9,10,15 Considering the limitations of the ITT and PP analyses, a method of estimating treatment effects only for compliers has been explored, namely complier average causal effect (CACE).6,10,16 According to the rationale of principal stratification, participants

Department of Biostatistics, Public Health College, Harbin Medical University, Harbin City, China. Correspondence: Professor M Liu, Department of Biostatistics, Harbin Medical University, Baojian Road 157, Harbin City 150086, China. E-mail: [email protected] Received 1 October 2014; revised 9 December 2014; accepted 29 December 2014

Estimating the causal effect of milk powder supplementation on BMD Y Chen et al

2 are divided into the following four strata: compliers, never-takers, always-takers and defiers.16–18 CACE model only focuses on the compliers. Under a series of statistical assumptions, CACE inferred the information of noncompliers according to the information of compliers. When the assumptions hold, CACE estimation can provide an unbiased and robust estimate of treatment effects for the compliant participants.10,19 In general, CACE can be represented as the treatment effect from the ITT analysis divided by the proportion of compliers.19,20 Although many literatures have been reported to use CACE to analyze the trials subjected to noncompliance, they are mainly limited to the areas of sociology and psychology; none of medical researchers used it.19–22 The aim of this paper is to apply the CACE analysis to a trial in medical research and explore the impact of noncompliance on estimates of treatment effect and the effect of baseline covariates on CACE. As assumptions about missing data are important, the mechanism of latent ignorability missing data was assumed in this paper.18 MATERIALS AND METHODS The study protocol and long-term follow-up were approved by the research ethics committee of the Harbin Medical University. All subjects provided written informed consent.

Subjects and randomization The calcium supplementation trial was a randomized controlled and double-blind trial, which was designed to investigate the effect of calcium supplementation on bone mineral density (BMD) in postmenopausal Chinese women. In Harbin City, China, the Hongqi Community Health Center was randomly selected as the target community from all teaching community hospitals of the Harbin Medical University. In this community, 373 volunteers were randomly recruited and those who met the inclusion criteria would enter into the study. The inclusion criteria were that postmenopausal women must be between 50 and 65 years of age at the time of the study and have lived in Harbin for at least 5 years. The subjects were excluded if they: (i) had disorders of calcium metabolism or calcium absorption; (ii) had disorders of the bone; (iii) had gastrointestinal disease, coronary heart disease, stroke, diabetes, cancer, thyroid or parathyroid disease, chronic liver disease or chronic kidney disease; (iv) suffered from ovarian surgery, premenopausal hysterectomy, gastric resection and thyroidectomy; (v) used estrogen at the time of the study or had taken drugs for a month or more; (vi) were milk powder intolerant; (vii) and were likely to migrate. Finally, 282 women were enrolled in the study. According to baseline T score of the spine, all participants were randomly assigned to four treatment groups (A, B, C and D) by block randomization. A, B and C were the calcium supplementation groups and D was the control group. The participants of three calcium supplementation groups received 50 g of high-calcium milk powder containing 400 IU vitamin D every morning and evening, respectively. Each 50 g of milk powder contains 300, 150 and 450 mg of calcium, respectively. For a trial with a control group and more than one intervention groups, CACE estimation is more complicated and suffers from more principal compliance categories and complicated identifiability assumptions.11 Therefore, in this paper, 141 subjects were analyzed involving an intervention group (C group, N = 69) and a control group (D group, N = 72). The C group was selected to investigate the effect of calcium supplementation as the subjects of this group received the most calcium. The participants of the intervention group were instructed to take 50 g of high-calcium milk powder every morning and evening, respectively. Each 50 g of milk powder contains 450 mg of calcium and 400 IU vitamin D. The participants of the control group continued with their usual diet and did not receive any placebo.

Follow-up The participants were followed up for 2 years and visited at baseline, 1 and 2 years, respectively. Data on BMD, food frequency, blood specimens of morning fast and urine of 24 h were collected. Data of food frequency were collected using the Food Frequency Questionnaire, which was designed in a case report form. At baseline, subjects were interviewed about their demographic and socioeconomic background, food frequency, past medical history, European Journal of Clinical Nutrition (2015) 1 – 7

reproductive and menstrual history, past physical activity level, calcium tablets and vitamin D supplementation, and mentality and reply. At 1 and 2 years, the same contents were involved, except past medical history and reproductive and menstrual history. The participants were faceto-face interviewed by trained investigators using a structured and validated questionnaire. Each subject recalled the diet of the past year with the help of estimating portion size through detailed pictorial information. The dietary nutrient intake was estimated using the 3-day food records, such as energy, protein, calcium, vitamin D and other microelements.

