To illustrate the analytical process we used data collected from a birth cohort of children observed over three years in a semi-urban community in south India. The aim of the study was to examine the change in serum IgG levels measured by ELISA units to the immunodominant gp15 antigen as a consequence of the first episode of symptomatic cryptosporidial infection [1 (link)]. A total of 452 children were recruited over an 18-month period starting in March 2002; 373 children completed the 3-year follow-up. Field-workers visited each child twice-a-week to record any morbidity. Surveillance stool samples were collected every two weeks and diarrheal stool samples were collected with each episode of diarrhea [2 (link)]. The diarrheal stool samples were examined for the presence of Cryptosporidium spp. by microscopy and the positive samples were subjected to PCR-RFLP for genetic characterization [3 (link)]. Fifty-three children in this cohort experienced a total of 58 episodes of confirmed cryptosporidial diarrhea, out of which 47 episodes were due to C. hominis (see details elsewhere [3 (link)]). For illustrative purposes, we used data from 40 children whose first episode of cryptosporidial diarrhea was due to C. hominis infection. For these 40 children we utlilized the results of ELISA testing in two surveillance stool samples collected before and after the child's first episode of cryptosporidial diarrhea. The original data are provided in supplemental material, which include information on IR values, sampling date and child's age (see Additional file 1 ). The details on measuring serum IgG levels to the gp15 antigen and normalization of ELISA units can be found elsewhere [1 (link),4 (link)]. For the purpose of this study, serum IgG levels are used as a measure of immune response.
The main objective for the performed statistical analysis is to derive inferences from a change in the immune responses measured in ELISA units at those two time points. In statistical terms we aim to detect the difference in the markers of immune responses in a study with a pre-post design delivering two repeated measurements for each subject.
In this tutorial we use the following notations: Yi - values for immune responses for i- child; each Yi consists of two values: Yt1 - first measurement and Yt2 - second measurement, where t1 - time of first measurement; t2 - time of second measurement. A degree of change on an individual level is defined in three ways: as an absolute difference, ΔYi = Yt2 - Yt1, an absolute difference of log-transformed values, ΔYi = lnYt2 - lnYt1 and log-fold change, ΔYi = ln(Yt2 /Yt1). We also specify tE as the time of the event of interest. Additional relevant information to the presented illustration includes age at measurement and date of measurements. Sections below demonstrate the importance of this information in better understanding the variability in immune responses.
The main objective for the performed statistical analysis is to derive inferences from a change in the immune responses measured in ELISA units at those two time points. In statistical terms we aim to detect the difference in the markers of immune responses in a study with a pre-post design delivering two repeated measurements for each subject.
In this tutorial we use the following notations: Yi - values for immune responses for i- child; each Yi consists of two values: Yt1 - first measurement and Yt2 - second measurement, where t1 - time of first measurement; t2 - time of second measurement. A degree of change on an individual level is defined in three ways: as an absolute difference, ΔYi = Yt2 - Yt1, an absolute difference of log-transformed values, ΔYi = lnYt2 - lnYt1 and log-fold change, ΔYi = ln(Yt2 /Yt1). We also specify tE as the time of the event of interest. Additional relevant information to the presented illustration includes age at measurement and date of measurements. Sections below demonstrate the importance of this information in better understanding the variability in immune responses.
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