Analysis of longitudinal data from animals with missing values using SPSS

Abstract

Testing of therapies for disease or injury often involves the analysis of longitudinal data from animals. Modern analytical methods have advantages over conventional methods (particularly when some data are missing), yet they are not used widely by preclinical researchers. Here we provide an easy-to-use protocol for the analysis of longitudinal data from animals, and we present a click-by-click guide for performing suitable analyses using the statistical package IBM SPSS Statistics software (SPSS). We guide readers through the analysis of a real-life data set obtained when testing a therapy for brain injury (stroke) in elderly rats. If a few data points are missing, as in this example data set (for example, because of animal dropout), repeated-measures analysis of covariance may fail to detect a treatment effect. An alternative analysis method, such as the use of linear models (with various covariance structures), and analysis using restricted maximum likelihood estimation (to include all available data) can be used to better detect treatment effects. This protocol takes 2 h to carry out.

Figure 1

Flow chart showing five-stage approach to analysing longitudinal data where some data are missing

Figure 2

Screenshots showing arrangement of data in SPSS. (A) short and (B) long formats. The eight measurements for a single animal (rat 29) are shown. Missing data are entered as a value lying outside of the dataset, here 999.00 (grey boxes). All experiments using animals were performed in accordance with relevant UK legislation and regulations and with Institutional approval.

Figure 3

Screenshots showing SPSS windows involved in specification of a model using the “MIXED” procedure. (A) Specification of the variable which identifies the subjects in the study (“rat”) and the variable which identifies the sessions during which repeated measurements were obtained (“wave”). Covariance structure is specified from the drop-down window. (B) Specification of the dependent variable (“outcome”) and the factor(s) and covariate(s) (“group”, “wave” and “mean_preop”) that are hypothesised to affect the dependent variable.

Figure 4

Screenshots showing SPSS windows involved in defining the model. (A) Specification of the factor(s), covariate(s) and interactions thereof that are hypothesised to affect the dependent variable. (B) SPSS allows users to estimate parameters using either Maximum Likelihood or Restricted Maximum Likelihood, by iteration to convergence based on the parameters and variables specified in the lower panels.

Figure 5

Screenshots showing SPSS windows involved in developing the linear model. (A) How to obtain pairwise comparisons of any significant factor(s), and (B) how to save a list of the model-based predicted and residual values.

Figure 6

Screenshot showing SPSS Syntax window defining linear model estimated using REML and with two additional lines of code requesting pairwise comparisons for the interaction of group by wave.

Figure 7

Screenshot of SPSS Output. (A) Results of significance testing for Fixed Effects (i.e., factor(s),covariate(s) and interaction(s) specified in Figure 4A). There is a significant effect of wave, group and an interaction of wave by group but no effect of covariate (green box). (B) Results of pairwise comparisons of any significant main effect(s) (as requested in Figure 5A) showing a difference between aged stroke rats treated with AAV-NT3 and those treated with AAV-GFP (green box).

Figure 8

Screenshot of SPSS Output. Results of pairwise comparison of significant interaction of wave by group. Top panel shows table header and bottom panel shows results for wave eight (bottom of table, after intervening part of table removed for clarity). There was a significant difference between aged stroke rats treated with AAV-NT3 and those treated with AAV-GFP at week eight (green box).