A) Talks to the LGC
1. October 23rd, Peter Froggatt Centre , QUB.
Professor Mary Frances McMullin of Queen's University Belfast gave a talk to the local group entitled:
'National trials in acute myeloid leukaemia: A standard of care'
Professor McMullin traced the development of a 'standard of care' for acute myeloid leukaemia (AML) patients which emerged from a programme of National randomised controlled clinical trials conducted over the last 50 years.
She began with a review of AML showing that it was a rare blood cancer of theelderly: incidence = 4.3 cases /100,000 population, median age at diagnosis =70 with 2520 cases expected in the UK annually. Survival was poor: 41.6% for those aged 65 or less and 5.4% for those aged >65years at diagnosis.
The major part of her talk then focussed on how treatment (generally various forms of chemo-therapy) had evolved over this period by means of a series National RCTs (several funded by the MRC) designed to improve prognosis (i.e., survival time) by evaluating different treatments, their dosages, cycles, and whether or not they were to be administered singly or in combination. It will be recalled that chemotherapy is aggressive and may itself pose a risk to life. Professor McMullin also covered treatment of Acute ProMyelocytic Leukaemia (a small subgroup of AML) where there are more effective therapies as well as the thorny problems attending the treatment of the elderly.
In all cases, standard of care decisions were made using Kaplan Meier Survival graphs in which the treatment comparisons were protected by randomisation. Statistical modelling of the underlying survival curves was not undertaken.
As Northern Ireland has a relatively small population participation in multicentre RCTs was beneficial in a number of ways notably ensuring that patients received the most up to treatment and care and hence the idea was to have the maximum number of patients participating in trials.
It was fascinating to see the scientific method in action refining Medical hypotheses and improving prognosis over time by means of well-designed RCTs. Professor McMullin made light of the labour that went into RCT protocol design, but the contrast between this and so-called real-world studies was obvious. This excellent talk was full of interest and was very well received by an appreciative audience.
2. November 6, Peter Froggatt Centre , QUB.
Dr. Francisco Javier Rubio of the University College London Department of Statistical Science gave a talk to the Local Group entitled:
Near-redundancy and Practical non-identifiability in survival models (and beyond)
Javier cast the setting of his talk firmly in the setting of parametric modelling in survival analysis. He drew attention to publications reporting inferential challenges: such as multimodal likelihoods, flat likelihood surfaces, or a “difficult” optimisation of the likelihood function, for some models and for some particular data sets. These problems arise because (a) the model is theoretically non-identifiable (i.e. two parameter values lead to the same model) or (b) in other cases, the model is theoretically identifiable (the MLEs are consistent and asymptotically normal) but the model behaves as a non-identifiable model for some specific samples.
He argued that in this latter case it was likely there was insufficient information with which estimate some of the parameters, so that the model could not be distinguished from a non-identifiable model based on the available information.
Further progress required the introduction the twin concepts of near-redundancy (NR)and practical non-identifiability of parameters (PNI) [Cole, 2020]. A nearredundant model is not parameter-redundant (non-identifiable), but occurs when the parameter estimates are close to a redundant nested model. And a model is practically non-identifiable if the log-likelihood has a unique maximum, but the length of the individual parameter’s likelihood-based confidence region tends to infinity in either or both directions.
Javier then introduced the General Hazard (GH) survival model [Rubio et al., 2019], with hazard function:
by way of illustration. This is a type of MPR (distributional regression) model in which the covariates are permitted to influence the baseline hazard and the usual risk function. Here x (tilde) is a subset of the covariates in x and we interpret h0(.) as the shape function. The model is PH (α = 0), AH (β=0) and AFT (α =β ). It is identifiable, provided that x does not contain columns that are linearly dependent, and that the baseline hazard is not a member of the Weibull family of distributions, when PH =AFT = AH [Chen and Jewell, 2001]. However, some authors have reported difficulties using this model.
He described two methods of detecting near-redundancy. The first was based on a measure of divergence (Hellinger distance) of the GH model from the Weibull family and the second was based on an eigen decomposition of the GH Hessian matrix (details omitted, see references). PNI was detected using a relative profile likelihood criterion which Rubio outlined briefly.