Outcome measurements The primary outcome was the BMD, which was measured by dual-energy X-ray absorptiometry (Norland Corp, Cranbury, NJ, USA) in Harbin Orthopedics Hospital. Measurements were taken at the following sites: the lumbar spine (L2–L4), the hip (femoral neck, greater trochanter and Ward’s triangle) and the total body. The primary indicators of BMD include T-score, Z-score, the absolute value of BMD and bone mineral contents. T-score is based on s.d. scores expressed in relation to reference data in normal premenopausal women, which would avoid problems associated with differences in calibration between instruments. In addition, it is used in preference to Z-score (agerelated s.d. units).23 In this study, T-score was used as the primary outcome.

Definition of compliance Throughout the study, the subjects in the intervention group were instructed to record their milk powder intake every day. The records and empty pouch were returned per two and half months and then the next batch of milk powder was provided. According to the records and returned pouch, compliance of each subject was determined. If the records of someone did not comply with the treatment protocol or the number of empty pouch was not consistent with the true number, she would be considered as a noncomplier. In addition, subject who did not get milk powder on time from the researchers would also be considered as a noncomplier. In this study, all-or-none treatment noncompliance was assumed. One would be always deemed as a noncomplier in this study even when she did not comply with the treatment protocol for one time.

Statistical analysis Data were reported as means ± s.d.'s for continuous variables and frequency (percent) for categorical variables. Differences of baseline characteristics between two groups were compared using the t-test for continuous normal variables, Χ2-test for categorical data and Wilcoxon test for non-normally distributed continuous variables. Fisher’s exact test was used when numbers were too small for the Χ2-test. The same approaches were used to test the differences between compliers and noncompliers in the intervention group for all baseline characteristics. The effect of treatment based on ITT and PP analyses was estimated using linear regression analysis adjusted for baseline covariates of dietary calcium intake, waist hip ratio (WHR), years since menopause, baseline T-score of the spine or hip, calcium tablet supplementation, vitamin supplementation, drinking tea, drinking coffee and drinking sodas. The differences between the compliers of the intervention group and the would-be compliers in the control group were calculated with CACE models. To obtain a CACE estimate, a generalized linear latent and mixed model was used with the gllamm command in STATA.24 The CACE model estimated the compliers in the control group and compared these to the observed compliers in the intervention group to estimate the CACE. Another CACE model including baseline covariates associated with the two responses, compliance status and outcomes, was fitted and compared with a null model using the likelihood ratio test. The compliance part of the model was adjusted for dietary calcium intake, years since menopause, WHR, calcium tablet supplementation, vitamin supplementation, drinking tea, drinking coffee and drinking sodas, which may be associated with compliance. The outcome part of the model was adjusted for dietary calcium intake, years since menopause, calcium tablet supplementation, vitamin supplementation, baseline T-score of the spine or hip, drinking tea, drinking coffee and drinking sodas, which may have effect on the BMD. As the missing mechanism of latent ignorability was assumed, a CACELI model based on latent ignorability was fitted to explore the impact of missing data. A range of outcomes were analyzed at one year and two years, and Bonferroni was used to adjust the P value. All tests were two-tailed. A 5% level was used to test the level of significance. All analyses were conducted using STATA v12.1 and the programs of SAS v9.2 (SAS Institute Inc., Cary, NC, USA). © 2015 Macmillan Publishers Limited

