Hypocaloric Nutrition in Critically Ill Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Hypocaloric Nutrition in Critically Ill Patients (NCT01531335), a randomized phase 3 study. The primary outcome is SOFA (Sequential Organ Failure Assessment) Score.

2. Clinical Question

3. Trial Design

This was a Phase 3, randomized, triple-masked, parallel-group trial. The registry record lists an enrollment of 80 and a completed status. Its listed start was 2011-08, and its primary completion was 2012-08. The record identifies Lafrancol S.A. as the sponsor. These registry entries describe the design and record status; they do not establish what procedures were used to implement masking or allocation.

Participants were assigned to standard care or hypocaloric hyperproteic nutrition. The standard-care regime was described as around 25 kcal per kg. The hypocaloric regime was described as 15 kcal per kg of body weight and 1.7 grams of protein per kg. The primary outcome was mean SOFA score, measured 48 hours after the nutritional regime started. A secondary outcome was insulin requirements, described in International Unit of insulin and assessed daily until day 21 or discharge from the ICU.

The posted primary outcome lists 40 participants in each arm, with means and standard deviations. The secondary outcome also lists 40 in each arm. These outcome counts should be read as the numbers recorded for those measures, not as proof that every randomized participant contributed data at every time point. The registry record does not report the original sample-size justification, allocation sequence procedures, masking procedures, or any trial analysis plan.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as SOFA (Sequential Organ Failure Assessment) Score, measured over 48 hours since nutritional regime starts.

The primary endpoint was SOFA (Sequential Organ Failure Assessment) score, expressed in units on a scale and summarized as a mean with a standard deviation. The timeframe was 48 hours since the nutritional regime started. The registry description says that SOFA evaluates six systems: respiratory, cardiovascular, coagulation, central nervous system, liver, and renal. Each system receives a score from 0, described as normal, to 4, described as abnormal; the component scores are summed.

The registry describes 0 as the minimum score and 24 as the maximum, with higher scores associated in its description with greater risk. Using a common score across several organ systems gives a way to summarize organ dysfunction at a specified assessment time. Comparing group means addresses whether average scores differ, but it does not by itself show the distribution of individual scores, changes in each organ system, or the incidence of organ failure. Those outcomes are not reported as the primary measure in this record.

The 48-hour measurement is a particular timepoint after the nutritional regime starts. It is not a description of the full course of illness or of longer-term outcomes. The record does not report additional primary endpoint timepoints or explain how the outcome was handled for participants without a recorded score.

7. Results Posted in the Registry

• Hypocaloric Hyperproteic Nutrition: mean 1.70 versus 0.70 on control; difference 1.00 (95% CI -0.05 to 2.05), standardized effect d = 0.42; z-test p = 0.062.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Insulin Requirements

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Hypocaloric Hyperproteic Nutrition: mean 10.40 versus 14.00 on control; difference -3.60 (95% CI -12.39 to 5.19), standardized effect d = -0.18; z-test p = 0.422.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Hypocaloric Hyperproteic Nutrition and the control. The interval gives the range of effects that remain compatible with the data.

The registry record lists one secondary outcome: insulin requirements, assessed daily until day 21 or discharge from the ICU. Its posted comparison is less precise than a simple directional summary might suggest: the mean-difference interval includes zero and extends in both directions. The unadjusted result therefore does not provide a clear separation between the groups on this measure.

The secondary result does not overturn or confirm the primary SOFA comparison. The endpoints measure different things and use different units and timeframes. SOFA summarizes organ-system scores at 48 hours after the nutritional regime starts, whereas insulin requirements are recorded daily until the stated stopping point. A pattern in one endpoint cannot be treated as a direct replication of the other, and a secondary result cannot establish the effect on the primary outcome.

Unadjusted secondary results generally carry less weight when several outcomes or analyses may be considered. General statistical explanation: when multiple comparisons are examined, the chance of obtaining an apparently unusual result can increase unless the analysis plan accounts for multiplicity. The registry record does not report a multiplicity strategy, a prespecified hierarchy of outcomes, or a detailed analysis plan. It also does not identify additional secondary endpoints in the posted results, but the absence of a reported procedure means the status of the secondary comparison within the trial’s planned testing framework is unclear.

The appropriate emphasis is therefore on the role and limitations of this secondary measure, not on treating its p-value as an independent confirmatory finding. The posted result is informative as a descriptive estimate with uncertainty, but it does not supply a complete account of how secondary outcomes were chosen, analyzed, or interpreted by the trial team.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Insulin Requirements

9. Statistical Interpretation

10. Statistical Methods Explained

The posted outcomes are continuous measures summarized using means and standard deviations. A mean describes the arithmetic average of observed values in a group. A standard deviation describes how spread out the observations are around that average; it is not the uncertainty in the mean itself. The primary comparison is reported as a mean difference between the hypocaloric hyperproteic nutrition group and standard care.

