What a Baseline Table Should Communicate
A baseline characteristics table lets readers see who was compared and how the treatment groups differed before and after adjustment. In an observational study, it is especially important to separate description from evidence of balance: the table describes observed characteristics, while balance measures summarize the size of observed differences. Neither a table nor a balance measure establishes that unmeasured confounding is absent.
A useful table makes its groups, samples, summaries, and denominators explicit. It should distinguish the original treatment groups from the matched or weighted analysis sample, and state which adjustment method produced each post-adjustment column. For a matched sample, report the number of treated and comparison units retained. For weighting, report the original unit counts and explain that the displayed summaries use weights; if relevant, also report a measure of the effective sample size.
The baseline time point and the analysis population need clear definitions. A variable measured after treatment begins may be affected by treatment, so presenting it as a baseline covariate can be misleading. Explain which participants are included in each column, including relevant exclusions or missing-data rules. The earlier material on missing-data reporting and analysis samples provides the broader reporting context; here the goal is to make those facts visible in the table itself.
Choose Summaries That Fit the Variable
For a roughly symmetric continuous variable, report the mean and standard deviation with units, such as age in years. For a strongly skewed variable, a median and interquartile range may communicate its distribution more faithfully. State which summaries are used and apply the choice consistently across the treatment groups. For a binary variable, report the count and percentage in a clearly identified category, such as “current smoker, n (%).” For a categorical variable with several levels, show each level, usually as its own row, with counts and percentages.
Always identify the denominator behind a percentage. If some values are missing, a percentage among observed values answers a different question from a percentage among everyone in that group. A compact table can include a separate missing row and a note that percentages for the categories use nonmissing observations. Where missingness is substantial or differs across groups, make the missing counts easy to find rather than hiding them in a footnote.
The same rule applies after adjustment: calculate each summary from the adjusted analysis sample and use the relevant weights when the design is weighted. A weighted percentage is the sum of weights for units in the category divided by the sum of weights for units with observed values for that characteristic. Thus, the displayed denominator may be the sum of weights, not the number of people. Label the column “weighted” and explain the denominator or convention in a note.
Worked Example: Choosing Rows and Reporting Unadjusted Denominators
Suppose a hypothetical cohort includes 120 treated patients and 180 comparison patients. At baseline, age is observed for all 300 patients. Smoking status is observed for 110 treated and 170 comparison patients; among those with observed status, 33 treated and 34 comparison patients are current smokers. Choose table entries and calculate the percentages.
For age, a mean and standard deviation are appropriate if the observed distributions are reasonably symmetric. The table should label the units, for example “Age, years, mean (SD),” and show summaries calculated separately for the 120 treated and 180 comparison patients. The specific means and standard deviations would come from the hypothetical cohort’s age measurements; they cannot be calculated from the counts given here.
For smoking, the percentage denominator is the number with observed smoking status, not the full group size. The treated percentage is \(33/110 \times 100 = 30.0\%\). The comparison percentage is \(34/170 \times 100 = 20.0\%\). The table can show “Current smoker, n (%)” as 33 (30.0%) and 34 (20.0%), followed by a “Missing, n” row showing 10 and 10. A note should say that smoking percentages use nonmissing observations as denominators.
This presentation makes both the characteristic and its missingness visible. Reporting 33 (27.5%) for treated patients, using all 120 as the denominator, would instead describe the proportion known to be smokers among the entire group while implicitly treating missing statuses as not current smoking. That is not the stated calculation and would need a different, explicit interpretation.
Show Pre-Adjustment and Post-Adjustment Results Separately
A practical layout places each treatment group in a separate column, with a clear grouping of columns for “Before adjustment” and “After adjustment.” Include the sample size in each group header. For example, a matched table might show the treated and comparison counts retained after matching; a weighted table might show both the number of observed units and a label indicating that post-adjustment summaries are weighted. Avoid a single ambiguous “adjusted” column when readers cannot tell which group or method it represents.
Before adjustment, summaries use the observed treatment groups in the specified starting cohort. After adjustment, summaries correspond to the sample and weights actually used for the analysis. In matching with replacement, for instance, a comparison person can contribute more than once to the matched analysis. The table note should clarify whether counts refer to unique people or matched uses, and the summaries must follow the method used to form the analysis sample. For weighting, the table should not imply that a weighted count is a literal count of people.
For continuous variables, report a mean (SD) or median (IQR) in every relevant column. For categorical variables, report category-specific counts and percentages. If a missing category is shown, clarify whether it is included in the percentage denominator for other categories. Use one consistent number of decimal places, include measurement units in row labels, and define abbreviations and any non-obvious summary conventions in a table note.
Worked Example: Calculating a Weighted Mean and Percentage
Consider a hypothetical weighted comparison group with three patients. Their baseline ages are 50, 60, and 70 years, with analysis weights 1, 2, and 1. Their smoking status is “yes,” “no,” and “yes,” respectively. Calculate the weighted mean age and weighted percentage who smoke.