Estimating the causal effect of milk powder supplementation on BMD Y Chen et al

RESULTS Baseline characteristics In this study, the mean age of all participants was 55.9 ± 3.9 years, height was 158.2 ± 5.2 cm, weight was 62.0 ± 8.8 kg, WHR was 0.9 ± 0.1, daily dietary calcium intake was 511.2 ± 169.2 mg/day (from 3-day food records), years since menopause was 5 ± 6 years, T-score of the spine was −1.8 ± 2.0, T-score of the hip was −0.9 ± 1.5, triglyceride was 1.4 ± 1.3 mmol/l, total cholesterol was 5.0 ± 0.9 mmol/l, high-density lipoprotein was 1.4 ± 0.3 mmol/l and low-density lipoprotein was 2.3 ± 0.6 mmol/l. Dietary calcium intake was from daily diet rather than calcium supplementation. Calcium intake from calcium supplementation was 900 mg/day for the calcium supplementation group and none for the control group. All baseline characteristics were balanced between two groups except dietary calcium intake (P = 0.0171) and calcium tablet supplementation (P = 0.0361; Figure 1). About 66.0% (93 out of 141) randomized participants provided the 2-year follow-up data, 54.2% for the control group and 78.3% for the intervention group. In the intervention group, 14 out of 69 (20.3%) participants who did not comply with the treatment protocol were considered as the noncompliers. The primary reasons of noncompliance were illness and moving away from Harbin. In the second year, 46 out of 55 (83.6%) compliers and 8 out of 14 (57.1%) noncompliers provided data on the outcome measurements. Therefore, noncompliers were more likely to become lost to follow-up with borderline significance (P = 0.0632). Complier characteristics Table 1 shows the baseline characteristics of compliers and noncompliers in the intervention group. In an univariate analysis, none of the variables were significantly different between the compliers and noncompliers, except total cholesterol (P = 0.0077) and WHR (P = 0.0495). WHR was significantly associated with compliance in a multivariate logistic regression (P = 0.0223). Table 2 shows the mean change of T-score and secondary outcomes from baseline in the control group and compliers and noncompliers of the intervention group. Compared with noncompliers, the following were significant changes in the compliers over 24 months: for T-score of the spine, 0.28 ± 0.64, 95% CI: (0.08, 0.47) in the compliers and 0.05 ± 0.56, 95% CI: (−0.54, 0.64) in the noncompliers in the first year; for weight, −1.06 ± 3.39,

Figure 1. Comparison of baseline characteristics between the calcium supplementation group and the control group. © 2015 Macmillan Publishers Limited

95% CI: (−2.03, −0.08) in the compliers and −0.31 ± 3.10, 95% CI: (−2.91, 2.28) in the noncompliers in the second year; for height, 0.26 ± 1.34, 95% CI: (−0.14, 0.65) in the compliers and −0.93 ± 0.95, 95% CI: (−1.72, −0.13) in the noncompliers in the first year; for total cholesterol, 0.02 ± 0.74, 95% CI: (−0.20, 0.23) in the compliers and 0.59 ± 0.63, 95% CI: (0.06, 1.11) in the noncompliers in the first year. Changes of T-score and the secondary outcomes over time Table 3 shows the changes of T-score and biochemical indices over time in the control group and the calcium supplementation group. T-score of the spine significantly increased from baseline in the control group (P = 0.0489) and the calcium supplementation group (P = 0.0064) in the first year. However, there were no significant changes in the second year in the two groups. T-score of the hip in the control group significantly decreased in the first and second year. In contrast, there were no significant changes in the calcium supplementation group in the first and second year. High-density lipoprotein significantly decreased in the control group in the second year (P = 0.0400) and increased in the calcium supplementation group in the first year (P o0.0001). Low-density lipoprotein significantly increased in the two groups in the first and second year. The changes of dietary calcium intake, height and weight over time in the control group and the calcium supplementation group were shown in Table 4. Dietary calcium intake in the two groups significantly decreased from baseline in the first and second year. Weight in the two groups significantly decreased from baseline in the second year. Estimates of treatment effect based on the CACE model Table 5 shows the estimates of treatment effect based on the CACE model. For T-score of the spine, in absence of covariates, the estimated treatment differences for the compliers were 0.009 (P = 0.9850) in the first year and −0.154 (P = 0.7460) in the second year, respectively. However, with covariates, the estimated treatment differences were −0.346 (P = 0.3480) in the first year and 1.170 (P = 0.0040) in the second year, respectively. More importantly, there was significant difference between the compliers of the control group and the intervention group in the second year. In addition, the positive treatment effect (1.170) confirmed that milk powder supplementation improved BMD. For T-score of the hip, there was no significant difference between the two groups over 24 months. The s.e.'s of estimates reduced substantially in the first and second year. Latent ignorability was assumed to explore the effect of missing data on CACE. The results of the CACELI model were consistent with those of the CACE model, including the estimated treatment effect, s.e. and P-value. This indicated that the missing mechanism of latent ignorability was reasonable. Covariate adjustment in the CACE model and CACELI model provided a statistically significant better fit for all models (likelihood ratio test Po0.05 for all models). The estimated effect of calcium supplementation on the secondary outcomes was shown in Table 6. The calcium supplementation group did not experience any significant weight gain over 24 months compared with the control group. Height loss was less in the calcium supplementation at 24 months than the control group (P = 0.0470). Calcium supplementation increased significantly the high-density lipoprotein at 12 months (P = 0.0340). The total cholesterol, triglyceride and low-density lipoprotein were not affected by calcium supplementation over 24 months. Estimates of treatment effect based on ITT and PP analyses For ITT analysis, without or with covariates, there was no significant difference between the control and the intervention groups. However, adjustment for the baseline covariates resulted European Journal of Clinical Nutrition (2015) 1 – 7