Example lung cancer survival data from North Central Cancer Treatment Group (contained in the R survival procedure) were analysed using a GH model with a Power Generalised Weibull baseline hazard which reverts to a non-identifiable Weibull when the parameter γ = 1. Thus, testing for NR amounts to testing this condition. The MLE of γ was 0.861, which indicates that the fitted model is not a (theoretically) parameter-redundant model (γ ≠ 1) at this parameter value. However, the minimum Hellinger distance and the Hessian method (with a 0.001 threshold) indicated the near-redundancy of parameters.
Javier continued with further developments concluding with a novel proposal which modelled the hazard function through a system of ODEs.
This was a technically excellent, but demanding talk, delivered with some aplomb. It was full of interest and very well received by an appreciative audience which thanked the speaker in the usual way. Javier then answered questions on the concordance between his measures of NR and their correlation with the measure of PNI. There was also a question on simplifying the structure of the system of ODEs. The Chairman thanked everyone for attending and the speaker for a fascinating talk.
References:
Y.Q. Chen and N.P. Jewell. On a general class of semi-parametric hazards regression models. Biometrika, 88(3): 687–702, 2001.
D. Cole. Parameter Redundancy and Identifiability. CRC Press, Boca Raton, FL, 2020.
F.J. Rubio, L. Remontet, N.P. Jewell, and A. Belot. On a general structure for hazard-based regression models: an application to population-based cancer research. Statistical Methods in Medical Research, 28:2404–2417,2019.
3. 4 December 2024, Lanyon Building, QUB.
Professor Ruth Keogh of the London School of Hygiene and Tropical Medicine gave a talk to the Local Group entitled:
A gentle introduction to causal inference for time-to-event outcomes.
Professor Keogh began by describing main ingredients involved in adopting a causal inference approach to survival analysis: they included, the question, treatment strategy, outcome, estimand, method of estimation and tools . She outlined the types of studies covered, their structure (overall survival, competing risks, and recurrent events), the estimands (marginal and conditional) and the method of measuring the effect (hazard ratios and risk differences). There are two main choices for addressing confounding: (a) using a treatment model which is the used to re-weight (e.g., inverse probability of treatment weights, IPTW) the data or (b) using a model for the outcome (e.g. G-methods). It was important to ensure that the models in both cases were correct.
With these ingredients in place, she introduced the central idea of counterfactual treatment allocation leading to counterfactual event time, T1 , for each subject when treated and another counterfactual time, T0 , for each subject when untreated. The causal effect (estimand) is then a risk difference:
Pr(T1 ≤ t) - Pr(T0 ≤ t) (1)
the difference measure being preferred to the Hazard Ratio on the basis of a (testable?) frailty argument (Hernan, 2010).
Ruth then went on to deal with Trial Emulation (TE) and other methods such as IPTW and standardization as well as Doubly robust methods. Making the case for TE was relatively straightforward. It was simply good practice when analysing observational studies to emulate a target RCT as far as was possible. This facilitated clarity of purpose, methods deployed all of which facilitated logical statistical analysis. She showed data from the observational Rotterdam Data Breast Cancer study of surgical treatment in which (bizarrely) the unadjusted Kaplan Meier curves showed that survival was worse among women who were treated! Use of the weighting methods and separately g-estimation analysis removed this anomaly, although the result from weighting appeared rather marginal.
Undeterred, Ruth moved on to Doubly Robust methods giving detailed formulae and explaining their utility, saying that these methods work in such a way that we get more than one chance to get a consistent estimate of our estimand. They also opened a door to incorporating machine learning methods and Ruth referenced the use of the SuperLearner (Westling et al., 2023) which combines several parametric and machine learning algorithms in an optimal way.
References
Hernan. The hazards of hazard ratios. Epidemiology 2010; 21; 13-15.
Rotterdam breast cancer cohort. R Software survival package
Westling et al. (2023). Inference for Treatment-Specific Survival Curves Using Machine Learning. JASA 2023.
This talk was a tour de force through the valleys of Causal Inference and the audience showed their appreciation in the usual way. Professor Keogh dealt with questions on assumptions and our the inability to test these and situations where no appropriate counterfactuals existed rendering claims for IPWT suspect and other situations when IP weighting did not properly account for selection effects on treatment. In most cases these were largely open questions. When the discussion abated, the Chair wrapped up the meeting, thanked Ruth and the attendees for an excellent meeting and wished everyone a Happy Christmas.
Professor Gilbert MacKenzie
01/04/2025.