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Figure 1: Results of a conventional meta-analysis of long-term outcomes of haemorrhoid surgery. OBJECTIVE. METHODS. Figure 2: Structure of the decision model. Mild symptoms. Symptoms. Moderate symptoms. RESULTS . Severe symptoms. Complications. Non-serious complications.

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## A model to calculate the absolute and relative risks of haemorrhoid surgery David Epstein, on behalf of the University

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**Figure 1: Results of a conventional meta-analysis of**long-term outcomes of haemorrhoid surgery OBJECTIVE METHODS Figure 2: Structure of the decision model Mild symptoms Symptoms Moderate symptoms RESULTS Severe symptoms Complications Non-serious complications Serious complications No symptoms or complications CONCLUSIONS A model to calculate the absolute and relative risks of haemorrhoid surgeryDavid Epstein, on behalf of the University of York Technology Assessment Group BACKGROUND THE STATISTICAL MODEL The overall number of patients with each outcome is shown in Table 1. The vector of number of patients with outcomes Rij1 to Rij6 for study i and treatment j follows a multinomial distribution with a vector of probabilities pij,1..6 NICE recently evaluated two surgical procedures for the treatment of haemorrhoids: a stapled procedure (SH) versus conventional surgery (CH). • Adverse outcomes –complications of surgery or return of symptoms - were reported in many ways: e.g. prolapse, bleeding, incontinence or re-interventions. • Meta-analyses of each outcome separately (Figure 1) do not take into account: • that the outcomes are not mutually exclusive (e.g. patients may report either prolapse or bleeding or both) • that the type of re-intervention undertaken offers information about the underlying severity of the symptom or complication The probabilities of each of the outcomes R1 to R6 were calculated in a two-step model. The first step calculated the probability of observing no symptom or complication, a complication, or a symptom, assuming the errors followed a logistic distribution, with random study effects for the intercepts and treatment effects each for complications and symptoms in the linear predictors. The second step calculated the probabilities that a symptom was mild, moderate or severe using a ordered logit (threshold) model, that is, assuming severity is the expression of a latent variable. The probability that a complication was serious was calculated using a binary logit model. • To construct a statistical model to calculate • The probabilities of symptoms and complications for CH surgery • The relative risks of symptoms and complications for the SH procedure Table 1: The overall number of patients with each outcome, from 16 RCTs • Long-term results of surgery reported in RCTs were classified into 6 mutually exclusive outcomes using a decision model structure (Figure 2): • Mild, moderate and severe symptoms • Non-serious and serious complications • No symptom or complication Table 2 shows the results of the statistical model, calculated using WinBUGS software using Markov Chain Monte Carlo simulation. Table 2: The coefficients and standard errors of the statistical model Assumptions of the model Symptoms (e.g bleeding, prolapse) occur independently Symptoms with no re-intervention are mild Symptoms with an outpatient or non-excisional re-intervention are moderate Symptoms with a surgical re-intervention are severe Complications (which are relatively rare) are mutually exclusive Unhealed wounds, urgency and incontinence are serious complications Mild, moderate and severe symptoms express an underlying (latent) scale of severity This study has calculated the probabilities of symptoms and complications after SH and CH. There were significantly more patients with symptoms following SH; OR = exp(0.88) = 2.4 (95%CI 1.6 to 3.6) There were no significant differences between CH and SH in the number of long term complications; OR = 0.61 (95%CI 0.33 to 1.12) The full report is available on the NICE website www.nice.org.uk

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