3

Estimating the causal effect of milk powder supplementation on BMD Y Chen et al

4 Table 1.

Baseline characteristics of randomized participants by compliance status

Variables

Control (72)

Calcium supplementation (69) Compliers (55)

Non-compliers (14)

x2/t

P-value

158.84 ± 5.19 62.95 ± 8.78 1.41 ± 1.24 5.05 ± 0.95 1.43 ± 0.32 2.32 ± 0.65 544.00 ± 201.70 6±7 0.86 ± 0.05 −1.78 ± 2.05 −0.81 ± 1.50

157.73 ± 5.31 61.81 ± 8.81 1.58 ± 1.56 5.04 ± 0.85 1.39 ± 0.32 2.36 ± 0.56 470.91 ± 121.90 5±5 0.86 ± 0.05 −1.92 ± 1.99 −1.09 ± 1.55

157.17 ± 4.42 58.21 ± 7.84 0.96 ± 0.30 4.64 ± 0.72 1.42 ± 0.25 2.09 ± 0.59 500.41 ± 107.06 5±3 0.83 ± 0.06 −1.49 ± 2.37 −1.28 ± 1.84

−0.3600 −1.3900 −2.7500 −1.6200 0.3100 −1.6100 0.8300 −0.2326 −2.0000 0.6900 −0.4000

0.7170 0.1689 0.0077 0.1093 0.7566 0.1130 0.4113 0.8161 0.0495 0.4930 0.6911

Drinking coffeec Yes No

15 (20.83) 57 (79.17)

17 (30.91) 38 (69.09)

3 (21.43) 11(78.57)

Drinking sodasc Yes No

21 (29.17) 51 (70.83)

18 (32.73) 37 (67.27)

3 (21.43) 11 (78.57)

Drinking teac Yes No

10 (13.89) 62 (86.11)

7 (12.73) 48 (87.17)

2 (14.29) 12 (85.71)

Vitamin supplementationc Yes No

7 (9.72) 65 (90.28)

9 (16.36) 46 (83.64)

4 (28.57) 10 (71.43)

Calcium tablet supplementationd Yes No

23 (31.94) 49 (68.06)

28 (50.91) 27 (49.09)

6 (42.86) 8 (57.14)

a

Height Weighta TGa TCa HDLa LDLa Dietary calcium intakea Years since menopauseb WHRa Baseline T score of the spinea Baseline T score of the hipa

0.7425

0.5261

1.0000 0.4428

0.2895

0.5906

Abbreviations: HDL, high-density lipoprotein; LDL, low-density lipoprotein; TC, total cholesterol; TG, triglyceride; WHR, waist hip ratio. aVariable was analyzed using t-test. bVariable was analyzed using Wilcoxon rank-sum test. cVariable was analyzed using Fisher’s exact probability. dVariable was analyzed using Χ2-test.

Table 2.

The mean change from baseline in the first and second year (mean change ± s.d. (95% CI))

Factors

All Control

T score of spine1st T score of spine2nd T score of hip1st T score of hip2nd Weight1st Weight2nd Height1st Height2nd TG1st TG2nd TC1st TC2nd HDL1st HDL2nd LDL1st LDL2nd

0.27 ± 0.82 − 0.16 ± 0.80 − 0.20 ± 0.51 − 0.19 ± 0.53 0.79 ± 3.09 − 1.08 ± 3.41 − 0.34 ± 2.31 − 0.42 ± 2.50 − 0.02 ± 0.70 − 0.08 ± 1.10 − 0.05 ± 0.88 − 0.09 ± 1.05 0.07 ± 0.27 − 0.10 ± 0.31 0.55 ± 0.55 0.47 ± 0.60

(0, 0.54) (−0.42, 0.10) (−0.36, − 0.03) (−0.36, − 0.02) (−0.11, 1.69) (−2.15, − 0.02) (−1.01, 0.33) (−1.20, 0.36) (−0.22, 0.19) (−0.43, 0.27) (−0.30, 0.21) (−0.41, 0.24) (−0.01, 0.14) (−0.20, 0) (0.39, 0.71) (0.28, 0.66)

Calcium supplementation Calcium supplementation 0.25 ± 0.63 0.03 ± 0.75 0.05 ± 0.44 0.07 ± 0.48 0.44 ± 3.48 − 0.95 ± 3.33 0.09 ± 1.35 0.09 ± 1.53 − 0.12 ± 0.53 − 0.17 ± 1.47 0.10 ± 0.75 − 0.17 ± 1.04 0.15 ± 0.23 0 ± 0.30 0.60 ± 0.53 0.34 ± 0.66

(0.07, 0.43) (−0.18, 0.23) (−0.07, 0.17) (−0.06, 0.20) (−0.51, 1.38) (−1.84, − 0.07) (−0.28, 0.45) (−0.32, 0.50) (−0.26, 0.03) (−0.55, 0.22) (−0.10, 0.30) (−0.44, 0.11) (0.09, 0.22) (−0.08, 0.08) (0.45, 0.74) (0.17, 0.52)

Compliers 0.28 ± 0.64 − 0.03 ± 0.76 0.04 ± 0.45 0.07 ± 0.47 0.38 ± 3.73 − 1.06 ± 3.39 0.26 ± 1.34 0.06 ± 1.50 − 0.14 ± 0.56 − 0.23 ± 1.57 0.02 ± 0.74 − 0.21 ± 1.09 0.12 ± 0.22 0 ± 0.30 0.55 ± 0.52 0.31 ± 0.71

Noncompliers

(0.08, 0.47) (−0.25, 0.20) (−0.10, 0.17) (−0.07, 0.21) (−0.71, 1.48) (−2.03, − 0.08) (−0.14, 0.65) (−0.37, 0.49) (−0.30, 0.03) (−0.68, 0.22) (−0.20, 0.23) (−0.52, 0.11) (0.06, 0.19) (−0.09, 0.09) (0.39, 0.70) (0.11, 0.52)

0.05 ± 0.56 0.34 ± 0.68 0.15 ± 0.38 0.08 ± 0.57 0.75 ± 1.46 − 0.31 ± 3.10 − 0.93 ± 0.95 0.29 ± 1.85 0.01 ± 0.27 0.21 ± 0.38 0.59 ± 0.63 0.07 ± 0.61 0.34 ± 0.21 − 0.01 ± 0.31 0.90 ± 0.53 0.52 ± 0.20

(−0.54, 0.64) (−0.23, 0.91) (−0.25, 0.55) (−0.40, 0.56) (−0.47, 1.97) (−2.91, 2.28) (−1.72, − 0.13) (−1.43, 2.00) (−0.21, 0.23) (−0.11, 0.52) (0.06, 1.11) (−0.44, 0.58) (0.17, 0.51) (−0.27, 0.25) (0.46, 1.34) (0.35, 0.69)

Abbreviations: CI, confidence interval; HDL, high-density lipoprotein; LDL, low-density lipoprotein; TC, total cholesterol; TG, triglyceride.

in that the effect size of treatment changed from −0.168 to 0.122, from −0.052 to 0.099 at the lumbar spine and hip at 24 months, respectively, although there was still no significant difference between the two groups. Moreover, the s.e. reduced considerably European Journal of Clinical Nutrition (2015) 1 – 7

after adjusting for the baseline covariates. That was to say the covariates can reduce bias and improve precision of ITT and PP analyses.11 The results of the PP analysis were similar to those of the ITT analysis. © 2015 Macmillan Publishers Limited

