Analysis of human immune responses in quasi-experimental settings: tutorial in biostatistics

Abstract

Background: Human immunology is a growing field of research in which experimental, clinical, and analytical methods of many life science disciplines are utilized. Classic epidemiological study designs, including observational longitudinal birth cohort studies, offer strong potential for gaining new knowledge and insights into immune response to pathogens in humans. However, rigorous discussion of methodological issues related to designs and statistical analysis that are appropriate for longitudinal studies is lacking.

Methods: In this communication we address key questions of quality and validity of traditional and recently developed statistical tools applied to measures of immune responses. For this purpose we use data on humoral immune response (IR) associated with the first cryptosporidial diarrhea in a birth cohort of children residing in an urban slum in south India. The main objective is to detect the difference and derive inferences for a change in IR measured at two time points, before (pre) and after (post) an event of interest. We illustrate the use and interpretation of analytical and data visualization techniques including generalized linear and additive models, data-driven smoothing, and combinations of box-, scatter-, and needle-plots.

Results: We provide step-by-step instructions for conducting a thorough and relatively simple analytical investigation, describe the challenges and pitfalls, and offer practical solutions for comprehensive examination of data. We illustrate how the assumption of time irrelevance can be handled in a study with a pre-post design. We demonstrate how one can study the dynamics of IR in humans by considering the timing of response following an event of interest and seasonal fluctuation of exposure by proper alignment of time of measurements. This alignment of calendar time of measurements and a child's age at the event of interest allows us to explore interactions between IR, seasonal exposures and age at first infection.

Conclusions: The use of traditional statistical techniques to analyze immunological data derived from observational human studies can result in loss of important information. Detailed analysis using well-tailored techniques allows the depiction of new features of immune response to a pathogen in longitudinal studies in humans. The proposed staged approach has prominent implications for future study designs and analyses.

Figures

Figure 1

Distribution of pre- and post- event measurements of immune responses. The distributions are depicted by a compact box-plot indicating five summary statistics: 5th, 25th, 50th (median), 75th, and 95th percentiles, as well as potential outliers that are substantially exceeding interquartile range (IQR) (higher then 1.5*IQR). Summary statistics for pre- and post- event measurements are shown in the Table 1.

Figure 2

Line graph of individual trajectories and a distribution of differences. Individual trajectories of change in immune response measurements (Panel A) reflect a general pattern and the degree of similarity among the responses. A histogram of the observed absolute differences in pre-post measurements (Panel B) indicate systematic increase in post measurements, except one case of a negative change, marked as an outlier. The dashed line indicates approximation by a normal distribution. Summary statistics for absolute difference values are shown. The distributions of pre- and post-event measurements (as box plots) and their difference (as histogram) for log-transformed values are shown in Panel C and D respectively.

Figure 3

Scatter-plot of pair measurements: the baseline IR values are shown on a horizontal axis -- labeled as "Pre-event immune response" -- and the measurements for the second time point -- labeled as "Post-event immune response" are on a vertical axis. An outlier is marked. Values of Pearson's and Spearman's correlation coefficients are shown for all subjects with and without the outlier.

Figure 4

Scatter-plot of pair measurements: Figure 4A depicts the average of pre- and post-event IR values are shown on a horizontal axis and the values for absolute difference are on a vertical axis. The horizontal line in the middle is the mean difference between the pre- and post-event IR values, and the dotted lines are the 95% CI for the pre-post difference. Figure 4B uses the log-transformed IR values and reveals a lesser dependency. An outlier is marked. Values of Pearson's and Spearman's correlation coefficients are shown for all subjects and by subgroups with and without the outlier.

Figure 5

Line graph of individual trajectories centered on the time of event reflects time elapsed between pre/post measurements. The measurements collected before an event are on left relative to a vertical dotted line and the post-event measurements are on right side. Thus, the negative values on a horizontal axis indicate the time of a surveillance sample taken before diarrheal episode and the positive values are times of surveillance sample since an episode. The summary statistics for measurement timing and shown in Table 2.

Figure 6

Line graph of individual trajectories centered on the time of event with the superimposed smoothed curve illustrates the general pattern temporal change in immune responses with respect to timing of measurements. A non-parametric (LOWESS) smoother with the window covering 1/3rd of data points is shown.

Figure 7

Predicted change in immune response, based on generalized additive modeling -- with cubic-splines supported by 5 knots -- reflects the average change for the whole range of measurement timing along with the 95% confidence interval indicating the degree of uncertainty in the detected pattern. The estimates of peak timing are shown.

Figure 8

Graph showing the immune responses of children aligned according to age. Panel A shows the line graph of individual trajectories of immune responses. Panel B shows the predicted values for fitted lines for measurements taken before child's diarrheal episode (dashed line) and for measurements taken after an episode (solid line) -- as obtained from a log-linear regression model.

Figure 9

Graph showing the immune responses of children aligned according to calendar time of measurement. Panel A shows the line graph of individual trajectories of immune responses. Panel B shows the predicted values for fitted lines for measurements taken before child's diarrheal episode (dashed line) and for measurements taken after an episode (solid line) -- as obtained from a log-linear regression model.

Figure 10

Needle-plot of a time series of log-fold change in immune responses aligned accordingly to time of event, bi-monthly summary of cases, and average change in responses show the temporal clustering.

Figure 11

Needle-plot of a time series of log-fold change in immune responses aligned accordingly to child's age at event of interest, summary of cases by age-groups, and average change in responses show age-related heterogeneity in immune response.