We describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates. This simple method can help prevent the problems that result from inappropriate linearity assumptions. We compare restricted cubic spline regression to non‐parametric procedures for characterizing the relationship between age and survival in the Stanford Heart Transplant data. We also provide an illustrative example in cancer therapeutics.

ALS is a progressive motor neuron disease with no effective treatment. The anti-excitotoxic drug riluzole (100 mg/day) has been shown to decrease mortality and muscular deterioration in ALS patients. To confirm and extend the therapeutic effect of riluzole, we performed a double-blind, placebo-controlled, multicenter, international, dose-ranging (50, 100, 200 mg/day), stratified study in 959 ALS outpatients treated for up to 18 months. Primary efficacy criterion was survival and the effect of treatment was analyzed before (Wilcoxon and log rank tests) and after adjustment on prognostic factors (Cox model). Secondary efficacy criterion was disease progression assessed through change in functional measures. Tracheostomy-free survival rates were: 50.4% (placebo), 55.3% (50 mg riluzole) (p = 0.23, Wilcoxon test; p = 0.25, log-rank test), 56.8% (100 mg riluzole) (p = 0.05, Wilcoxon test; p = 0.076, log-rank test), and 57.8% (200 mg riluzole) (p = 0.061, Wilcoxon test; p = 0.075, log-rank test). At the end of the 18-month study, there was a significant dose-related decrease in risk of death or tracheostomy (p = 0.04). Adjustment for baseline prognostic factors showed a 35% decreased risk of death with the 100-mg dose compared with placebo (p = 0.002). No significant treatment effects were detected for the functional assessments. The most frequent dose-related adverse events included nausea, asthenia, and elevated liver enzyme levels. This study confirms the therapeutic effect of riluzole in a large representative ALS sample, over an 18-month period. Riluzole is well tolerated and decreases the risk of death or tracheostomy in ALS patients.

We analyzed 9,005 deaths from amyotrophic lateral sclerosis recorded in France between the years 1968 and 1982. The overall adjusted mortality rates were 1.45/100,000 for men and 0.90/100,000 for women. We found excess male mortality in every age group. Age-specific mortality rates increased with age until 65-74 years and then declined in the older population. There was no meaningful regional pattern. We found a substantial increase in ALS mortality over time: the adjusted rates (per 100,000) in the period 1968 to 1971 were 1.11 for men and 0.63 for women. In the period 1979 to 1982, the corresponding figures were 1.92 and 1.12. The increase was mainly due to persons over 55 years of age and affected mostly the women during the first part of the study (1968 to 1978). In the recent years, increase appeared similar in both sexes. The temporal trends are consistent across studies in different countries.

Background We aimed to estimate the seroprevalence of SARS-CoV-2 infection in France and to identify the populations most exposed during the first epidemic wave. Methods Random selection of individuals aged 15 years or over, from the national tax register (96% coverage). Socio-economic data, migration history, and living conditions were collected via self-computer-assisted-web or computer-assisted-telephone interviews. Home self-sampling was performed for a random subsample, to detect IgG antibodies against spike protein (Euroimmun), and neutralizing antibodies with in-house assays, in dried blood spots (DBS). Results The questionnaire was completed by 134,391 participants from May 2nd to June 2st, 2020, including 17,441 eligible for DBS 12,114 of whom were tested. ELISA-S seroprevalence was 4.5% [95% CI 3.9–5.0] overall, reaching up to 10% in the two most affected areas. High-density residences, larger household size, having reported a suspected COVID-19 case in the household, working in healthcare, being of intermediate age and non-daily tobacco smoking were independently associated with seropositivity, whereas living with children or adolescents did not remain associated after adjustment for household size. Adjustment for both residential density and household size accounted for much of the higher seroprevalence in immigrants born outside Europe, twice that in French natives in univariate analysis. Conclusion The EPICOV cohort is one of the largest national representative population-based seroprevalence surveys for COVID-19. It shows the major role of contextual living conditions in the initial spread of COVID-19 in France, during which the availability of masks and virological tests was limited.

As a regulatory strategy, it is nowadays not uncommon to conduct one confirmatory pivotal clinical trial, instead of two, to demonstrate efficacy and safety in drug development. This paper is intended to investigate the statistical foundation of such an approach. The one-study approach is compared with the conventional two-study approach in terms of power, type-I error, and fundamental statistical assumptions. Necessary requirements for a single-study model is provided in order to maintain equivalent evidence as that from a two-study model. In general, one-study model is valid only under a 'one population' assumption. In addition, higher data quality and more convincing and robust results need to be demonstrated in such cases. However, when 'one-population' assumption is valid and appropriate methods are selected, a one-study model can have a better power using the same sample size. The paper also investigates statistical assumptions and methods for making an overall inference when a two-study model has been used. The methods for integrated analysis are evaluated. It is important for statisticians to select correct pooling strategy based on the project objective and statistical hypothesis.