Baseline

© 2015 Macmillan Publishers Limited 0.0489 0.0236 0.8735 0.6985 0.0991 o 0.0001

−0.16 ± 0.80 −0.19 ± 0.53 −0.08 ± 1.10 −0.09 ± 1.05 −0.10 ± 0.31 0.47 ± 0.60

158.84 ± 5.19 62.95 ± 8.78

594.24 ± 240.62

Baseline

−0.34 ± 2.31 0.79 ± 3.09

−103.85 ± 217.51 0.3076 0.0823

0.0018

−0.42 ± 2.50 −1.08 ± 3.41

−92.54 ± 259.57

0.2842 157.62 ± 5.12 0.0462 61.08 ± 8.69

0.0260 532.33 ± 165.94

Change in the first year P-value Change in the second year P-value Baseline

Control

0.0064 0.4252 0.1059 0.3298 o 0.0001 o 0.0001

0.09 ± 1.35 0.44 ± 3.48

−136.42 ± 186.58

0.6406 0.3569

o0.0001

Change in the first year P-value

0.03 ± 0.75 0.07 ± 0.48 −0.17 ± 1.47 −0.17 ± 1.04 0 ± 0.30 0.34 ± 0.66

0.7905 0.2923 0.3962 0.2283 0.9611 0.0002

0.09 ± 1.53 −0.95 ± 3.33

−60.36 ± 193.53

0.6699 0.0352

0.0221

Change in the second year P-value

Calcium supplementation

0.25 ± 0.63 0.05 ± 0.44 −0.12 ± 0.53 0.10 ± 0.75 0.15 ± 0.23 0.60 ± 0.53

Change in the second year P-value

Calcium supplementation Change in the first year P-value

Changes of dietary calcium intake, height and weight over time in the control group and the calcium supplementation group

Dietary calcium intake Height Weight

Factors

Table 4.

Baseline

0.2136 −1.83 ± 2.06 0.0256 −1.13 ± 1.60 0.6482 1.45 ± 1.42 0.5928 4.96 ± 0.83 0.0400 1.40 ± 0.30 o 0.0001 2.31 ± 0.57

Change in the second year P-value

Abbreviations: HDL, high-density lipoprotein; LDL, low-density lipoprotein; TC, total cholesterol; TG, triglyceride.

0.27 ± 0.82 −0.20 ± 0.51 −0.02 ± 0.70 −0.05 ± 0.88 0.07 ± 0.27 0.55 ± 0.55

Change in the first year P-value

Control

Changes of T score, TG, TC, HDL and LDL over time in the control group and the calcium supplementation group

T score of the spine −1.74 ± 2.03 T score of the hip −0.77 ± 1.48 TG 1.41 ± 1.24 TC 5.05 ± 0.95 HDL 1.43 ± 0.32 LDL 2.32 ± 0.65

Factors

Table 3.

Estimating the causal effect of milk powder supplementation on BMD Y Chen et al

5

European Journal of Clinical Nutrition (2015) 1 – 7

Estimating the causal effect of milk powder supplementation on BMD Y Chen et al

6 Table 5.

Estimated effect of calcium supplementation on bone mineral density using CACE

Factors

CACELIa

CACE Adjustedb

Crude

Crude

Adjusted

Estimates (s.e.)

P-value

Estimates (s.e.)

P-value

Estimates (s.e.)

P-value

Estimates (s.e.)

P-value

0.009 −0.154 0.277 −0.077

0.9850 0.7460 0.4680 0.8440

−0.346 1.170 0.059 −0.111

0.3480 0.0040 0.6930 0.4120

0.002 −0.170 0.279 −0.074

0.9970 0.7160 0.4630 0.8480

−0.309 0.751 0.065 −0.107

0.2150 0.0040 0.6590 0.4580

T score of spine1st T of spine2nd T score of hip1st T score of hip2nd

(0.50) (0.47) (0.38) (0.39)

(0.39) (0.40) (0.15) (0.14)

(0.50) (0.47) (0.38) (0.38)

(0.25) (0.26) (0.15) (0.14)

Abbreviations: CACE, complier average causal effect; WHR, waist hip ratio. aLatent ignorability data-missing mechanism was assumed. bThe compliance part of the model was adjusted for dietary calcium intake, WHR, calcium tablet supplementation, vitamin supplementation, drinking tea, drinking sodas and drinking coffee; the outcome part of the model was adjusted for dietary calcium intake, years since menopause, T score of the baseline spine or hip, calcium tablet supplementation, vitamin supplementation, drinking tea, drinking sodas and drinking coffee.

Table 6.

Estimated effect of calcium supplementation on secondary outcomes using CACE Factors

Weight Height TG TC HDL LDL

First year

Second year

Estimates (s.e.)

P-value

Estimates (s.e.)

P-value

−0.416 −0.035 −0.097 0.251 0.120 0.075

0.5970 0.9330 0.6340 0.1640 0.0340 0.5540

0.215 1.040 −0.120 −0.068 0.131 −0.144

0.7980 0.0470 0.6970 0.8120 0.1060 0.3590

(0.79) (0.41) (0.20) (0.18) (0.06) (0.13)

(0.84) (0.52) (0.31) (0.28) (0.08) (0.16)

Abbreviations: CACE, complier average causal effect; HDL, high-density lipoprotein; LDL, low-density lipoprotein; TC, total cholesterol; TG, triglyceride.

DISCUSSION In scientific experiments involving human participants, noncompliance and partial compliance are very common in practice. If compliance information is ignored, misleading conclusions are likely to occur. The assumption and definition of noncompliance are important for the interpretation of the results. Because calcium supplementation was a consecutive and long-term course, discontinuous calcium supplementation would reduce its effects.23 In this study, all-or-none treatment noncompliance was assumed. One would be always deemed as a noncomplier even when she did not comply with the treatment protocol for one time. For T-score of the spine and hip, the estimates of both ITT and PP analyses showed that treatment effects were not statistically significant without or with covariates. One of the reasons may be that both methods ignored the information of noncompliers and thus provided biased results. Another reason may be the small sample size when excluding noncompliers. Differences of dietary calcium intake and calcium tablet supplementation between the two groups may affect the estimates of treatment effect. However, the estimations of treatment effect became positive when adjusting for the baseline covariates. To some extent, this demonstrated that calcium supplementation can improve BMD, although this was not significant. Meanwhile, this confirmed that covariates can reduce bias and improve precision of ITT and PP analyses.11 An as-treated analysis was not reported in this study as this method is considered to be misleading and does not provide robust estimates when involving noncompliance.19,21 Compared with the results of ITT and PP analyses, the CACE model provided the more robust estimation of treatment effect among the compliers. There was no statistical significance between the compliers of the control group and the intervention group in European Journal of Clinical Nutrition (2015) 1 – 7

the first and second year without covariates, but with adjustment for baseline covariates, a significant treatment effect in the second year was observed at the lumbar spine. This was consistent with the perspective that consecutive and long-term milk powder supplementation has a beneficial effect on BMD.23,25–28 However, it was demonstrated that bias in the CACE estimate can be reduced substantially by adjusting for covariates even when there was violation of the assumption of Exclusion Restriction.10 Although the bias introduced by violation of the Exclusion Restriction would be increased if the compliance rate was very low,10 it was not applicable to the current paper. Compliance rate within the milk powder supplementation group was 79.71%. Over 24 months, there was no significant difference in the hip between the calcium supplementation group and the control group. Since significant treatment effects in the spine can often be detected within two years but three or more years may be required to detect such effects in the proximal femur,23 the follow-up period of this study, two years, was beneficial to detect such effects in the spine. Under the latent ignorability assumption used in the CACE analysis, the treatment effects were consistent with the results of the CACE model ignoring the data-missing mechanism. The evidence from a previous methodological work suggests that CACE estimates from the generalized linear latent and mixed model are insensitive to the missing-data assumption, such as missing at random or latent ignorability.29 This study showed that calcium supplementation reduced height loss, which was consistent with the study by Lau and Cooper.1 However, subjects who were given high-calcium milk powder did not have a weight gain, which was consistent with the study by Chee et al.2 Therefore, the protective effect of calcium supplementation in the lumbar spine could not be attributed to the weight gain. The high-density lipoprotein rather than total cholesterol, triglyceride and low-density lipoprotein was affected significantly by the calcium supplementation. Li et al.30 reported that the total cholesterol increased significantly after 24 months in the calcium group, but serum triglyceride, high-density lipoprotein and lowdensity lipoprotein were not significantly affected after 24 months. As three or more arm trials using CACE estimates will be complicated, and the CACE model will suffer from more principal compliance categories and complicated identifiability assumptions,11 two groups were selected to analyze in this paper. In the future, CACE estimates of the four groups will be provided to demonstrate the conclusion in this paper. CONCLUSION High calcium milk powder supplementation improves bone mineral density at the lumbar spine among healthy postmenopausal Chinese women. Considering the rapidly aging population, © 2015 Macmillan Publishers Limited

Estimating the causal effect of milk powder supplementation on BMD Y Chen et al

7 consecutive and long-term calcium supplementation should be advocated to prevent osteoporosis in China. CONFLICT OF INTEREST The authors declare no conflict of interest.

ACKNOWLEDGEMENTS We thank Zhiqiang Wang and Yang Yang for their help with the language and constructive suggestions. This study was funded by the National Key Technology R&D Program of China (2011BAI09B02).

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