What does the mean difference represent?

The mean difference is calculated as the intervention-group mean minus the comparator-group mean. For SOFA, the posted estimate is 1.0, based on means of 1.7 and 0.7, respectively. A positive estimate therefore means the intervention-group average was higher on the score. The direction must be interpreted in light of the score’s meaning: the registry describes higher component scores as more abnormal. A difference in averages does not mean that every individual had a higher score, and it does not reveal how many participants had a particular score.

For insulin requirements, the posted mean difference is -3.6. A negative value means the average in the intervention group was lower than the average in standard care, given the same subtraction order. This is a descriptive comparison of group means. Without the trial’s analysis plan, it should not be assumed that the posted value is adjusted for other variables or represents a particular model beyond the reported mean difference.

What do standard deviations and standard errors describe?

Standard deviations characterize variation among individual observations within a group. Standard errors characterize uncertainty in an estimated mean; the posted results list standard errors of 0.443 and 0.300 for the primary outcome. General statistical explanation: when observations are more variable, a mean based on a fixed amount of data is generally estimated less precisely. Standard deviations and standard errors are not interchangeable: one describes individual-level spread, while the other describes sampling uncertainty in an estimate.

The reported pooled standard deviation for the primary comparison is 2.393. A pooled spread is a combined summary used in some comparisons of two group means. The record does not report the trial’s detailed statistical method, so the presence of a pooled spread does not establish which test or model the trial team used. The registry record lists no reported analyses.

How should a confidence interval be read?

General statistical explanation: a confidence interval expresses the uncertainty around an estimated effect under the assumptions of the method used. It gives a range of values reasonably compatible with the observed data and that method; it is not a guarantee that the true effect lies inside the interval. For the primary mean difference, the reported interval extends from just below zero to 2.049. Because zero lies within that interval, the results do not exclude a zero mean difference at the interval’s stated confidence level. The registry record does not identify the confidence level or describe how the interval was constructed.

The secondary mean-difference interval extends from -12.39 to 5.194, also including zero. An interval that includes zero can still contain effects in either direction, and its width conveys uncertainty about the size and direction of the comparison. The interval alone does not tell whether any value in it is clinically important; the registry record does not report a threshold for clinical importance.

What does the p-value add?

The unadjusted p-value for the primary comparison is 0.062. General statistical explanation: a p-value measures how unusual data at least as incompatible with a specified null hypothesis would be, assuming that hypothesis and the statistical model are true. It is not the probability that the null hypothesis is true, nor the probability that the result occurred by chance. The record does not state the trial’s prespecified testing procedure or threshold. The term “unadjusted” indicates that the posted value is not described as adjusted for multiple comparisons; the registry does not report whether another analysis was performed.

Interpret the p-value alongside the estimated difference, confidence interval, endpoint definition, and limitations of the record. The numerical value should not be turned into a binary conclusion without knowing the planned analysis and the role of other outcomes. The registry record reports zero analyses and lists no reported analyses, so the posted comparison does not document a complete statistical analysis plan or its implementation.

Why does variability matter?

General statistical explanation: when outcome values vary substantially within groups relative to the difference between their means, the data may provide limited precision about the between-group effect. The primary group standard deviations are 2.8 and 1.9, while the mean difference is 1.0. The confidence interval reflects uncertainty about the comparison and is more informative about that uncertainty than the point estimate alone. The data also cannot be fully characterized by means and standard deviations: distributions, outliers, and the number of observations at each score are not reported in the registry record.

SOFA scores are formed by summing scores across several systems, but the posted analysis treats the endpoint as a continuous measure summarized by a mean. The registry record does not report whether alternative approaches were used or whether assumptions were checked. General statistical explanation: a statistical method’s assumptions affect how its uncertainty estimates should be interpreted. No claim about a particular model, diagnostic check, or adjustment can be made from the registry entry.

11. Confidence Intervals and Precision

The primary mean difference is 1.0, and its confidence interval extends from just below zero to 2.049. The lower end is slightly below zero, while the upper end is positive. That span means the data do not pin down a single effect size: the interval is compatible with no mean difference and with a positive difference on the SOFA scale. The point estimate is not itself a measure of precision; the interval provides additional information about uncertainty.

The interval’s width indicates that the estimate remains uncertain relative to the point estimate. It does not establish which values within the interval are clinically important. The registry record does not report a clinically meaningful threshold for the SOFA difference, a confidence level for the interval, or details of the method used to calculate it. Those omissions constrain interpretation of the interval’s practical meaning.

For insulin requirements, the mean-difference interval runs from -12.39 to 5.194 and includes zero. It therefore permits estimates in either direction. Its presence does not confirm a difference or demonstrate equivalence. Equivalence would require a prespecified margin and a suitable analysis; no such margin or analysis is reported in the registry record.

Precision is also distinct from whether a result is statistically significant under a chosen decision rule. A confidence interval and p-value summarize aspects of the same comparison, but neither supplies the missing design and analysis details. The posted results should be read as estimates with uncertainty, not as exact measurements of the underlying effects.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm for these continuous outcomes, not total events. The illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses a target effect equal to the stated fraction of the observed effect. The original trial’s own sample-size assumptions and justification are not reported in the registry record; the planning figures are not a reconstruction of that design.

For 80% power, the listed figure means the number of participants per arm in a hypothetical study designed to have an 80% chance of detecting the specified effect under those assumptions, if that effect is the true one and the assumptions hold. The 90% power column expresses the analogous planning target with a higher chance of detection. These are prospective planning illustrations, not a measure of what the completed trial achieved. This is not observed power.

The scenarios use 100%, 75%, and 50% of the observed effect. For the primary SOFA comparison, planning for 100% of the observed effect gives 90 participants per arm for 80% power and 121 participants per arm for 90% power. Planning for 75% gives 160 participants per arm for 80% power and 214 participants per arm for 90% power. Planning for 50% gives 360 participants per arm for 80% power and 482 participants per arm for 90% power.

The pattern illustrates why smaller effects need more participants: when the effect to detect is reduced, a larger study is needed under the same planning assumptions. The figures depend on the observed effect used as their starting point, so they are not independent evidence that this effect is stable or clinically important. They should be used as planning illustrations, not as evidence about the trial’s original intentions.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 1.000; pooled standard deviation σ = 2.393.
2. n = 2 × (1.96 + 0.842)² × 2.393² / 1.000² = 89.9, rounded up to 90 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- 1                      # observed difference in means
sigma <- 2.39269722280108                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(1531335)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 90 (80% power), 121 (90% power)
 75% of observed effect: n per arm = 160 (80% power), 214 (90% power)
 50% of observed effect: n per arm = 360 (80% power), 482 (90% power)
power.t.test: 90.8 
Simulated power at n = 90 per arm: 0.797 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists a primary SOFA outcome and one secondary outcome, insulin requirements. It reports no analyses and no reported analyses. It does not state whether the displayed comparisons follow a prespecified analysis plan, whether other outcomes were measured but not posted, or whether a hierarchy or multiplicity adjustment was used. As a result, the role of the unadjusted secondary comparison in the trial’s overall evidence cannot be established from this record.

General statistical explanation: when several outcomes or comparisons are tested, interpreting each p-value as if it were the only test can overstate how much evidence an unusual result represents. A prespecified testing order or adjustment can help address this issue, but the registry record does not report either. The posted p-values are explicitly unadjusted, so they should not be read as multiplicity-adjusted evidence.

The record does not report how missing outcome values were handled, whether all randomized participants were included in each analysis, or which analysis populations were used. The outcome entries list 40 participants per arm, but these entries alone do not establish whether the analysis followed an intention-to-treat principle, excluded participants, or used another population definition. The record also does not explain how missing SOFA scores or insulin measurements were treated.

These are not small technical details: analysis populations and missing-data methods can affect the interpretation of a group comparison. General statistical explanation: if outcome availability is related to participants’ condition or treatment, analyzing only recorded outcomes may not preserve the original comparison. No assertion can be made about whether such a problem occurred in this trial. The necessary details are not reported in the registry record.

The original sample-size justification, interim analyses, and trial-specific statistical plan are also not reported in the registry record. This prevents a reader from checking whether the posted outcome timing, analysis, and interpretation match the trial’s planned procedures. The limitations concern what the registry documents; they do not establish that the trial team failed to conduct any particular procedure.

15. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 1% reporting threshold.

The posted serious adverse event figures list 0 affected participants in the standard-care group and 0 in the hypocaloric hyperproteic nutrition group, with 40 at risk recorded for each group. The figures therefore show no serious adverse events recorded in these entries. They should be interpreted as registry-reported counts, not as proof that no adverse events occurred outside the categories, period, or data captured by these entries.

The record also lists 0 affected participants for other adverse events in each group, with 40 at risk recorded in each. Death counts are null for both groups, rather than reported as zero. A null value means the death count is not reported in the registry entry; it should not be converted into a claim that no deaths occurred.

No top serious adverse event terms are listed. The registry record does not provide further detail about adverse-event definitions, collection methods, follow-up duration for safety, or whether the counts were assessed by an analysis population. These entries are limited safety information and do not establish comparative safety or exclude uncommon harms.

16. What the Result Does, and Does Not, Mean

The posted primary result is a comparison of mean SOFA scores 48 hours after the nutritional regime started. The intervention-group mean was higher than the standard-care mean, and the estimated difference was 1.0. The confidence interval includes zero, and the unadjusted p-value is 0.062. The result therefore remains uncertain about the size and direction of the underlying mean difference. It should not be reduced to a claim that one group definitively had a better or worse outcome.

The endpoint is also narrower than the registry’s stated hypothesis about the incidence of organic failure. A mean score at one timepoint is not itself an incidence estimate. It cannot show how many participants developed organ failure, whether particular systems drove the group means, or what happened after the 48-hour assessment. Those outcomes are not reported in the registry record.

The secondary insulin-requirements comparison is another distinct outcome with its own timeframe and uncertainty. It does not provide a direct confirmation of the primary result. The registry record does not report a multiplicity strategy or detailed analysis populations, so the secondary result should be treated as supportive description rather than conclusive evidence.

General statistical explanation: a trial result is best interpreted through the estimated effect, its precision, the outcome’s clinical meaning, and the analysis plan. A p-value alone cannot establish clinical importance, and a non-zero point estimate does not guarantee a true effect. The record does not report a threshold for a clinically meaningful SOFA difference or the original assumptions used to plan the trial.

Accordingly, the posted data describe these group summaries and their uncertainty; they do not warrant medical advice or a definitive treatment claim. The registry record does not report the information needed to assess all relevant outcomes, the handling of missing data, or the full analysis strategy. Those limits should accompany any interpretation of the comparison.

17. Why This Trial Matters Statistically

This trial illustrates an important distinction between a clinical hypothesis and the endpoint used to evaluate it. The stated hypothesis concerns incidence of organic failure, while the posted primary endpoint is mean SOFA score at a specified time. A score-based group mean can be informative, but it does not directly answer an incidence question. Careful interpretation begins by identifying the estimand: what quantity the comparison actually describes.

The result also shows why effect estimates and uncertainty matter together. The primary point estimate is 1.0, but the interval extends from just below zero to 2.049. Reporting only the direction of the point estimate would conceal the uncertainty. The unadjusted p-value of 0.062 is another summary of the comparison, not a substitute for describing its range of plausible values or the outcome’s meaning.

The planning illustration adds a separate lesson. Required participants per arm increase when the target effect is set to a smaller fraction of the observed effect. This makes the choice of planning effect important, and it underscores that sample-size calculations depend on assumptions. The registry record does not report the trial’s original sample-size justification, so the illustration should not be confused with the trial’s design rationale.

Finally, the record exposes how trial interpretation depends on more than outcome numbers. Analysis populations, missing-data procedures, multiplicity handling, and a prespecified statistical plan are not reported. Their absence from the registry record limits what can be concluded from posted comparisons, without demonstrating that the trial team did or did not use particular methods. Distinguishing documented results from undocumented methods is central to sound statistical reading.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record gives limited context for the enrolled population beyond “Critically Ill.” It does not report detailed eligibility criteria, baseline characteristics, or information that would allow readers to assess how representative the participants were. The posted arm counts and endpoint summaries do not describe participant-level distributions or differences in baseline status.

The primary outcome is a mean SOFA score at 48 hours. The record does not report component-level results, individual score distributions, or an incidence measure for organ failure. Consequently, the posted mean comparison cannot show which organ systems contributed to the result or whether the stated incidence hypothesis was directly evaluated. It also does not describe longer-term SOFA outcomes.

The registry record does not report the trial’s original sample-size assumptions, statistical analysis plan, analysis populations, missing-data handling, multiplicity approach, or interim analyses. It does not provide details of the randomization or masking procedures beyond listing the trial as randomized and triple masked. These gaps restrict assessment of how the reported comparisons were planned and conducted.

Safety entries report zero affected participants in the listed serious and other adverse event categories, while death counts are null. The record does not report additional safety definitions or collection details. These entries cannot establish the absence of all harms.

These limitations are specific to the information documented in the registry record. They should not be interpreted as evidence that unreported procedures were not performed or that unreported outcomes were unfavorable. They define the boundary of what can be evaluated from the posted information.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Hypocaloric Nutrition in Critically Ill Patients — NCT01531335.
• Registry record last updated 2015-12-11; status last verified 2015-11.
• Results first posted 2015-12-11.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT01531335 is a completed, randomized, triple-masked, parallel-group Phase 3 trial sponsored by Lafrancol S.A. It compared standard care, described as around 25 kcal per kg, with hypocaloric hyperproteic nutrition, described as 15 kcal per kg of body weight and 1.7 grams of protein per kg.

The primary outcome was mean SOFA score 48 hours after the nutritional regime started. The posted mean difference was 1.0, with a confidence interval extending from just below zero to 2.049 and an unadjusted p-value of 0.062. The record also lists insulin requirements as a secondary outcome. It does not report trial analyses, the original sample-size justification, or key details of the analysis plan.