Illustrating risk difference and number needed to treat from a randomized controlled trial of spinal manipulation for cervicogenic headache

The methods for this prospective randomized controlled trial are presented in detail in two previous publications [11, 12]. Briefly, participants were randomized to receive either spinal manipulation or a minimal light massage control (n = 40 per group) provided by a chiropractor. Participants were further randomized to eight or 16 treatments over eight weeks. Treatment visits were 10 minutes in duration. Dose had little effect on outcomes in this study [11], and was therefore ignored in the analysis for this report. Randomization was conducted using computer-generated, design adaptive allocation to balance seven variables across groups (see Statistical analysis). Allocation was concealed from all personnel prior to randomization using this technique [11, 12].

Data used in this report were collected at two baseline screening visits and by mailed questionnaire at 12 and 24 weeks. Missing data were imputed from outcomes collected through phone interview by a blinded research assistant at four, eight, 16, and 20 weeks. The primary outcome, identified in advance, was self-reported cervicogenic headache pain intensity. Analysis was conducted using the intention-to-treat principle. The trial was approved by the University of Western States Institutional Review Board (FWA 851).

Volunteers were eligible if they had a history of at least 5 cervicogenic headaches per month for 3 months, with cervicogenic headache as defined by the International Headache Society in 1998 (excluding the radiographic criterion) [14]. Participants had a minimum score of 25 on the 100-point pain intensity scale to prevent floor effects. Participants were ineligible if they had contraindications to spinal manipulation [15], referred neck pain of organic origin, or pregnancy. Persons were also ineligible if they experienced other types of headache with etiologies that might have confounded the effects of manipulation on the cervicogenic component: cluster, metabolic/toxic, sinus, and headache associated with temporomandibular disease, tumors, and glaucoma [11, 12].

A chiropractor/faculty member with 15 years experience screened volunteers for study eligibility through case history, standard orthopedic/neurological exam, heat sensitivity test, and 3-view cervical x-ray using the protocols of Vernon [16] and Souza [17] for cervicogenic headache and those of Gatterman and Panzer [15] for the cervical region. Four chiropractors with over 20 years of experience each served as the study treatment providers.

The treatment group received high velocity, low amplitude spinal manipulation of the cervical and upper thoracic (transitional region) spine at each visit as described by Peterson and Bergmann [18]. Modifications in manipulation recommended for older participants were permitted as required [19, 20]. To relax the neck and upper back in preparation for spinal manipulation [21], the chiropractor administered a moist heat pack for five minutes and conducted a light massage for two minutes (described next).

The control group received five minutes of moist heat followed by five minutes of light massage. Light massage consisted of gentle effleurage (gliding) and gentle pétrissage (kneading) of the neck and shoulder muscles [22, 23]. This allowed us to control contact with the participant with an intervention that was expected to have relatively small specific effects. This was because SMT had been shown to be superior to deep massage[24] and the LM application was much lighter and of much shorter duration than found in massage trials and common practice [25, 26].

Cervicogenic headache pain (CGH) intensity and disability were evaluated using the Modified Von Korff pain scale of Underwood et al [27]. The primary outcome was the pain scale and is the average of three 11-point numerical rating scales: CGH pain today, worst CGH pain in the last four weeks, and average CGH pain in the last four weeks. The disability scale (secondary outcome) is the average of three 11-point scales evaluating interference with daily activities, social and recreational activities, and the ability to work outside or around the house. The scales are scored from 0 to 100 with a lower score more favorable. The third outcome was the number of CGH in the previous four weeks. Baseline variables were used as covariates in the analysis. These included CGH pain and number, age, gender, self-reported previous diagnosis of migraine, confidence in care, and expected number of treatments needed for improvement. Treatment expectancy was evaluated with six-point Likert scales on participant confidence in the success of the two interventions using Interstudy's Low Back Pain TyPE Specification instrument [28].

An intention-to-treat analysis was conducted with each participant included in the original allocation group with missing data imputed [11]. Five subjects were eliminated from this analysis due to lack of follow-up after baseline. For this secondary analysis, the continuous outcomes were dichotomized with 30% and 50% improvement as the threshold values for benefit and success, respectively.

Adjusted RDs between manipulation and control interventions were calculated using a test of proportions called binomial regression (a generalized linear regression model) that takes into account differences between groups in baseline covariates [29, 30]. The covariates for all analyses are listed under Study variables above. Multiple logistic regression was first performed to calculate an initial estimate of the mean of the dependent variable for the binomial regression analysis. When a binomial regression model failed to converge and yield an estimate of the RD, multiple linear regression was used to estimate the RD between groups [31, 32]. All analyses used robust standard errors to minimize distributional assumptions [31]. The adjusted NNT and 95% confidence intervals were then computed by inverting the adjusted RD and its 95% confidence limits. Logistic regression was also used to compute odds ratios comparing interventions adjusted for the baseline covariates [29]. All analyses were conducted with Stata 11 (Stata Corp, College Station, TX).

Table 2 shows the observed percentage of participants achieving improvement in the spinal manipulation and control groups, as well as the adjusted RD and adjusted NNT. A substantial percentage of participants achieved the 30% and 50% thresholds for improvement at 12 and 24 weeks after randomization. The difference between treatment and control groups strongly favored spinal manipulation over the light massage control after correcting for baseline differences between groups (P = .005 to .028). The NNT was about four; that is, only four participants required treatment for one participant to benefit from manipulation itself, above that which was achieved by light massage.

Table 2 can be interpreted as follows, using the third row of data as an example (participants achieving 50% improvement at 12 weeks): Successful outcomes were achieved in 42% of SMT participants and 23% of control participants. When correcting for baseline differences between the two study groups, the adjusted RD = 26%. This means that we can estimate that 26% or about one in four participants are expected to have a successful treatment outcome that is directly attributable to SMT above the success rate that we can expect from a minimal light massage. The confidence interval for the adjusted RD was 7.9% to 45%. This tells us that the true RD for the study population may be considerably lower or higher than 26%; this is a consequence of the modest sample size. The statistical significance is P = .005. It suggests that the favorable results for SMT are unlikely due to chance (sampling error) alone. The p-value applies to both the adjusted RD and NNT. Putting it all together, we can conclude that an advantage for SMT is likely real (P = .005) and substantial (adjusted RD = 26%), but the advantage can range with equal probability from the small (lower 95% confidence limit = 7.9%) to the extremely large (upper 95% confidence limit = 45%).

The adjusted NNT is, in essence, a rewording of the adjusted RD. It shows that we expect to treat 3.8 participants for one participant to benefit from SMT over the control intervention (i.e., about one in four participants benefit directly). The confidence interval shows that the NNT in the true study population is likely between a mediocre 13 and an extremely favorable two. Note that in general, NNT of large magnitude indicate trivial differences between interventions and small NNT indicate large differences. One is the smallest possible NNT and occurs in the extremely unlikely case of a 100% success in the treatment group and 0% success in the control group.

Reduction in the monthly number of headaches also favored SMT (Table 2). At 12 weeks, the adjusted RD was 21% to 23% and the adjusted NNT was 4.3 to 4.7 participants. At 24 weeks, the adjusted RD was 14% and the adjusted NNT was 7.2. The results were statistically significant (P < .05) except for 50% improvement at the 24-week follow-up (P = .094).

Note that for results that are not statistically significant, one side of the 95% confidence interval (CI) will be negative for both RD and NNT. The CI can be interpreted moving from the left limit to the right limit of the CIs for 50% improvement at 24 weeks in Table 2. For RD, the CI is -2 to 30. The left limit is -2, indicating a possible advantage for the control group; the CI passes zero (the break-even point); and the upper limit is 30, indicating the largest advantage for the treatment group in the CI. The CI for NNT (-42, ± ∞, 3.3) is more complicated. It starts with the smallest negative number on the left (-42), which indicates the largest advantage for the control group. Moving toward the center of the CI, the negative value increases to negative infinity (NNT = 1/RD = -1/0 = -∞), the smallest advantage for the control (none). As the break-even point is crossed, the value flips to positive infinity (+1/0 = +∞), the smallest advantage for SMT (none). The positive number decreases in size until the upper limit is reached (3.3), the largest advantage for the treatment group.

Results were mixed for headache disability (Table 2). Outcomes were favorable for manipulation at 50% improvement albeit marginally failing to reach statistical significant at 24 weeks (NNT = 3.5, P = .015 and NNT = 4.9, P = .061). There were no significant outcomes for 30% improvement.

Table 3 shows the traditionally reported adjusted odds ratios comparing study groups. A comparison of Table 2 and Table 3 show that statistical significance for RD and odds ratios were not consistent for all comparisons between manipulation and control. There were four statistically significant results for the odds ratio and four additional statistically significant findings using binomial regression.

Figure 2 was designed as a pragmatic tool for estimating the probability of improvement for the treatment of cervicogenic headache with spinal manipulation. It shows the percentage of participants that achieved ≥ 0%, ≥25%, ≥75%, and 100% improvement at 12 and 24 weeks in the study. Quartiles were chosen for the convenience of creating easily readable bar graphs for the three study outcomes. Figure 2 shows that the percent improvement in disability and number of headaches was greater than the improvement in pain, although manipulation outperformed the control more for pain (Table 2). Outcomes at 12 weeks were durable to 24 weeks. About 40% to 60% of participants achieved a success threshold of 50% improvement and at least 10% had complete relief for at least one of the three outcomes. It should also be noted that about 10% to 20% reported poorer scores than at baseline at one of the follow-up time points, and there is room for improvement.

Adjusted RD and adjusted NNT are recommended to take into consideration baseline differences between groups on important predictors of outcomes. This is especially important in small studies where imbalances in baseline characteristics are more likely to occur. Binomial regression is a generalized linear model that can compute differences between groups after adjusting for baseline covariates when the dependent variable (outcome) is a proportion; it assumes a binomial distribution for the outcome measure [29, 30]. The shortcoming of binomial regression is that it uses an iterative algorithm that must converge to an RD estimate. Often the model fails to converge or gives a poor estimate of the RD [31]. One way to get around this is to run a logistic regression model to give an estimate of risk (probability of improvement in our study) for each individual. This risk can then be used to pre-specify the initial estimate of the mean for the dependent variable for the iterative process in binomial regression. This method was used for all our binomial regression analyses, because many models failed to converge without an initial estimate of the mean. In the two cases where the models still failed to converge, the following analysis was conducted.

An alternative analysis to binomial regression is ordinary least-squares multiple linear regression with the dependent variable coded as zero or one for the two values of the dichotomized outcome [31, 32]; this is also called modified least-squares regression when a robust standard error is used [31]. The usual estimate of the difference between group means (grouping variable regression coefficient) turns out to be an estimate of the difference between group proportions as in binomial regression.

Odds ratios from logistic regression are commonly reported in epidemiological studies. In randomized trials, logistic and binomial regression can give different perspectives on outcomes. For example, consider two experiments were the RD = 40% - 20% = 20% in one and 10% - 5% = 5% in the other. The RD of the first is four times that of the second, but the odds ratios are similar, 2.67 and 2.1, respectively [5]. Binomial regression is more difficult to use because of the convergence problem [31], but logistic regression cannot be readily used to compute the NNT.