The weighted mean age is the sum of each age multiplied by its weight, divided by the sum of the weights:
The weighted percentage who smoke uses the weight sum for patients with observed smoking status as its denominator. Here all three statuses are observed, and the two smokers have total weight \(1+1=2\):
The corresponding table entries are a weighted mean age of 60.0 years and a weighted smoking percentage of 50.0%. The unweighted mean age is also 60 years in this small example, but the unweighted smoking percentage is \(2/3 \times 100 = 66.7\%\). The equality of the two age means is incidental; it does not make unweighted summaries appropriate for the weighted analysis.
Balance Measures Belong Alongside the Descriptions
A baseline table can pair group summaries with an absolute standardized mean difference (SMD) for each covariate, before and after adjustment. The earlier material on covariate balance diagnostics covers the interpretation and calculation of balance measures. For reporting, the key point is to make the comparison scale clear: an SMD is a summary of the magnitude of an observed difference, while a count, percentage, mean, or median describes the covariate itself. Report the chosen balance measure consistently and explain how it was calculated if the convention is not standard for the displayed variable.
Do not use hypothesis-test p-values as a measure of balance. A p-value depends on sample size as well as the observed difference: a small difference may be statistically significant in a very large sample, while a potentially important difference may not be significant in a small one. A non-significant result does not demonstrate that groups are balanced. For this reason, omit routine significance tests from baseline tables and use descriptive summaries plus appropriate balance measures instead.
A short justification clarifies why standardized differences are more useful for this purpose than p-values. A significance test evaluates a null hypothesis about a population difference relative to its sampling uncertainty. Its test statistic therefore changes with sample size, even if the estimated difference stays fixed. A balance summary intended to describe the observed discrepancy should foreground the magnitude of that discrepancy, not whether a sample-size-dependent test crosses a significance threshold. This does not make an SMD a test of causal validity or a guarantee of balance on unmeasured variables.
Worked Table Design and Common Failure Modes
Worked Example: Structuring a Before-and-After Table
A hypothetical study begins with 200 treated and 300 comparison participants. Matching retains 160 treated and 160 comparison participants. Suppose the reported baseline age summaries are: before matching, treated mean 64.0 years (SD 10.0) and comparison mean 59.0 years (SD 11.0); after matching, treated mean 63.5 years (SD 10.1) and comparison mean 63.2 years (SD 10.0). Design the relevant table columns and interpret what the entries establish.
Use the column headers “Before matching: treated (n = 200),” “Before matching: comparison (n = 300),” “After matching: treated (n = 160),” and “After matching: comparison (n = 160).” In the “Age, years, mean (SD)” row, enter 64.0 (10.0), 59.0 (11.0), 63.5 (10.1), and 63.2 (10.0), respectively. The matched summaries must be calculated from the 160 retained participants in each group, as stipulated in the example.
The unadjusted difference in the displayed means is \(64.0-59.0=5.0\) years; after matching it is \(63.5-63.2=0.3\) years. These calculations describe the change in the observed age difference. They do not establish balance on every covariate, show that unmeasured confounding is absent, or by themselves establish a causal treatment effect. A complete table would also display other prespecified baseline characteristics and the chosen balance measures.
A note should state the matching method and clarify that the post-matching counts refer to retained participants. If matching were with replacement, the note would also distinguish unique comparison participants from repeated matches. These details let readers understand which data each column summarizes rather than infer the analysis sample from the values.
Several table choices can undermine an otherwise sound analysis. Combining original and matched sample summaries under one unlabeled pair of columns hides which population is being described. Showing weighted percentages without labeling them as weighted obscures the calculation. Omitting missing counts can make groups with different data completeness appear directly comparable when they are not. Finally, reporting a p-value next to every characteristic invites readers to treat “not significant” as proof of balance. The correction in each case is to identify the sample, method, denominator, and descriptive measure explicitly.
Tables also have limits. They summarize selected measured covariates and can conceal distributional differences when a single mean or proportion is used. They cannot replace examination of the full covariate distributions, the study’s overlap and missingness assessments, or appropriate balance diagnostics. If a summary is likely to hide important structure, add a suitable diagnostic elsewhere in the report rather than making the table excessively dense.
Check Your Understanding
Answer each question, then compare with the brief solutions.
- A binary covariate is observed for 80 of 100 treated participants, and 24 observed participants have the characteristic. What percentage should be reported if the table defines percentages among observed values, and what missing count should appear?
- Why should a post-weighting percentage be labeled as weighted?
- A very large cohort has a small baseline difference with a tiny p-value. Does that p-value show that the groups are poorly balanced? Explain.
- After matching, 90 treated and 90 comparison participants remain. What extra clarification may be needed if matching used comparison participants more than once?
- Give two reasons a table should identify its pre-adjustment and post-adjustment columns separately.
Solutions. (1) The percentage is \(24/80 \times 100=30.0\%\); the missing count is \(100-80=20\). (2) Weighting changes each unit’s contribution to the summary, so the weighted percentage may differ from the raw proportion and its denominator is based on weights. (3) No. A p-value reflects sample size as well as the observed difference and is not a balance measure; report the descriptive difference and an appropriate balance summary. (4) State whether the count refers to unique comparison participants or repeated matched uses, and make clear how summaries were calculated. (5) Separate labels show which sample and adjustment method each summary describes, and prevent readers from mistaking adjusted summaries for the original cohort’s characteristics.