Institute of Environmental Medicine, Unit of Intervention and Implementation Research, Karolinska Institutet, Nobels v. 13, 171 77, Stockholm, Sweden

Nordic Institute of Chiropractic and Clinical Biomechanics, Clinical Locomotion Network, Forskerparken 10A, 5230, Odense M, Denmark

Institute of Regional Health Services Research, University of Southern Denmark, Winsloewparken 19.3, 5000, Odense, Denmark

Abstract

Background

Repeated data collection is desirable when monitoring fluctuating conditions. Mobile phones can be used to gather such data from large groups of respondents by sending and receiving frequently repeated short questions and answers as text messages.

The analysis of repeated data involves some challenges. Vital issues to consider are the within-subject correlation, the between measurement occasion correlation and the presence of missing values.

The overall aim of this commentary is to describe different methods of analyzing repeated data. It is meant to give an overview for the clinical researcher in order for complex outcome measures to be interpreted in a clinically meaningful way.

Methods

A model data set was formed using data from two clinical studies, where patients with low back pain were followed with weekly text messages for 18 weeks. Different research questions and analytic approaches were illustrated and discussed, as well as the handling of missing data. In the applications the weekly outcome “number of days with pain” was analyzed in relation to the patients’ “previous duration of pain” (categorized as more or less than 30 days in the previous year).

Research questions with appropriate analytical methods

1:

2

3:

4:

5:

Conclusions

We have illustrated several ways of analysing repeated measures with both traditional analytic approaches using standard statistical packages, as well as recently developed statistical methods that will utilize all the vital features inherent in the data.

Background

Information collected for clinical research is usually gathered from the participants using questionnaires (paper- or web-based) or diaries. Diaries are often used when several points of measure are of interest, in studying the progress or the development of a condition over time. In theory, this is an excellent method. However, studies have shown that respondents have a tendency to backfill entries

The term “Ecological Momentary Assessment” (EMA) has been used to describe the “repeated sampling of subjects’ current behaviors and experiences in real time in subjects’ natural environment”

The “SMS-Track Questionnaire”

The analysis of such repeatedly collected data, regardless of collection tool, presents new challenges. Even when compliance is high, invariably most respondents will have some missing values when measured repeatedly over months or years. Further, as the data produced contain repeated measurements of the same individuals over time, within-subject correlation must be considered in the analysis. In addition, when considering patients, they will often come from different clinics, introducing one more level into the analysis. Finally, it is desirable to analyze the complex outcome measure so that it can be interpreted in a clinically meaningful way.

The overall aim of this commentary is to describe different methods of analyzing repeated data. An overview of different statistical methods were applied to a model data set based on actual data collected with text messages in two of the referenced studies

Methods

Participants and measurements

The data used to make the model data set were aggregated from two clinical studies, one Danish

The patients in both studies were informed about the text message method, the exact wording of the text message question (asking about the number of days with bothersome LBP during the preceding week) as well as the answer options (a number between 0 and 7) at inclusion. In both studies patients were followed for 18 weeks with weekly text message questions.

It should be noted that this model data set represents a clinical situation in which patients initially report relatively high levels of pain. A treatment period follows, in which pain reduction is aimed for. Thus, the model data set is not a surveillance of patients in a steady or normal state of health, in which recurrence or inception of a condition would be of interest.

Analytic approaches

The method of analysis depends mainly on the research question asked. In general terms, SMS-track data can be used as an outcome in variable oriented (group level) prognostic or effect studies. The analysis may also be person oriented

The method of analysis also depends on the data. Some analyses are suitable only for continuous data and not for categorical data. Further, data may have to be converted by a log or square root transformation to fit the assumption of normal distribution of the outcome.

Many methods of analysis assume independence of data and therefore are not suitable for repeated data. When a subject is measured repeatedly, the data from that individual (within-subject) are bound to show a stronger correlation compared to those between individuals (between-subject). Failure to account for this co-variance may result in inaccurate confidence intervals, that is, the nominal coverage of e.g. 95% will not be accomplished.

In this commentary, clinically relevant research questions are presented with an overview of some of the possible analytic approaches. We have treated the measure “number of pain days” as both a continuous and a count variable to illustrate the different methods of analysis. Each method is then discussed in relation to the results of the different subset analyses. The research questions 1–4 are variable-oriented (related to group level analyses), and question number 5 is person-oriented.

Missing data

Repeated data collection invariably contains some missing data. Without special precautions many analytical methods for longitudinal data cannot directly handle individuals who have missing data for any of the time points and those individuals are simply excluded from analysis, which is known as listwise or casewise deletion. This might introduce bias when the follow up time of a study is long with many measurements, as most subjects will have some missing data, and missing data most often do not occur at random. Exclusion of individuals will, apart from the risk of bias, also lead to less efficient estimates, e.g. larger confidence intervals.

Imputation of missing data is an alternative to facilitate analysis of repeated measures. One of the earliest imputation techniques for longitudinal data is the “last value carried forward”, where the missing value is simply replaced by the previously recorded value. When studying a clinical course, this would probably be a crude but rather accurate action, as each individual value correlates the strongest with the measurements closest in time. However, over recent decades more elaborate ways of imputation of data have been developed, see Little and Rubin

These methods aim to not only impute values but also to take into account the increased sampling variability due to the imputation of missing data. However, in the examples presented in this commentary, no imputations were done, but the problems of missing longitudinal data deserve special attention. A second approach to handling missing data is direct maximum likelihood (DML), see Enders

Without imputation techniques we have handled non-responding in various ways before analysis. One option was to only include a participant if a certain percentage, e.g. 80%, of the entire number of replies during the follow-up period was answered. Another alternative was to define a certain period of particular clinical importance where replies must be given in order to avoid exclusion. In this commentary, the results from the following alternatives are reported; a) the full data set, b) respondents with a minimum of 80% response rate and c) those answering all the first eight weeks, respectively. The latter was chosen as these patients were included in the studies while experiencing an episode of LBP, and thus the eight first weeks of the trial were chosen as the period of the most interesting development.

Research questions with appropriate analytical methods, results and discussions

We have raised some research questions that are relevant to researchers in the area of musculoskeletal pain and illustrated appropriate analytical methods with which to answer them. We have started with the very basic, descriptive analyses. Then, specific time points were selected for analyses. As a third step, a specific event was selected but time was allowed to vary, and in the fourth approach, both time and event may vary. Finally, the existence of subgroups was the basis for the last set of analyses.

How many days with pain do patients experience?

**Research question**

**Outcome**

**Method of analysis**

**Results from the model data set**

**All respondents, n = 244**

**Highly compliant respondents, answering 80% (≥15/18 weeks), n = 161**

1A: Crude outcome

Total number of 1: days with pain from 18 weekly measures, 2: weeks reported

Summaries.

1: Mean 33.0, Range 0 – 126 Short duration: Mean 24.5, Range 0-124 Long duration: 41.1, Range 0-126 2: Mean 15.2. Range 2-18

1: Mean 36.4. Range 0-126 Short duration: Mean 27.4, Range 0-124 Long duration: mean 45.4, Range 4-126 2: Mean 17.3, Range 15-18

1B: Difference in weekly outcome between groups

Average number of pain days per week

Student’s

Short duration: 1.6 Long duration: 2.8 p < 0.001

Short duration: 1.6 Long duration: 2.6 p < 0.001

2A: Proportion with different levels of the condition

Incidence of recovered = reporting 0 pain days week by week

Proportion, i.e. percentage of subjects who are recovered compared to those who are not

Illustrated in Figure

Illustrated in Figure

2B: Incidence at a prespecified time point

Proportion of patients recovered = reporting 0 or 1 pain days at the chosen time, e.g. the 5th week

Logistic regression (or other generalised linear regression models)

Short duration: 58.7% Long duration: 27.7% OR = 3.71 (2.1-6.6) RR = 1.75 (1.4 – 2.3) Long duration reference category

Short duration: 58.2% Long duration: 28.0% OR = 3.58 (1.8 - 7.0) RR = 1.72 (1.34 – 2.3) Long duration reference category

It has been suggested that the total number of days with back pain over a period would be a good way of assessing chronicity **.** In the model sample, the total number of days with LBP ranged from zero to 126, with a mean of 33.0 days. When analyzing the high compliers only, the mean was slightly higher.

The individual means were calculated as sum of reported pain days divided by the number of weeks the individual actually reported data. When analyzing the subset of high compliers, the estimate of the group with long duration changed marginally.

Generally, summary outcomes are easy to interpret and give clinically meaningful estimates, and summarizing weekly data may indeed distinguish patients with a more persistent course. Summary scores could also be used as an outcome in multivariate models. On the other hand, the simplification of data that is the core feature of the summary statistics ignores course patterns and time to improvement. Potentially important differences could be missed e.g. would the sum score during ten weeks be equal for a patient having pain level 3 during all weeks and a patient with five weeks of “pain 6” followed by five weeks of “pain 0”.

Percentage of patients recovered (LBP days = 0) and unrecovered in each of 18 weeks following a first visit to a chiropractor (n = 212 week one; n = 186 week 18)

**Percentage of patients recovered (LBP days = 0) and unrecovered in each of 18 weeks following a first visit to a chiropractor (n = 212 week one; n = 186 week 18).**

To describe the between-individual variance of the population, one possibility is to present the proportion that meet a criterion of interest at different time points. In our studies, recovery at different time points was studied. Thus, a dichotomised outcome “recovered “(defined as reporting zero days with LBP

Repeatedly collected data can also be used in ordinary logistic regressions choosing a specific time point as the time of interest (to patients, clinicians or to third party payers), i.e. not selecting time points on the basis of Figure

Defining recovery as the event of interest, maybe “relief rates” would be a better term than hazard rates, as the outcome parameter. Using this outcome, the numbers and proportions of patients with a successful course can be estimated, and also the numbers needed to treat can be calculated. However, individual trajectories are ignored at the expense of population overview.

**Research question**

**Outcome**

**Method of analysis**

**Results from the model data set**

**All respondents, n = 244**

**Highly compliant respondents, answering 80% (≥15/18 weeks), n = 161**

3A: Incidence during the full study period for the whole sample and for subgroups

Recovery, i.e. reporting 0 or 1 pain days in 2 consecutive weeks = Event

Time to event analysis, with Kaplan Meier curves. Log rank test for differences between groups

Illustrated in Figure

Logrank testfor effect of previous duration: p = 0.002

3B: Incidence for the full study period in relation to the selected predictive variables

Recovery, i.e. reporting 0 or 1 pain days in 2 consecutive weeks = Event

Time to event analysis with a) Cox proportional hazard regression or b) Discrete hazard regression

Hazard ratio (HR) showing recovery, long duration reference, estimate and 95% CI: a) 1.95 (95% CI: 1.4-2.6), b) 2.03 (95% CI: 1.5-2.7).

Hazard ratio (HR) showing recovery, long duration reference, estimate and 95% CI: a) 1.95 (95% CI: 1.4-2.6), b) 2.03 (95% CI: 1.5-2.7).

3 C: Time point for an event during the pain course

The time point of change in the course of pain = Event

Spline regressions, the event defined as the intersection of linear regression lines (the knot).

Short duration: knot at 4.5 weeks Long duration: knot at 5.9 weeks

Short duration: knot at 4.4 weeks Long duration: knot at 5.8 weeks

Incidence of “recovery” (reporting zero or one pain days in two consecutive weeks), stratified by previous duration (> 30 days in pink, < 30 days in blue) for the full data set

**Incidence of “recovery” (reporting zero or one pain days in two consecutive weeks), stratified by previous duration (> 30 days in pink, < 30 days in blue) for the full data set.**

Using repeated measures, it is possible to monitor a population at risk to study the incidence of an event over time, that is, an extension of the approach in section 2 above. To our knowledge, this type of data has thus far been unobtainable and provides a “true” incidence of the event studied. When exploring different conditions/variables, the event will be defined according to clinical/medical or other parameters.

In survival analysis, one of the main application areas for this kind of analysis, mortality was the event under study. As we would expect the patients to get better, we studied the positive event “recovery”, for this example data set defined as zero or one pain day reported in two consecutive weeks

Kaplan-Meier curves stratified by a predictor variable and a test for difference between categories of the predictor were the starting point for this analysis. More elaborate analysis allowing for several predictor variables can be done with Cox Proportional Hazard regression

When the outcome event was considered to be measured at discrete time points and no assumptions were made of proportional hazards, a discrete hazard regression analysis showed a statistically significant hazard ratio of 2.03 (95% CI: 1.5-2.7) between the groups, again pointing towards the patients with a shorter previous duration of LBP having the best chance of recovery during the study period. Performing the analysis with the high compliers only did not change the estimate.

Having access to repeatedly observed data, detailed changes in the course of the condition can be studied. Concerning LBP, it is often observed that the patient’s course is different in a first phase up to approximately the fourth or fifth week with a rapid recovery

Looking at incidences by means of hazard ratios yields interpretable results in terms of proportions recovered and holds the possibilities of the analytic methods used for survival analyses

Further, the definition of event will influence the Kaplan-Meier curve. Had we defined recovery as four consecutive weeks with little or no pain (instead of two weeks), a smaller number of patients would have accomplished this and thus the curves would have been more horizontally oriented.

Throughout, regardless of the outcome parameters, the type of data (continuous or count) and the level of compliance, the group with a short previous duration of LBP had significantly higher “risks” (chance) of recovery. This suggests that for our model data set, the methods were robust as the conclusions pointed in the same direction regardless of method. Further, incidences over the full study period as well as at a specific point in time can be calculated from the full data set, as including poor compliers only marginally changed the estimates. In other data sets, this may, however, not be the case. In the mentioned Swedish study

Finally, we also illuminated a method to estimate the point of change in a course of pain using spline regression analysis. Again, a difference between the two groups was noted, and the use of only high compliers did not change the estimates to any large degree. Spline regression is, of course, an approximation of the true, rather fluctuating, course of pain during the 18 weeks. The specification of the spline regression has, however, been done with those few parameters that were of vital clinical interest. To capture all the features of the course of pain would surely need several more parameters and such an approach would probably lose clinical interpretability.

**Research question**

**Outcome**

**Method of analysis**

**Results from the model data set**

**All respondents, n = 244**

**Highly compliant respondents, answering 80% (≥15/18 weeks), n = 161**

4A: Association of baseline variables with outcome

Weekly recorded pain days, count variable, assuming a binominal distribution

Multilevel mixed-effects logistic regression or generalized estimating equation assuming a logit link function (Long previous duration reference category)

Subject specific OR = 3.31 (95% CI: 2.1-5.1) Population average OR = 1.96 (95% CI 1.4-2.6) (Note: Interaction duration*week significant)

Subject specific OR = 2.67 (95% CI: 1.6-4.5) Population average OR =1.52 (95% CI 1.1- 2.2) (Note: Interaction duration*week significant)

4B: Association of baseline variables with outcome

Weekly recorded pain days, count variable, assuming a Poisson distribution

Multilevel mixed-effects Poisson regression assuming a log link function (Long previous duration reference category)

Subject specific IRR = 1.92 (95% CI: 1.5 – 2.4) (Note: Interaction duration*week significant)

Subject specific IRR = 1.82 (95% CI: 1.4 – 2.4) (Note: Interaction duration*week significant)

4 C: Association of baseline variables with outcome

Weekly recorded pain days, considered a count variable and assuming a normal distribution

Generalized linear regression or mixed linear model assuming an identity link function

Average difference in pain days for Long duration – Short duration 1.20 (95% CI: 0.8 – 1.5) (Note: Interaction duration*week significant)

Average difference in pain days for Long duration –Short duration 0.95 (95% CI: 0.6-1.4) Note: Interaction duration*week significant)

In these examples, we examined the association of the baseline variable “previous duration” with the outcome “number of pain days”. Throughout, the effect of time is considered a fixed effect (to account for systematic differences between weeks and to obtain estimates for each separate week). All models in this section are statistically and computationally more advanced than those in the previous sections. This whole area of statistical models has expanded very much during the last 10–15 years thanks to theoretical advancements as well as the development of suitable software. It is outside the scope of this article to give details here, we recommend texts such as those by Twisk

A: This approach used either a multilevel mixed-effects logistic regression or a Generalized Estimating Equation (GEE)

B: As above, the outcome was considered a count variable, but a Poisson distribution was assumed instead of a binomial distribution. The multilevel analysis showed a significant difference (Incidence Rate Ratio, IRR = 1.92, 95% CI 1.5-2.4) between the patients with a short previous duration of pain compared to those with a long previous duration, indicating that the former had lower odds of reporting many pain days. The estimate was lowered somewhat when analyzing the high compliers only. In this case, a multilevel Poisson regression

The outcome parameter is an Incidence Rate Ratio (IRR). A property of the Poisson distribution is that the mean and the variance are equal. In some applications this may not be the case, and in particular the variance can be greater than the mean, which is referred to as a case of over dispersion. Then an analysis using a negative binomial distribution may be appropriate (not described here, see

C: Considering “days with pain,” a continuous outcome may not be the obvious choice either for our model data set, as the outcome variable “number of pain days” was discrete and had an upper limit of 7. In the investigation of other conditions, the outcome could be continuous. If so, the association with baseline variables can be studied using mixed linear models. In our example, an autoregressive covariance model was chosen assuming decreasing correlation with increasing time and confirmed with Akaike’s Information Criterion

Performing the analysis for the high compliers lowered the estimate, but did not change the significance. Including more baseline variables in the model did not affect the parameter estimates noticeably (analysis not shown).

These methods are designed for repeated measures and take correlation between outcomes measures and different time points into account. In this way the richness of the data is maintained and trustworthy significance levels are achieved. However, the results may sometimes be more difficult to interpret in a clinically meaningful way. The models are statistically more sophisticated, require more work for the specification of the analyses, but they are implemented in standard statistical software (such as SPSS, STATA, SAS) and our analyses and results are based on these softwares.

With GLM it is possible, as demonstrated, to use both count and continuous variables, and the outcome could be binomially, Poisson, or normally distributed. In our model data, regardless of model, the results all pointed in the same direction. We conclude that for our chosen variable and outcome, the choice of method may not have been utterly important. However, because our repeated outcome was most accurately classified as a count variable following a binomial distribution, we trusted the estimates from the generalized estimating equation model and the corresponding multi-level model to be the most valid estimates.

A final note has to be added to the results of this section about the significant interaction found between previous duration and week, the latter variable representing time under observation.

This implied that a second step in the analysis was necessary to fully understand how the pain course developed over time for the two duration groups. In the present context with examples and suggestions for analysis this step is not further elaborated.

Are there subgroups of patients with similar courses of pain within the studied population?

There are several methods that are useful when looking for patterns within repeated data using person-oriented approaches. The examples below range from purely descriptive (A) which rely on a clinical impression, through hierarchical methods (B) which are mathematical in origin but requires a supplementary clinical judgment, to the very mathematical methods (C) which rely on the acceptance of a pre-specified statistical model.

**Research question**

**Outcome**

**Method of analysis**

**Results from the model data set**

**All respondents, n = 244**

**Respondents answering ≥ 80%, n = 161**

**Respondents answering all first 8 weeks, n = 133**

5: Are there subgroups of patients?

Subgroups as clusters with low within-cluster variation and high between-cluster variation

A. Visual inspection based on plots of the course of pain in a graphical presentation where predefined criteria of directions in early and late phases, a qualitative approach

A: Illustrated in Table

Not applied

Not applied

B: Regression coefficients from spline regression (1 knot) derived from each subject were used in Wards’ hierarchical cluster analysis. Optionally this analysis was followed by K-means cluster analysis. Inspection of number of clusters based on the Calinski-Harabasz criterion and the criteria by Duda & Hart

B: Not done due to lack of degrees of freedom in spline regression of some individual subjects

B: 4 clusters suggested.

Not applied

C: Wards’ hierarchical cluster analysis, optionally followed by K-means cluster analysis, applied directly on the weekly number of pain days for the first 8 weeks. Cluster criteria as in B.

Cluster 2: 79

Percentage with short duration in these clusters:

C: 6 clusters suggested. Percentage with short duration the previous year in these clusters:

C: Not applied

Cluster 1: 39

Cluster 1: 58

Cluster 2: 49

Cluster 3: 20

Cluster 3: 85

Cluster 4: 33

Cluster 4: 37

Cluster 5: 52

C: Not applied

Cluster 6: 50

**Possible categories describing the entire course by visual analysis**

**Individuals in each subgroup, n, (%)**

**Total number of pain days in each subgroup, mean (sd)**

**Percentage with short duration the previous year**

The first step is to categorize the pattern in relation to the early course (improved, unchanged or worsened). Afterwards that category is combined with the relevant late course.

Improved-Mainly recovered

25 (12)

8.92 (6.01)

76

Improved-Stays in the category

64 (30)

26.83 (14.65)

33

Improved-Fluctuating

23 (11)

37.43 (21.17)

30

Improved-Moves towards mainly worsened

2 (1)

95.00 (11.31)

0

Unchanged-Mainly recovered

13 (6)

5.54 (5.68)

54

Unchanged-Moves towards mainly improved

18 (8)

38.11 (21.81)

50

Unchanged-Stays in the category

10 (5)

45.60 (51.21)

33

Unchanged-Fluctuating

40 (19)

51.28 (30.95)

38

Unchanged-Moves towards mainly worsened

2 (1)

84.00 (29.70)

0

Worsened-Mainly recovered

1 (0.5)

12

0

Worsened-Moves towards mainly improved

2 (1)

37.5 (17.68)

50

Worsened-Fluctuating

13 (6)

55.00 (20.29)

0

Worsened-Stays in the category

2 (1)

111.5 (17.68)

50

The course of a disease (LBP in our model sample) can be described by a graphical representation of each participant’s development over time, in this case the number of pain days by weeks. In studies with relatively few individuals (up to about 200 participants) it is possible to analyze such courses by hand by describing the characteristics of the pain courses including when the changes take place; thus attempting to identify groups of patients with similar pain patterns. The inter-observer reliability of such a visual evaluation was found to be substantial (kappa = 0.7) between two observers analyzing 78 courses

The combination of the categories for the early and the late course resulted in 13 possible categories. All the 13 categories were represented in the model data set, consisting of from one (0.5%) to 64 (30%) patients (Table

The trend course of the outcome variable over the study period can be explored with cluster analysis to search for subgroups. The simplest alternative would be to use all individual 18 weekly data points as cluster parameters, but this is practically difficult both with respect to the burden of heavy computations and of missing data. Therefore, the individual courses in our model sample were summarized with different mathematical approaches, limiting the number of cluster parameters. The parameters were then used in a hierarchical cluster analysis, Ward’s method

A dendrogram obtained with Ward’s method, describing the formation of clusters

**A dendrogram obtained with Ward’s method, describing the formation of clusters.**

a) Each course was described by two regression lines describing the early trend and the later trend, respectively. Using a spline (nonlinear regression) technique, the intersection between the two was then calculated. From these analyses, four parameters described each profile: the intercept and slope of the early trend, the difference in slope between the early and late trend and the intersection between the two regression lines. These four parameters were then used as cluster parameters. Note that the regression parameters serve to approximate the weekly variation in the data, and they must be evaluated with respect to the degree of fit for each patient.

Cluster 1 (28 individuals): This subgroup contained the oldest individuals (mean age 47 years), who reported the highest number of total pain days (50 days).

Cluster 2 (68 individuals): This subgroup contained the youngest individuals (mean age 42 years), who reported 33 pain days throughout.

Cluster 3 (20 individuals): The patients here were mainly male (70%), reported the most leg pain (40%), reported least pain days (20 days) and most (85%) had had short previous duration of LBP.

Cluster 4 (45 individuals): This subgroup contained the largest proportion of patients (63%) that had had long previous duration of LBP and reported 36 days of pain throughout.

b) Each course was described by the eight first weekly measurements only. As mentioned earlier, this was considered the period where the most change in pain days is likely to be noticed in our population. Thus, in this cluster analysis, eight cluster parameters were used.

Cluster 1 (12 individuals): This subgroup had many women (67%) and reported 37 pain days throughout.

Cluster 2 (24 individuals): This subgroup had the youngest patients (mean age 40 years), mainly women (67%) and reported 35 pain days throughout.

Cluster 3 (15 individuals): This group had mainly patients with long previous duration of pain (80%), and reported 58 days of pain throughout.

Cluster 4 (28 individuals): These patients were mainly male (64%), and most (79%) reported short duration of previous pain. They had 21 pain days throughout.

Cluster 5 (46 individuals): This group reported fewest days of pain, only 13.

Cluster 6 (8 individuals): This was the subgroup with the oldest individuals (mean age 49 years), they reported most leg pain (50%)and had the highest number of pain days, 101 in total.

C:

The cluster analysis shown here is just one of several different alternatives that can be used for this and similar data sets. An excellent overview of cluster methods in theory and in applied research is found in Everitt BS, “Cluster Analysis”

Several other possibilities also exist for aggregating data points into useful descriptions of the course suitable for cluster analysis. Adding to the linear regression, a second or third degree regression can be used to also approximate the course. Similarly, the spline function can be extended to contain two or more knots. Clinical judgement should be used to evaluate what is relevant for any particular condition. We have previously argued that to secure solid course estimates, only highly compliant responders (arbitrarily defined as those answering more than 80% of the time) should be used in these kinds of analyses (in a))

Further, in both A and B, the subgroups/clusters formed in this mathematical way should be examined for clinical meaningfulness. For instance, the available clinical baseline variables associated with each cluster can be tested for difference between clusters.

We have illustrated possible ways of exploring the model data set for subgroups based on the repeated data. Concerning non-specific LBP, our approach was based on the hypothesis that patients with the same “category” of LBP might exhibit a similar clinical course. The visual description of individual’s pain patterns was a pragmatic and clinically meaningful way to distinguish between obviously different patient profiles, but the method is time consuming and only doable in small samples. However, the choice of subgrouping methods is, as for all analyses, dependent on which assumptions of the data and their distributions the researcher is willing to accept.

A number of data mining approaches can be used for pattern recognition instead, e.g. cluster analysis, latent class analysis, artificial neural networks, and probabilistic data mining. It is beyond the intents of this commentary to test, describe and compare these.

Conclusions

When new methods of data collection are introduced, it is always pertinent to consider the possibilities, advantages, implications and challenges this entails. Making use of a technology available to a majority of people in the modern world, mobile phones, doors are opened to repeated measurements from large populations.

Having access to repeated data, it is not self-evident what methods of analysis to use. We have intended to give an overview of some approaches to analyses considered by our group of researchers, but other relevant methods exist and, possibly, different data from other research areas may require yet different methods. In this commentary, the methods are presented very briefly, and we encourage readers to use the references included for a deeper understanding.

Ultimately, the choice of analytic approach will depend on the following questions: what is the research question to be answered, what kind of data is the outcome variable, what distribution does it have and what is the within-subject correlation? The answers will determine the most appropriate method of analysis.

In analyzing repeated data, the issue of within-subject correlation can be avoided by aggregating the individual measures into a summary measure prior to analysis. However, information on individual variation is then lost, resulting in over-simplification. Thus, methods of analysis that account for this covariance may be the most appropriate.

In our model data, patients with > 30 days LBP the preceding year consistently demonstrated an increased risk of a “poor prognosis” compared to those with < 30 pain days in all the variable oriented analyses. Further, different patient profiles could be identified based on the pain trajectories emerging from cluster analyses of the frequently repeated outcome measure. Thus, it seems that repeated measures can be analysed in several meaningful ways with both traditional analytic approaches using standard statistical packages, as well as recently developed statistical methods that will utilize all the vital features inherent in the data.

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

IA was involved in the design of this commentary, participated in the analyses and wrote the first manuscript draft. LB was responsible for the analyses. AK and NW were involved in the design and analyses of the data. IJ and GB were supervising the study process. All authors were involved in finalizing the manuscript.

Acknowledgements

We would like to thank Professor Charlotte Leboeuf-Yde, who instigated this article. This work was funded in part by the Swedish Chiropractors’ Association and by the European Chiropractors’ Union.

Pre-publication history

The pre-publication history for this paper can be accessed here: