A prospective cohort study investigates a novel serum biomarker (Biomarker X) for predicti… — USMLE Step 3

A prospective cohort study investigates a novel serum biomarker (Biomarker X) for predicting disease progression in $120$ patients with idiopathic pulmonary fibrosis. Patients are categorized into three baseline severity groups: mild ( $n=40$ ), moderate ( $n=40$ ), and severe ( $n=40$ ).

The following data are collected after $1$ year of follow-up:
- Absolute change in Biomarker X levels (pg/mL) from baseline. A Shapiro-Wilk test indicates these data are severely right-skewed.
- Quality of life score on a $10$ -point Likert scale (ordinal).
- Occurrence of acute exacerbation during the $1$ -year period (dichotomous: yes/no). Across the entire cohort, a total of exactly $6$ patients experienced an exacerbation.
- The exact number of days from enrollment to the first acute exacerbation.

The researchers consult a biostatistician to finalize the data analysis plan, which will include multivariable adjustments for patient age and smoking history.

Based on the study design and data characteristics, which of the following planned statistical analyses are appropriate? (Select all that are correct)

Kruskal-Wallis test to compare the absolute change in Biomarker X levels across the three baseline severity groupsAnswer
Fisher's exact test to compare the occurrence of acute exacerbation across the three baseline severity groupsAnswer
C
One-way analysis of variance (ANOVA) to compare the quality of life scores across the three baseline severity groups
D
Multiple logistic regression to evaluate the independent effect of baseline Biomarker X on the number of days to the first acute exacerbation, adjusting for age and smoking history
E
Paired Student t-test to compare the Biomarker X levels at baseline to those at $1$ year within the severe group

Answer

The appropriate statistical analyses are the Kruskal-Wallis test for the skewed continuous biomarker data and Fisher's exact test for the categorical exacerbation data with low expected cell counts.

The selection of statistical tests depends on the type of data (continuous, ordinal, categorical, or time-to-event), the distribution (normal vs. skewed), and the number of groups being compared. The Kruskal-Wallis test is the appropriate non-parametric alternative to one-way ANOVA for comparing a continuous, non-normally distributed variable (change in Biomarker X) across more than two independent groups (mild, moderate, severe). Fisher's exact test is the appropriate method for analyzing categorical data (occurrence of exacerbation) across independent groups when the expected frequency in any cell of the contingency table is less than 5. In this study, the overall event rate is 6 out of 120 patients. For any severity group of 40 patients, the expected number of exacerbations is exactly 2 (40 * 6/120). Since more than 20% of the cells have expected frequencies less than 5, Pearson's Chi-square test is invalid, and Fisher's exact test must be used.

Step-by-Step Solution

Analyze the variable type and distribution for the 'absolute change in Biomarker X levels'.

It is a continuous variable that is severely right-skewed, being compared across three independent groups.

Identifying the variable type, distribution, and number of groups is the first step in selecting between parametric and non-parametric tests.

Select the appropriate test for the continuous, non-normally distributed Biomarker X data.

The Kruskal-Wallis test is selected over one-way ANOVA.

Kruskal-Wallis is the non-parametric equivalent of ANOVA, required when comparing continuous data across three or more independent groups that violate the assumption of normality.

Calculate the expected cell frequencies for the 'occurrence of acute exacerbation' outcome.

It is a dichotomous variable (yes/no) across three groups (

3\times2

table). With

6

total events and

120

total patients, the expected number of events for each group of

40

(40 \times 6) / 120 = 2

The choice between Chi-square and Fisher's exact test depends on whether any expected cell frequencies in the contingency table are less than

5

Select the appropriate test for the categorical exacerbation data.

Fisher's exact test is selected over Pearson's Chi-square test.

Pearson's Chi-square is invalid because

50\%

of the cells (

3

out of

6

) have expected frequencies less than

5

. Fisher's exact test is required.

Evaluate the validity of the remaining proposed analyses based on their statistical assumptions.

ANOVA is invalid for ordinal Quality of Life data. Logistic regression is invalid for time-to-event (days to exacerbation) data. The paired t-test is invalid for paired data where the differences are highly skewed.

Applying statistical tests that violate fundamental assumptions regarding data type (e.g., treating time-to-event data as a simple binary outcome) leads to biased and invalid conclusions.

Key Concept

Selection of statistical tests based on variable scale (continuous, ordinal, categorical, time-to-event), data distribution (parametric vs. non-parametric), number of comparison groups, and sample size assumptions (expected cell frequencies).

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic